IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 355 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Report on an Analytic Network Process (ANP) Model to Estimate the Benefits, Opportunities, Costs, and Risks (BOCR) that Gun Policies and Violence Prevention Interventions Have on Legal Users of Firearms Amos N. Guiora Professor of Law S.J. Quinney College of Law University of Utah Marcel C. Minutolo Professor of Strategic Management School of Business Robert Morris University Luis G. Vargas Professor of Business Analytics & Operations Katz Graduate School of Business University of Pittsburgh ABSTRACT Balancing public good with individual rights is a difficult task; gun policies attempt to do just this. To ensure public safety, local, state, and federal agencies piece together policies that each entity believes will meet the needs of public welfare. When legislating new gun policies, the impact the policies have on gun owners are perceived as a zero-sum game; some groups are perceived to gain while others think they are losing, but the reality is much more nuanced. The reason the impact of these policies on all lawful gun owners has been considered a zero-sum game is largely because to date there has been no research measuring the impact. Further, there have been no attempts to quantify the impact that the policies have on lawful gun owners. The sole argument that has been made is about constitutionality. In this paper, we develop an approach based on the Analytic Hierarchy Process (AHP). The approach allows us to develop criteria for evaluating the impact of these policies on lawful gun owners and generate priorities for the criteria from pairwise comparisons. Criteria are compared in pairs, thus the term pairwise comparisons. This allows us to score, as with a scorecard model, gun policies for various types of gun owners with respect to the criteria according to the Benefits, Opportunities, Costs, and Risks, thereby determining the impact of each policy. We show how relative measurements are derived and illustrate with an example how ratings (absolute measurement) work in the context of an organ donor model. Next, we IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 356 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 develop a gun policy model hierarchy to show how the approach might be structured. A hypothetical gun policy  a single shot only policy  is evaluated against the model for various types of lawful gun owners to illustrate the approach. Since the model will need to be tested with a large group of stakeholders, we discuss how to develop the priorities from large groups. Finally, we discuss how this approach might be implemented. This work may be of interest to policy makers at the federal, state, and local levels since gun control policy happens at every level of governance in the United States. Additionally, this work may be of interest to lawful gun owners who may wish to apply the approach to their own context to see how they may be personally impacted by a given gun control policy. Finally, researchers may find this research of interest because the approach is applicable in other contexts and presents a novel way to consider the impacts of policy decisions. Keywords: gun laws; Benefits; Opportunities; Costs and Risks; Analytic Hierarchy Process 1. Introduction This paper is not about the gun debate in America, but about how gun control policies impact legal gun owners. In the process of developing a model to measure the impact of gun control policies, we need to introduce a theory based on relative measurement. Relative measurement is used when there are no scales to measure certain attributes known as intangibles. An intangible is an attribute that cannot be measured with a scale common to all members of a society, for example, love. There is no common scale to represent how much you love a person. However, everyone has an idea of the intensity of their love for other people. On the other hand, a tangible attribute is one that society measures using a commonly agreed upon tool. For example, temperature, distance, and weight, are measurable using a scale that society has agreed to use, but even when different societies use different scales, the results can be compared depending on the type of scale used. The impacts of gun control policies are not just monetary for some users, but also include intangibles, like not being able to enjoy hunting, or target shooting, or being afraid if they do not have a way to defend themselves. We are not only trying to understand how gun control policies impact legal gun owners, but also which type of gun owner is most affected. There are not many statistics about how existing laws impact behavior, let alone how they impact people’s lives. However, we believe that society as a whole has an idea about how those laws impact and influence what we do from day to day. So, why do we want to measure the impact gun policies have on legal gun owners? Perhaps we want to make sure that we allocate resources more efficiently when developing gun control policies. For example, in countries where citizens are not allowed to have any type of gun, there may not be a need for a background check policy. This is not the case in the United States. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 357 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Studying the impact that a law has on the society in which it is applied helps to better understand the balance that exists between advantages and disadvantages the law creates. (Forji, 2010) writes: “It is in the interest of the legal order that it strive for genuine justice in order to dissuade individuals from inducements to contra bonos mores. When from a particular conduct, the benefits or advantages are more than the disadvantages or sufferings to an individual; that individual can certainly be expected to opt for compliance, because the benefits (pleasures) of compliance outweigh the disadvantages (pains) of violation. The reverse conduct would be true for a legal system which is prone to injustice, hardship and sufferings to some or most of its subjects, given that the latter beside their pains are not giving any motivation to abide to the legal order. In this case, the advantages of violation seem just as good if not better as of compliance (p. 86).” This paper is not addressing the issue of what law helps prevent more suicides, mass murders or domestic violence. Perhaps, that could be the subject of another paper. Here, we are interested in measuring the impact of gun control policies on people who legally own a gun. Because the impacts of these gun policies involve intangibles, we need to use relative measurement (see Appendix A). The example that follows shows how to use ratings (scorecard) to develop an ordered list of potential recipients of a cadaver liver from a donor. 2. Example of how Absolute Measurement (or ratings) works Cook et al. (1990) proposed the use of an AHP model to develop a rating system using absolute measurement for the allocation of cadaver livers for orthotopic transplantation. Five major criteria for comparison were established, defined, and rated relative to one another. They were logistic considerations, tissue compatibility, waiting time, financial considerations, and medical status. Subcriteria were also established and prioritized in relative terms (see Figure 2). Patients that met appropriate inclusion screening criteria were rated according to the scales in Figure 3. The final weighting can be used to develop an alternative to the rigid computerized multifactorial point system that existed at the time of the publication (see Figure 1). In Figure 4, the existing list in 1990 showed that patient #6 was the desired choice with a score of 39.76 points. This score was obtained by assigning points to the patient according to the scales in Figure 3. The donor points 8  can be seen in the upper right- hand corner of Figure 6 next to the word Logistics. Using Cook et al.’s system, the list of patients given in Figure 4 were also scored (or rated). The patient that was selected for the transplant is now in the 7 th position (see Figure 5). Clearly, both systems do not provide the same rankings. How does one decide which one is more acceptable? Some criteria to consider would be accountability, clarity of weight assignment and capability to explain how the weights were derived. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 358 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Figure 1 Scoring system for liver assignment in 1990 Logistics Medical Urgency Distance Donor Recipient Class Points (miles) Points Points 0-50 12 6 1 4 50-500 10 5 2 8 500-1000 8 4 3 12 1000-1500 6 3 4 16 1500-2000 4 2 5 20 2000-2500 2 1 6 24 > 2500 0 0 Waiting Time Points (% to the time waited) Longest wait 10 IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 359 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Figure 2 Equitable allocation of livers for transplantation Figure 3 Priorities of criteria, subcriteria and rating scales Equitable Allocation of Livers for Transplantation Logistics Compatibility Waiting Time Financial Medical Status Urgency Replant Complexity Graft Preservation ABO X-matching Size Adequate Insurance $ but not Adequate Insurance No dollars No Insurance Primary Anatomy 0-6 months Urgency 1, 2, 3 Urgency 4, 5, 6 Re-transplant 1 Multiorgan <10hrs 6 months - 1 yr Re-transplant 2 "Routine" 11-20hrs 1-2 yrs No Deterrent Deterrent >20hr >2 yrs Age Cancer HIV Hept ETOH Drug 0.065 IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 360 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Figure 4 Example of a liver donor and an ordered list of potential recipients IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 361 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 *Numbers in the column Total do not add to 1 because of rounding off error. Figure 5 Final ordered list of patients from Figure 4 obtained using the proposed AHP model Alternative Total Logistic|Complexity|(L: .206)Logistic|Graft Preservation|(L: .794)Compatibility|(L: .502)Waiting Time|(L: .037)Financial|(L: .065)Medical Status|Urgent|(L: .347)Medical Status|Replant|(L: .653) Patient 2 0.092 Routine <10hrs Perfect 0-6 months Insurance #4 Primary Patient 3 0.082 Routine <10hrs Perfect 0-6 months No $ #3 Primary Patient 7 0.074 Routine 11-20hrs Perfect 13-24 months Insurance #3 Primary Patient 8 0.072 Routine 11-20hrs Perfect 7-12 months Insurance #3 Primary Patient A 0.071 Routine 11-20hrs Perfect 0-6 months Insurance #3 Primary Patient 4 0.07 Difficult 11-20hrs Perfect >24 months No $ #3 Primary Patient 6 0.07 Difficult >20hrs Perfect >24 months $ #3 Primary Patient 9 0.07 Routine 11-20hrs Perfect 0-6 months $ #3 Primary Patient 1 0.068 Routine >20hrs Perfect 0-6 months Insurance #3 Primary Patient C 0.053 Routine 11-20hrs Adequate 13-24 months $ #5 Secondary Patient 5 0.051 Routine 11-20hrs Adequate 0-6 months Insurance #5 Primary Patient B 0.049 Routine 11-20hrs Adequate 7-12 months $ #4 Secondary Patient 11 0.048 Routine 11-20hrs Adequate 0-6 months Insurance #4 Primary Patient 10 0.045 Routine 11-20hrs Adequate >24 months $ #3 Primary Patient 12 0.043 Difficult >20hrs Adequate 0-6 months Insurance #4 Primary Patient D 0.042 Difficult 11-20hrs Adequate 7-12 months No $ #4 Primary IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 362 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 3. Hierarchy of impacts of gun control policies We propose building a similar system as illustrated in the liver donor model to evaluate the effects of gun control policies on lawful owners of firearms. The difference resides with considering not just benefits and costs, but the uncertainty in benefits, that we call opportunities, and the uncertainty within costs, termed risks. The goal of the model is to measure the impact that gun control policies have on legal gun owners. Thus, if we model it as a hierarchy we would have the following: 1. Goal: Measure the impact of a gun control policy on lawful gun owners. 2. Strategic Criteria: At the macro-level, gun control policies have an impact on society as a whole. When considering the enactment of gun control policies, policymakers need to consider strategic issues. The political, economic, social, technological environmental, and legal (PESTEL) framework is commonly used to capture the macro-environment when making strategic decisions. a. Political impact: these impacts may include things like the pressure that is being placed on legislators to enact or repeal gun laws; the importance that gun control measures play in an election cycle; the donations being made by lobbying groups; etc. b. Economic impact: these impacts may be seen in the growth or contraction around the gun industry related to gun manufacturing. For instance, the IMPLAN 1 application has industry code 257, “small arms, ordnance, and accessories manufacturing,” employing 20,768 people with $1.6M in labor income. Gun control laws that impact this industry may have an economic impact through direct, induced, and spillover effects. c. Social impact: when considering the impact that a gun policy has, social issues need to be considered as well. For instance, there are matters of public good, safety, and health that may be impacted. d. Technological impact: research and development, among other technological areas, may be impacted by gun control policies. e. Environmental impact: the manufacturing, use, and disposal of guns, accessories, and material may have an environmental impact. Hence, consideration of the environment needs to be taken. f. Legal impact: the legal framework needs to be considered since gun control policies may be affected by existing laws and statutes. 3. Benefits, Opportunities, Costs, and Risks 4. Intensity Scales for each of the Benefits, Opportunities, Costs, and Risks. 1 Economic Impact Analysis for Planning  https://www.implan.com IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 363 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 The proposed hierarchy is illustrated in Figure 6. It is common sense to assume that not all gun owners think the same about the impact of gun control policies. Thus, the strategic criteria need to be prioritized according to different types of gun owners, including 2 : a. Recreational i. Hunters – there are a variety of types of hunters. For instance, a bird hunter might prefer a shotgun, whereas a deer hunter might prefer a cartridge. There are some hunters that prefer black-powder, whereas others may prefer high-power. Some hunters hunt for recreation, whereas others hunt to supplement their food. We do not separate the various types of hunters, but recognize there is a variety. ii. Shooting – paper fixed targets, skeet, and pop-up. iii. Enthusiasts – these are generally people who feel an affinity to guns. iv. Collectors – this category of gun owner tends to possess them for the potential appreciation in value. They may display their guns and could have many in their possession. v. Historical reenactment – this category may have weapons for recreating battles such as Gettysburg, may participate in demonstrations such as Veteran’s Day parades, or take part in filming. b. Protectionists i. Private security guards – these individuals are typically contracted out through a firm to cover banks, buildings, and other locations. They may be required to own their own gun, though their employer may provide one. ii. Private citizens – homeowners, personal protection, automobile. iii. Law enforcement – these individuals will often be issued a service weapon, but may also have personal weapons that they may decide to carry while working and may also carry while off-duty. iv. Retired and active duty military – military members may have basic weapons training, but may also have advanced weapons training. These individuals may have a variety of types of weapons. c. Gun shop owners - Dealers d. Survivalists – these individuals may purchase weapons with the idea of needing them should social structures and services fall into disarray. 2 These categories are not mutually exclusive, and a gun owner might fall into multiple categories. It is important to distinguish the categories since a gun policy may affect one type of gun owner more than another. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 364 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 e. Paramilitary – these individuals may possess weapons for the purpose of serving in a militaristic type of organization which is not government backed or supported. The selection of the types of gun owners is based, in part, on a review of the literature for what lawful gun ownership looks like ((Moore, 1983). To develop priorities for each group, we needed to compare the strategic criteria according to their perceived importance for each group. For example, for a given group, given two criteria, e.g., political and economic, which one is more important when considering a gun control policy, and how much more important? These pairwise comparisons of the criteria are then used to derive priorities that different groups assign to the different dimensions of a gun control policy. Next, we needed to identify the impacts of each specific gun control policy. Any gun control policy has several favorable and unfavorable aspects to consider. Some of these are certain, others are less so and only likely to materialize. The favorable concerns that are certain are called Benefits (B) while the unfavorable ones are called Costs (C). The uncertain concerns of a decision that are positive are characterized as Opportunities (O) that the decision might create and the negative as Risks (R). These concerns can have monetary and non-monetary implications. Thus, intangible attributes are at the heart of the measurement of the impacts of a gun control policy on legal owners of guns. The specific impacts of a gun control policy need to be evaluated in terms of the concerns (e.g., benefits), and each of the concerns is measured on its own scale. For example, assume that gun control policies impact the benefit of protection with different intensity that can range from none (i.e., no protection) to very high (i.e., very high protection). The scale for each intangible impact needs to be developed using pairwise comparisons. Let us assume we want to construct the intensity scale for the protection benefit. The following matrix shows an example of the pairwise comparisons obtained in response to the following question: “Given two intensity levels, e.g., none and low, how much more intense (important) is low than none using the fundamental scale from Table 1 in Appendix A.” 1 1 1 1 3 5 7 9 1 1 1 3 5 7 1 1 3 5 1 3 1 2 3 4 5 Priorities Ideal 1. None 1 0.033 0.06 2. Low 3 1 0.063 0.12 3. Medium 5 3 1 0.129 0.25 4. High 7 5 3 1 0.261 0.51 5. Very High 9 7 5 3 1 0.513 1                The values under the word “Priorities”, in the table above, are the relative intensities of the Benefit Protection rating scale. Sometimes, it is more convenient to use the ideal form which is obtained by dividing each relative priority by the largest value. In this example, IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 365 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 each priority is divided by 0.513. This will be done for each impact in the concerns identified under benefits, opportunities, costs, and risks. These scales will have to be constructed individually for benefits, opportunities, costs, and risks because the intensity of the scale’s levels depends on the dimension for which they will be used. For example, the pain of a loss or cost is usually perceived to be greater than the pleasure of an equal gain or benefit. Thus, the scales will have to reflect these perceptions (Kahneman & Tversky, 1979). Benefits 3 : a. Security and Peace of Mind – the ability of the gun owner to derive a sense of calmness from knowing that she/he owns a weapon that is available for use should the need arise. The sense of security and peace of mind derives from several sub-criteria: 1. Protection – under protection, a lawful owner views the gun as an instrument of protection. The protection may be for oneself, one’s family or perhaps property. The scale used to rate potential policies or laws ranges from “provide no protection” to “provides a lot of support for protection or “very high”. 2. Respect – under this criterion, the gun owner may possess the weapon out of a sense of esteem derived from the perception that others see the owner as possessing some ‘power’. The scale used to rate the policy or law ranges from “none, it provides no support for a sense of respect” to “very high, the policy supports the owner’s sense of respect.” 3. Posturing – this criterion derives from a recognition that there are some gun owners who may possess the weapon in order to present a certain pretense. Gun policies and laws may diminish or support the ability of the lawful gun owner to present this pretense. Like protection and respect, the scale used to evaluate the policy ranges from none to very high. b. Psychological – the security and peace of mind cluster largely constitutes external considerations. This cluster derives from internal positive feelings in this case. The difference between this cluster and the security and peace of mind cluster is subtle, but we estimated that the source of the benefit is derived from differing motivations. It is comprised of the following sub-criteria: 1. Self-esteem – this is a measure of how the lawful gun owner feels about him or herself because of the fact that he or she can own a gun. The scale ranges from none to very high. 2. Identity – this is a measure of the degree to which gun ownership is integral to how the owner identifies him or herself. The scale ranges from none to very high. 3 Here we consider direct, known gains that the lawful gun owner receives. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 366 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 3. Turf – here, we capture the idea that one might own a gun with the intent of defending one’s territory or have the means to defend one’s territory if necessary. This is different from self-defense or protection where the owner is concerned about his or her home. 4. Community (belonging) – there are some gun owners who possess the gun because they feel a sense of belonging with others. The act of ownership facilitates the inclusion into a group that is larger than just the individual, e.g., being part of the National Rifle Association or a local hunting club. c. Recreation – this category of lawful gun owners possess guns primarily for recreational purposes or enjoyment. 1. Hunting – these are lawful gun owners whose primary reason for gun ownership is for hunting purposes (fowl, deer, etc.). 2. Ornamental – gun ownership for the purpose of display. 3. Stress Release – gun ownership for the purpose of releasing tension. 4. Target shooting – these gun owners enjoy shooting at targets (paper, pop- up, clay, etc.). The target shooters are more competitive than those that shoot for stress release and may participate in competitions. d. Constitutional right – this category of individuals tends to possess guns because they consider it a constitutional right. The possession of the weapon is an act of maintaining the right itself. 1. Freedom – these types of gun owners possess weapons as an expression of independence. 2. Militia – these gun owners possess weapons as an act of upholding the Second Amendment imperative to maintain “a well-regulated militia.” 3. Bear arms - these gun owners possess weapons as an act of upholding the Second Amendment right to “bear arms.” Opportunities 4 : a. Insurance – this is largely a measure of an individual wanting to keep a gun for safety in case something should happen. b. Appreciation – some gun owners hold their guns for an investment. c. Identity – these gun owners feel that the gun is a function of their identity and without it may lose some sense of self. Costs 5 : a. Economic – these include the fiscal costs associated with the implementation of a gun control policy. 1. Purchase Price – defined as the initial purchase costs associated with the gun or related matter need for the ownership of the gun. 4 Potentialities, things that the gun owner may get at some time in the future. 5 Direct cost of lawful gun ownership. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 367 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 2. Operational – the ongoing costs of maintaining the ownership of the gun. 3. License – the monetary costs associated with legally owning the gun. 4. Insurance – the costs associated with indemnifying the gun owner against potential claims. b. Social costs – the costs that society may incur from the implementation of the policy, such as lives lost, injuries, and so on. c. Time – the amount of time spent maintaining legal ownership that may result from applying for a license, waiting, etc. d. Holding – costs associated with maintaining required storage of the gun associated with policies. e. Reporting – costs associated with reporting requirements that may be imposed by the gun policy. Risks 6 : a. Safety – the risk to the environment (i.e., damage to personal property). b. Bodily harm – the injury to oneself or others. c. Noncompliance – the ability to maintain legal ownership status as policies change. d. Identity – the risk that one may lose some sense of self through the implementation of a particular policy or policies. e. Constitutionality – the risk that a policy may be perceived as counter to the intent of the Constitution. f. Restrictions – defined as the extent to which the lawful gun owner may perceive that the policy places additional or undue restrictions on the owner. g. Liability – the perception that the policy places additional liability on the gun owner. h. Surrender – the extent to which the gun owner perceives that she or he may be required to surrender personal property. i. Intrusion - the extent to which the policy is perceived as an imposition in the life of the gun owner. It is important to understand the relative priorities that gun owners place on the criteria to determine the impact that a gun policy has. In a 2019 study, the Pew Research Center 7 found that 67% of gun owners state that protection is the number one reason why they own guns, 38% claim ownership for hunting, 30% for sport shooting, 13% for gun collecting, and 8% for their work. While it may be true that the gun owner’s primary reason for owning a gun is protection, this does not mean that they do not use it for sport 6 The future, potential negative impacts of lawful gun ownership. 7 Pew Research Center (2019), “7 facts about guns in the U.S.” https://www.pewresearch.org/fact- tank/2019/10/22/facts-about-guns-in-united-states/ https://www.pewresearch.org/fact-tank/2019/10/22/facts-about-guns-in-united-states/ https://www.pewresearch.org/fact-tank/2019/10/22/facts-about-guns-in-united-states/ IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 368 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 shooting or work. Hence, by capturing the relative priorities, we are able to get a more nuanced view of gun ownership and establish a more accurate impact score. Figure 6 is a graphic representation of the sample hierarchy developed here. The details of the various clusters inside each of the boxes are presented in Table 3 along with the intensity scales. Table 4 gives the priorities derived for the strategic criteria and the benefits, opportunities, costs, and risks. We derived these priorities to illustrate how the framework can be used to evaluate the impact of specific gun control policies on different groups of legal owners of firearms. To obtain the impact of a gun control policy in terms of, e.g., benefits, we multiplied for each benefit, e.g., protection, its priority (0.0555) by the numeric value of the intensity level with which that benefit is perceived, e.g., none (0.065), and summed across all the benefits. The same was done for opportunities, costs, and risks. The resulting values were combined using the formula: 𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠 (𝐵)×𝑂𝑝𝑝𝑜𝑟𝑡𝑢𝑛𝑖𝑡𝑖𝑒𝑠 (𝑂) 𝐶𝑜𝑠𝑡𝑠 (𝐶)×𝑅𝑖𝑠𝑘𝑠(𝑅) . We illustrate its applicability with a fictitious gun control policy we invented for this purpose that we call the “single shot” law. Figure 6 Hierarchy to measure the impact of gun control policy Goal: Measure the Impact of a gun control policy Strategic Criteria: Political Economic Social Technological Environmental Legal Benefits: a. Security & Peace of Mind a. Protection b. Respect c. Posturing b. Psychological a. Self-esteem b. Identity c. Turf d. Community (belonging) c. Recreation a. Hunting (satisfaction) b. Ornamental c. Stress Release d. Target shooting d. Constitutional right a. Freedom b. Militia c. Bear arms Opportunities: a. Appreciation (value) b. Identity c. ‘Insurance’ (safety) Costs: a. Monetary Costs a. Purchase Price b. Maintenance c. License d. Insurance b. Social costs c. Time d. Holding (storage) e. Reporting Risks: a. Constitutionality b. Identity Risks c. Liability d. Non-compliance e. Restrictions f. Safety h. Bodily harm to self or others i. Surrender j. Intrusion IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 369 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 4. Illustrative example For illustrative purposes, we developed an example case wherein we simulated an ‘expert’ opinion to develop the priorities of the strategic criteria and the Benefits, Opportunities, Costs, and Risks (BOCR) model. The choice of a fictitious policy was intentional to avoid any prior bias of the policy that reviewers may have. The policy that we chose to evaluate was a “Single Shot” law. The “Single Shot” law would make it such that all lawful gun ownership would be limited to firearms that were capable of only a single shot at a time. The single shot policy would make it illegal to own semiautomatic weapons of any kind. A revolver, rifle, or other types of firearms would need a limiting device that would prohibit the use of semiautomatic firing. Next, we took the position of the four types of stakeholders, the anti-gun person, the collector, the law officer, and the protectionist and rated the policy with respect to each of the criteria to develop the overall score for the policy. The total scores are reported in Tables 5-8. In Table 3, we demonstrate how the intensity scales for each element were prioritized. Following Table 3, we included sample scoring sheets for a ‘blank’ scoring where we intentionally produced a score of “1” to illustrate the method (Table 4). Following the ‘blank’, in Table 5, we included a scoring of a hypothesized individual who is against gun ownership followed by the perspective of a collector (Table 6), a police officer (Table 7), and someone who owns a gun for protection (Table 8). IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 370 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Table 3 Intensity scales Gun Control Policy: Benefits[1]: a. Security & Peace of Mind a. Protection None Low Medium High Very High b. Respect None Low Medium High Very High c. Posturing None Low Medium High Very High b. Psychological a. Self-esteem None Low Medium High Very High b. Identity None Low Medium High Very High c. Turf None Low Medium High Very High d. Community (belonging) None Low Medium High Very High c. Recreation a. Hunting (satisfaction) Absent Weak Moderate Strong Very Strong b. Ornamental No Value Low Value Moderate Strong Very Strong c. Stress Release None Low Medium High Very High d. Target shooting Not Allowed Controlled Strictly Controlled Limited Allowed d. Constitutional right a. Freedom No Support Low Support Moderate Strong Very Strong b. Militia No Support Low Support Moderate Strong Very Strong c. Bear arms No Support Low Support Moderate Strong Very Strong Opportunities[2]: a. Appreciation (value) None Low Medium High Very High b. Identity None Low Medium High Very High c.      ‘Insurance’ (safety) None Low Medium High Very High Costs[3]: a. Monetary Costs a. Purchase Price No Impact Limited Moderate High Prohibited b. Maintenance Low Moderate High Very high Extreme c. License Low Moderate High Very high Extreme d. Insurance Low Moderate High Very high Extreme b. Social costs No Injuries Minor Injuries Substantial Injuries (full recovery) Substantial Injuries (partial recovery) Deaths c. Time No Effort Simple Paperwork Paperwork with waiting period Multiple Forms Substantial Time Investment d. Holding (storage) No Requirement Simple requirement (e.g. lockbox) Complex Requirement (e.g. safe) Heavy Requirement (e.g. weapon and ammunition separation) Extreme (everything under lock and separation e. Reporting No Effort Simple Paperwork Paperwork with waiting period Multiple Forms Substantial Time Investment Risks[4]: a. Constitutionality In Line with 2nd Amendment Some Limitations Moderate Limitations High Limitations No Weapons for Civilians b. Identity Risks None Low Medium High Very High c. Liability None Some Moderate Class Restrictions & Accessories Highly Liable Fully Liable d. Non-compliance None Low Medium High Full e. Restrictions None Limited (e.g. class 3) Moderate Class Restrictions & Accessories Significant Restrictions Extreme Restrictions f. Safety None Prevent Adult from Misuse Prevent Child from Misuse Prevent Domestic Abuse Mayhem h. Bodily harm to self or others No Injuries Minor Injuries Substantial Injuries (full recovery) Substantial Injuries (partial recovery) Deaths i. Surrender None Low Medium High Very High j. Intrusion None Low Medium High Very High [1] Here we consider direct, known gains that the lawful gun owner receives. [2] Potentialities, things that the gun owner may get at some time in the future. [3] Direct cost of lawful gun ownership. [4] The future, potential negative impacts of lawful gun ownership. Evaluation Scales IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 371 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Table 4 Priorities of Benefits, Opportunities, Costs, and Risks Gun Control Policy: Single Shot Policy Totals BO/CR Benefits[1]: Weights Ratings Labels Ratings Numeric 1.0000 a. Security & Peace of Mind 0.0650 a. Protection 0.0555 None 0.0650 b. Respect 0.0555 None 0.0650 c. Posturing 0.0555 None 0.0650 b. Psychological a. Self-esteem 0.0308 None 0.0650 b. Identity 0.0953 None 0.0650 c. Turf 0.0150 None 0.0650 d. Community (belonging) 0.0473 None 0.0650 c. Recreation a. Hunting (satisfaction) 0.0214 Absent 0.0650 b. Ornamental 0.1068 No Value 0.0650 c. Stress Release 0.1068 None 0.0650 d. Target shooting 0.1068 Not Allowed 0.0650 d. Constitutional right a. Freedom 0.2169 No Support 0.0650 b. Militia 0.0434 No Support 0.0650 c. Bear arms 0.0434 No Support 0.0650 Opportunities[2]: Weights 0.0650 a. Appreciation (value) 0.4933 None 0.0650 b. Identity 0.2568 None 0.0650 c.      ‘Insurance’ (safety) 0.2499 None 0.0650 Costs[3]: Weights 0.0650 a. Monetary Costs a. Purchase Price 0.0489 No impact 0.0650 b. Maintenance 0.0098 Low 0.0650 c. License 0.0219 Low 0.0650 d. Insurance 0.1093 Low 0.0650 b. Social costs 0.5134 No Injuries 0.0650 c. Time 0.1161 No Effort 0.0650 d. Holding (storage) 0.0881 No requirement 0.0650 e. Reporting 0.0926 No Effort 0.0650 Risks[4]: Weights 0.0650 a. Constitutionality 0.3924 In Line with the 2nd Amendment 0.0650 b. Identity Risks 0.0207 None 0.0650 c. Liability 0.0266 None 0.0650 d. Non-compliance 0.1329 None 0.0650 e. Restrictions 0.0251 None 0.0650 f. Safety 0.1492 None 0.0650 h. Bodily harm to self or others 0.0717 No Injuries 0.0650 i. Surrender 0.1254 None 0.0650 j. Intrusion 0.0561 None 0.0650 [3] Direct cost of lawful gun ownership. [4] The future, potential negative impacts of lawful gun ownership. Benefits (B) Opportunities (O) Costs (C) Risks (R) [1] Here we consider direct, known gains that the lawful gun owner receives. [2] Potentialities, things that the gun owner may get at some time in the future. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 372 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Table 5 Anti-gun perspective Gun Control Policy: Single Shot Policy Totals BO/CR Benefits[1]: Weights Ratings Labels Ratings Numeric 0.9494 a. Security & Peace of Mind 0.2934 a. Protection 0.0555 Very High 1.0000 b. Respect 0.0555 Very High 1.0000 c. Posturing 0.0555 Very High 1.0000 b. Psychological a. Self-esteem 0.0308 Low 0.1236 b. Identity 0.0953 Medium 0.2515 c. Turf 0.0150 High 0.5099 d. Community (belonging) 0.0473 High 0.5099 c. Recreation a. Hunting (satisfaction) 0.0214 Absent 0.0650 b. Ornamental 0.1068 No Value 0.0650 c. Stress Release 0.1068 Low 0.1236 d. Target shooting 0.1068 Not Allowed 0.0650 d. Constitutional right a. Freedom 0.2169 No Support 0.0650 b. Militia 0.0434 No Support 0.0650 c. Bear arms 0.0434 Strong 0.5099 Opportunities[2]: Weights 0.0800 a. Appreciation (value) 0.4933 None 0.0650 b. Identity 0.2568 Low 0.1236 c.      ‘Insurance’ (safety) 0.2499 None 0.0650 Costs[3]: Weights 0.0944 a. Monetary Costs a. Purchase Price 0.0489 No impact 0.0650 b. Maintenance 0.0098 Moderate 0.1236 c. License 0.0219 Low 0.0650 d. Insurance 0.1093 Moderate 0.1236 b. Social costs 0.5134 No Injuries 0.0650 c. Time 0.1161 No Effort 0.0650 d. Holding (storage) 0.0881 Simple requirement (e.g., lockbox) 0.1236 e. Reporting 0.0926 Paperwork with a waiting period 0.2515 Risks[4]: Weights 0.2621 a. Constitutionality 0.3924 Moderate Limitations 0.2515 b. Identity Risks 0.0207 High 0.5099 c. Liability 0.0266 Some 0.1236 d. Non-compliance 0.1329 Low 0.1236 e. Restrictions 0.0251 Extreme restrictions 1.0000 f. Safety 0.1492 Prevent adult misuse 0.1236 h. Bodily harm to self or others 0.0717 Substantial injuries (full recovery) 0.2515 i. Surrender 0.1254 Low 0.1236 j. Intrusion 0.0561 Very High 1.0000 [2] Potentialities, things that the gun owner may get at some time in the future. [3] Direct cost of lawful gun ownership. [4] The future, potential negative impacts of lawful gun ownership. Benefits (B) Opportunities (O) Costs (C) Risks (R) [1] Here we consider direct, known gains that the lawful gun owner receives. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 373 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Table 6 Collector’s perspective Gun Control Policy: Single Shot Policy Totals BO/CR Benefits[1]: Weights Benefits (B) 4.5307 a. Security & Peace of Mind 0.4700 a. Protection 0.05546 Low 0.1236 b. Respect 0.05546 Medium 0.2515 c. Posturing 0.05546 Low 0.1236 b. Psychological a. Self-esteem 0.03075 Low 0.1236 b. Identity 0.09531 Low 0.1236 c. Turf 0.01502 Low 0.1236 d. Community (belonging) 0.04730 High 0.5099 c. Recreation a. Hunting (satisfaction) 0.02135 Absent 0.0650 b. Ornamental 0.10675 Strong 0.5099 c. Stress Release 0.10675 Low 0.1236 d. Target shooting 0.10675 Allowed 1.0000 d. Constitutional right a. Freedom 0.21687 Very Strong 1.0000 b. Militia 0.04337 No Support 0.0650 c. Bear arms 0.04337 Low Support 0.1236 Opportunities[2]: Weights 0.1720 a. Appreciation (value) 0.49329 Medium 0.2515 b. Identity 0.25677 Low 0.1236 c.      ‘Insurance’ (safety) 0.24994 None 0.0650 Costs[3]: Weights 0.1099 a. Monetary Costs a. Purchase Price 0.04888 Limited 0.1236 b. Maintenance 0.00978 Low 0.0650 c. License 0.02186 Low 0.0650 d. Insurance 0.10930 Low 0.0650 b. Social costs 0.51340 Minor Injuries (full recovery) 0.1236 c. Time 0.11613 Simple paperwork 0.1236 d. Holding (storage) 0.08810 Simple requirement (e.g., lockbox) 0.1236 e. Reporting 0.09256 No Effort 0.0650 Risks[4]: Weights 0.1624 a. Constitutionality 0.39245 In Line with the 2nd Ammendment 0.0650 b. Identity Risks 0.02069 High 0.5099 c. Liability 0.02658 Some 0.1236 d. Non-compliance 0.13290 Low 0.1236 e. Restrictions 0.02507 Extreme restrictions 1.0000 f. Safety 0.14918 Prevent child misuse 0.2515 h. Bodily harm to self or others 0.07172 Minor Injuries (full recovery) 0.1236 i. Surrender 0.12536 Medium 0.2515 j. Intrusion 0.05606 None 0.0650 Ratings Numeric Ratings Labels [1] Here we consider direct, known gains that the lawful gun owner receives. [2] Potentialities, things that the gun owner may get at some time in the future. [3] Direct cost of lawful gun ownership. [4] The future, potential negative impacts of lawful gun ownership. Opportunities (O) Costs (C) Risks (R) IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 374 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Table 7 Officer’s perspective Gun Control Policy: Single Shot Policy Total BO/CR Benefits[1]: Weights 1.7153 a. Security & Peace of Mind 0.4908 a. Protection 0.0555 Very High 1.0000 b. Respect 0.0555 Low 0.1236 c. Posturing 0.0555 Low 0.1236 b. Psychological a. Self-esteem 0.0308 Low 0.1236 b. Identity 0.0953 Medium 0.2515 c. Turf 0.0150 Low 0.1236 d. Community (belonging) 0.0473 Medium 0.2515 c. Recreation a. Hunting (satisfaction) 0.0214 Weak 0.1236 b. Ornamental 0.1068 Low Value 0.1236 c. Stress Release 0.1068 Low 0.1236 d. Target shooting 0.1068 Allowed 1.0000 d. Constitutional right a. Freedom 0.2169 Very Strong 1.0000 b. Militia 0.0434 Low Support 0.1236 c. Bear arms 0.0434 Strong 0.5099 Opportunities[2]: Weights 0.1884 a. Appreciation (value) 0.4933 Low 0.1236 b. Identity 0.2568 Medium 0.2515 c.      ‘Insurance’ (safety) 0.2499 Medium 0.2515 Costs[3]: Weights 0.2250 a. Monetary Costs a. Purchase Price 0.0489 Moderate 0.2515 b. Maintenance 0.0098 Moderate 0.1236 c. License 0.0219 High 0.2515 d. Insurance 0.1093 Moderate 0.1236 b. Social costs 0.5134 Substantial injuries (full recovery) 0.2515 c. Time 0.1161 Paperwork with a waiting period 0.2515 d. Holding (storage) 0.0881 Simple requirement (e.g., lockbox) 0.1236 e. Reporting 0.0926 Paperwork with a waiting period 0.2515 Risks[4]: Weights 0.2396 a. Constitutionality 0.3924 In Line with the 2nd Ammendment 0.0650 b. Identity Risks 0.0207 Low 0.1236 c. Liability 0.0266 Highly liable 0.5099 d. Non-compliance 0.1329 High 0.5099 e. Restrictions 0.0251 Limited class (e.g., class 3) 0.1236 f. Safety 0.1492 Prevent child misuse 0.2515 h. Bodily harm to self or others 0.0717 Substantial injuries (full recovery) 0.2515 i. Surrender 0.1254 Low 0.1236 j. Intrusion 0.0561 Very High 1.0000 [2] Potentialities, things that the gun owner may get at some time in the future. [3] Direct cost of lawful gun ownership. [4] The future, potential negative impacts of lawful gun ownership. Ratings Labels Ratings Numeric Risks (R) Costs (C) Opportunities (O) Benefits (B) [1] Here we consider direct, known gains that the lawful gun owner receives. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 375 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Table 8 Protectionist’s perspective Table 9 summarizes the total priorities for benefits, opportunities, costs, and risks for the four types of gun owners illustrated in Tables 5-8. Figure 7 shows that information in a radar display that illustrates the similarities and dissimilarities of the four groups. Gun Control Policy: Single Shot Policy Total BO/CR Benefits[1]: Weights 0.6321 a. Security & Peace of Mind 0.1698 a. Protection 0.0555 None 0.0650 b. Respect 0.0555 None 0.0650 c. Posturing 0.0555 None 0.0650 b. Psychological a. Self-esteem 0.0308 Low 0.1236 b. Identity 0.0953 Low 0.1236 c. Turf 0.0150 None 0.0650 d. Community (belonging) 0.0473 Low 0.1236 c. Recreation a. Hunting (satisfaction) 0.0214 Very Strong 1.0000 b. Ornamental 0.1068 No Value 0.0650 c. Stress Release 0.1068 Low 0.1236 d. Target shooting 0.1068 Strictly Controlled 0.2515 d. Constitutional right a. Freedom 0.2169 Moderate 0.2515 b. Militia 0.0434 No Support 0.0650 c. Bear arms 0.0434 Moderate 0.2515 Opportunities[2]: Weights 0.1236 a. Appreciation (value) 0.4933 Low 0.1236 b. Identity 0.2568 Low 0.1236 c.      ‘Insurance’ (safety) 0.2499 Low 0.1236 Costs[3]: Weights 0.1069 a. Monetary Costs a. Purchase Price 0.0489 No impact 0.0650 b. Maintenance 0.0098 Low 0.0650 c. License 0.0219 Moderate 0.1236 d. Insurance 0.1093 Low 0.0650 b. Social costs 0.5134 Minor Injuries (full recovery) 0.1236 c. Time 0.1161 No Effort 0.0650 d. Holding (storage) 0.0881 Simple requirement (e.g., lockbox) 0.1236 e. Reporting 0.0926 Simple paperwork 0.1236 Risks[4]: Weights 0.3105 a. Constitutionality 0.3924 Moderate Limitations 0.2515 b. Identity Risks 0.0207 High 0.5099 c. Liability 0.0266 Some 0.1236 d. Non-compliance 0.1329 Low 0.1236 e. Restrictions 0.0251 Extreme restrictions 1.0000 f. Safety 0.1492 Prevent adult misuse 0.1236 h. Bodily harm to self or others 0.0717 Substantial injuries (full recovery) 0.2515 i. Surrender 0.1254 High 0.5099 j. Intrusion 0.0561 Very High 1.0000 Risks (R) Costs (C) Opportunities (O) Benefits (B) Ratings Numeric Ratings Labels [1] Here we consider direct, known gains that the lawful gun owner receives. [2] Potentialities, things that the gun owner may get at some time in the future. [3] Direct cost of lawful gun ownership. [4] The future, potential negative impacts of lawful gun ownership. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 376 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Table 9 Benefits, Opportunities, Costs, and Risks for four groups of gun owners Anti-Gun Collector Officer Protectionist Ideal Costly Benefits 0.2934 0.4700 0.4908 0.1698 1.0000 0.0650 Opportunities 0.0800 0.1720 0.1884 0.1236 1.0000 0.0650 Costs 0.0944 0.1099 0.2250 0.1069 0.0650 1.0000 Risks 0.2621 0.1624 0.2396 0.3105 0.0650 1.0000 BO/CR 0.9494 4.5307 1.7153 0.6321 236.7 0.0040 To bracket the scores, we developed both the ideal state which includes all of the benefits and opportunities and none of the costs or risks, as well as a costly state where there are no benefits or opportunities, and only costs and risks. In the ideal state, the highest score that a given gun policy could achieve is a 236.7, whereas the lowest score that a policy can receive is a 0.004. This provides a bracket for evaluating the impact that gun control policy can achieve. The distance from the ideal or the costly provides some perspective on the overall gain or loss of a proposed policy. Figure 7 Graphical depiction of proposed fictitious gun control policy IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 377 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 With respect to the consideration of lawful gun owners, the goal is to maximize the volume in the area in the radar chart between the benefits and the opportunities. Note that in Figure 7, the full area between benefits and opportunities is taken up in the ideal state, whereas the full area between costs and risk is taken up in the costly state. In Figure 8, we remove the brackets and focus solely on the four hypothetical types of lawful gun owners in order to more clearly visualize their cases. In Figure 8, we see that the officer’s radar chart (grey) has more area in the benefits and opportunities than the collector (orange), but that the officer also has more volume in the costs and risks offsetting the additional area in the benefits; the two have similar area in the opportunities. The result for the two is that the single-shot policy is better from the collector’s perspective than from the officer’s perspective. Figure 8 Four perspectives without ideal and costly The BOCR approach illuminates many ideas. According to benefits and opportunities, the collector and the officer seem in agreement; according to costs the anti-gun activist, the collector and the protectionist seem to agree; and according to risks the protectionist, the anti-gun activist and the officer are closer to each other. These conclusions can be seen in numerical format in Table 9. Overall, the protectionist is most impacted, followed by the anti-gun perspective. The one that benefits most is the collector, but the officer sees more benefits and opportunities than costs and risks. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 378 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 The implementation of this framework is predicated in two steps: 1. Developing priorities for the strategic criteria for the group profiles, and 2. Evaluating existing or proposed gun control policies by different constituent groups. The information required to accomplish the first step is predicated on the study of preferences of large groups. The next section describes a methodology that could help attain this objective. Another possibility to accomplish this goal is to use focus groups. 5. How to develop priorities for large groups Developing priorities for large groups is not the same as achieving consensus for a group in a decision-making situation. In the latter, using the AHP we would seek judgments from decision makers and the geometric mean of those judgments could be used as the representative of the group. Of course, this would require using some statistical analysis to see if the geometric mean really represents the group. In the former, the situation is like voting, but with intensity of preferences. The issue here is how to combine the different judgments. Judgments are from an absolute scale if Saaty’s 1-9 scale is used. (Vargas, 2016) showed that each vote is equivalent to a pairwise comparison in which the intensity of preference is very large. Consider two candidates 1A and 2A . Comparing them according to a criterion, we can express how strongly we prefer one candidate to the other. For example, if 1A is preferred to 2A with intensity a the result is a reciprocal matrix of pairwise comparisons given by 1 2 1 1 2 1 1 A A A a A a          The vector of priorities is given by the principal right eigenvector given by 1 1 1 a a a              that converges to the vector (1, 0) T as a   . Thus, voting for a candidate is equivalent to pairwise comparing them with an intensity of infinity. When many users are asked for their opinion, the answers (rankings) they provide is called a profile in voting theory. For example, if we ask 100 people how they prefer IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 379 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 candidates 1A and 2A , if 75 1 2 75n   prefer 1A to 2A ( 1 2 75n   ), then 25 should prefer 2 A to 1A ( 2 1 25n   ). We assume that there no ties. Then, the profile is written as follows: 1 2 2 1 1 2 1 2 2 1 2 1 ( ) ( ) (75) (25)n n A A A A A A A A                         , and the pairwise voting matrix is given by A A A A n nA A A An n                      1 2 1 2 1 2 2 11 1 2 22 1 1 2 751 1 25 25 11 75 . If all the voters that prefer 1A to 2A have an intensity of preference 12a , then we can represent the pairwise voting matrix as follows: 12 12 21 21 21 21 12 12 75 1 1 25 1 25 1 1 75 1 a a a a a a a a                                       so that when 12a   we obtain the pairwise voting matrix given above. The principal right eigenvector of this matrix is given by IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 380 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 12 12 12 21 12 21 21 21 12 21 12 21 75 1 75 25 1 1 25 1 75 25 1 1 a a a a a a a a a a a a                                                     and when 12a   , the voting priorities are given by 75 100 25 100         . If all the voters have different intensity of preference ( )k i j a  , then the pairwise voting matrix is given by 1 2 2 1 2 1 1 2 ( ) ( ) 12 ( ) 1 12 ( ) ( ) 21 ( ) 1 21 ( ) ( ) 21 ( ) 1 21 ( ) ( ) 12 ( ) 1 12 1 1 1 1 1 1 n k k k n k k k n k k k n k k k a a a a a a a a                                                        . Finally, if we compare m candidates, the pairwise voting matrix with intensity of preferences would be given by IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 381 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 11 2 1 2 1 2 2 ( )( ) ( )( ) 112 ( )( ) 11 112 ( ) ( ) ( )( ) 121 ( ) ( ) 1 121 1 ( ) ( ) 2 ( ) 1 2 ( ) ( ) 2 ( ) 1 2 11 1 1 1 1 1 1 1 m m m m nn kk m kk kk m n n kk m k k k k m n k m k k m n k m k k m aa aa aa a a a a a a                                                        (3) where ( ) i j n   and ( )k ij a represent the number of voters that prefer i to j and the intensity with which the k th voter prefers i to j, respectively. Note that if ( ) , for all and k ij a i j  , the pairwise voting matrix converges to the matrix 12 1 21 2 1 2 1 ( ) ( ) ( ) 1 ( ) ( ) ( ) 1 m m m m w w w w w w                     where ( ) ( ) , ( ) 0 ( ) i j ij j i j i n w n n          , and the voting priorities of the m candidates are given by the principal right eigenvector of the matrix. Consider the following profile in which four alternatives are compared by 14 individuals: 1 2 3 4 2 3 4 1 3 4 1 2 4 1 2 3 (4) (3) (5) (2) a a a a a a a a B a a a a a a a a             . If we were to use the counting method, the voting priorities are given by the principal right eigenvector of the matrix: IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 382 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Let us now consider that each decision maker has her own intensity of preference according to Table 10. Combining the intensity of preferences as in Equation 3, we obtain the following matrix: which yields priorities close to the priorities produced by the ranking method. On the other hand, the matrix of geometric means given by yield priorities that are not as close to the priorities obtained by the Ranking method. Thus, we believe that a way to capture priorities of large groups is by using the ranking method within the context of the eigenvector method of pairwise comparisons. Counting a1 a2 a3 a4 Priorities a1 1 11/3 6/8 4/10 0.2436 a2 3/11 1 9/5 7/7 0.2027 a3 8/6 5/9 1 12/2 0.3589 a4 10/4 7/7 2/12 1 0.1948 Ranking a1 a2 a3 a4 Priorities a1 1 3.400928 0.789474 0.557616 0.2634 a2 0.294037 1 1.734146 1.026261 0.2095 a3 1.266667 0.576653 1 5.463415 0.3477 a4 1.793349 0.974411 0.183036 1 0.1794 GM a1 a2 a3 Priorities a1 1 2.013483 0.923194 0.6671 0.2624 a2 0.496652 1 1.237874 1.076316 0.2220 a3 1.083195 0.807837 1 2.336644 0.2958 a4 1.499026 0.929095 0.427964 1 0.2198 IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 383 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 Table 10 Profile B intensity of preferences a1>a2>a3>a4 a2>a3>a4>a1 a3>a4>a1>a2 a4>a1>a2>a3 a1 a2 a3 a4 Priorities | a1 a2 a3 a4 Priorities | a1 a2 a3 a4 Priorities | a1 a2 a3 a4 Priorities a1 1 3 5 9 0.5806 | a1 1 0.142857 0.2 0.333333 0.0521 | a1 1 5 0.2 0.333333 0.1364 | a1 1 3 5 0.111111 0.1733 a2 0.333333 1 3 5 0.2554 | a2 7 1 5 5 0.6194 | a2 0.2 1 0.142857 0.2 0.0489 | a2 0.333333 1 3 0.2 0.0967 a3 0.2 0.333333 1 3 0.1141 | a3 5 0.2 1 3 0.2195 | a3 5 7 1 3 0.5558 | a3 0.2 0.333333 1 0.142857 0.0473 a4 0.111111 0.2 0.333333 1 0.0499 | a4 3 0.2 0.333333 1 0.1090 | a4 3 5 0.333333 1 0.2589 | a4 9 5 7 1 0.6828 | | | a1 a2 a3 a4 Priorities | a1 a2 a3 a4 Priorities | a1 a2 a3 a4 Priorities | a1 a2 a3 a4 Priorities a1 1 5 7 9 0.6485 | a1 1 0.2 0.333333 0.333333 0.0720 | a1 1 4 0.333333 0.2 0.1272 | a1 1 5 7 0.2 0.2844 a2 0.2 1 3 5 0.2009 | a2 5 1 3 3 0.4925 | a2 0.25 1 0.142857 0.333333 0.0547 | a2 0.2 1 5 0.333333 0.1259 a3 0.142857 0.333333 1 5 0.1100 | a3 3 0.333333 1 5 0.3051 | a3 3 7 1 5 0.5646 | a3 0.142857 0.2 1 0.2 0.0466 a4 0.111111 0.2 0.2 1 0.0407 | a4 3 0.333333 0.2 1 0.1304 | a4 5 3 0.2 1 0.2536 | a4 5 3 5 1 0.5431 | | | a1 a2 a3 a4 Priorities | a1 a2 a3 a4 Priorities | a1 a2 a3 a4 Priorities | a1 1 2 3 5 0.4650 | a1 1 0.166667 0.2 0.333333 0.0503 | a1 1 7 0.5 0.333333 0.2082 | a2 0.5 1 3 5 0.3273 | a2 6 1 7 7 0.6584 | a2 0.142857 1 0.2 0.2 0.0536 | a3 0.333333 0.333333 1 2 0.1342 | a3 5 0.142857 1 5 0.2106 | a3 2 5 1 2 0.4070 | a4 0.2 0.2 0.5 1 0.0736 | a4 3 0.142857 0.2 1 0.0807 | a4 3 5 0.5 1 0.3312 | | | a1 a2 a3 a4 Priorities | a1 a2 a3 a4 Priorities | a1 1 4 5 7 0.5758 | a1 1 3 0.2 0.2 0.0978 | a2 0.25 1 4 6 0.2613 | a2 0.333333 1 0.2 0.2 0.0576 | a3 0.2 0.25 1 5 0.1187 | a3 5 5 1 5 0.5885 | a4 0.142857 0.166667 0.2 1 0.0442 | a4 5 5 0.2 1 0.2560 | | | a1 a2 a3 a4 Priorities | a1 1 5 0.2 0.333333 0.1364 | a2 0.2 1 0.142857 0.2 0.0489 | a3 5 7 1 3 0.5558 | a4 3 5 0.333333 1 0.2589 | IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 384 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 6. Implementation of the proposed approach Thus far, we have illustrated an approach that may be used to develop a measure of the impact of existing and proposed gun policies for lawful gun owners. Assessing the impact of gun policies on lawful gun owners is an important activity since the implementation of any policy may impose unintended hardships on them. While the legislation of any policy is ultimately carried out with the best intentions, without considering the impact on the gun owner the full impact of the policy is unknown. In this effort, the authors assumed the roles of the various stakeholders for sake of illustration. To fully develop the models requires much more involvement and greater input. Since gun policies are developed at every level of our government, and gun owners are varied, the final assessment needs to reflect the various levels and types of gun owners. To this end, we propose additional work that needs to be conducted as follows: 1. Identification of national-level focus groups with subject matter experts, 2. Identification of state-level focus groups with subject matter experts, 3. Hold discussions with gun-owner focus groups, 4. Develop criteria, 5. Develop a distributed platform for priority generation, and 6. Estimate policy and law ratings. National and state-level focus groups will provide greater insights into what the criteria for evaluation should be. The results will be a hierarchical structure that more accurately reflects the criteria and priorities at each level. Ideally, each state should have a focus group study done such that the criteria that are important to that state and the resultant priorities accurately reflect the state’s interests. The results from the focus groups can be put into a web-based platform for distributed release. The platform will allow users to input their own ratings on existing and proposed legislation to see their resulting scores. The collection of the data along with demographics will facilitate a continuous evaluation of the BO/CR of gun policy in the U.S. that will be updated as priorities and concerns shift and change. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 385 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 7. How to use the results of the study Disagreement between different gun advocate groups is one of the most important issues confronting American society. According to (Pierre, 2019), “The gun debate in America is often framed as a stand-off between two immutable positions with little potential to move ahead with meaningful legislative reform. Attempts to resolve this impasse have been thwarted by thinking about gun ownership attitudes as based on rational choice economics instead of considering the broader socio-cultural meanings of guns.” In this paper, we present a mechanism to begin a dialogue between different stakeholders in the hope that by identifying the differences in thinking a compromise can be reached. By measuring the impact of a gun policy (law) on different groups one could perhaps modify, in incremental steps, the policy being evaluated, so that the groups can be closer to each other in most of the issues they consider important. It is possible that by using this methodology some groups may discover some misinterpretations or misunderstandings they have about the policy that can help them feel more at ease with it or know how they could lobby for or against it. The focus groups must consist of knowledgeable people from the different constituencies. Experience suggests the recommended size of each group should be between five and ten people (Cummings et al., 1974). We would need a session to develop priorities for the strategic criteria, the benefits, the opportunities, the costs, and the risks, and a second session to evaluate different gun control policies. It is possible that this evaluation could be done through an electronic questionnaire, in which case it may not be easy to determine who is answering the evaluation. However, given the importance of this step it is preferable to use focus groups. This paper facilitates the development of a proof of concept to show that our methodology captures what stakeholders think about different gun laws and their impact on lawful gun owners. This will enable policy makers to develop policies that are beneficial to society at large. Ultimately, the validity of our proof of concept will result in the development of a distributed platform. This platform will enable any stakeholder to rate a proposed/existing policy, and thereafter, policy makers can assess its impact and legislate accordingly. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 386 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 REFERENCES Cook, D. R., Staschak, S., & Green, W.T. (1990). Equitable allocation of livers for orthotopic transplantation: An application of the Analytic Hierarchy Process. European Journal of Operational Research, 48(1), 49-56. Doi: https://doi.org/10.1016/0377- 2217(90)90060-o Cummings, L., Huber, L., George, P., & Arendt, E. (1974). Effect of size and spatial arrangements on group decision making. Academy of Management Journal, 17(3), 460- 475. Doi: https://doi.org/10.2307/254650 Forji, A. G. (2010). The correlation between law And behaviour as pillars of human society. International Journal of Punishment and Sentencing, 6(3), 84-96. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291. Doi: https://doi.org/10.2307/1914185 Moore, M.H. (1983). The bird in hand: A feasible strategy for gun control. Journal of Policy Analysis and Management, 2(2), 185-196. Pierre, J. M. (2019) The psychology of guns: risk, fear, and motivated reasoning. Palgrave Communications, 5, 159. Doi: https://doi.org/10.1057/s41599-019-0373-z. Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234-281. Doi: https://doi.org/10.1016/0022- 2496(77)90033-5 Saaty, T. L. (1980). The Analytic Hierarchy Process, McGraw-Hill Publications. Saaty, T. L. (1996). The Analytic Network Process. Pittsburgh, PA: RWS Publications. Vargas, L. G. (2016). Voting with intensity of preferences. International Journal of Information Technology & Decision Making, 15(4), 839-859. Doi: https://doi.org/10.1142/S0219622016400058 https://doi.org/10.1057/s41599-019-0373-z IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 387 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 APPENDIX A: RELATIVE MEASUREMENT Relative measurement is the development of a scale to measure an intangible attribute, i.e., an attribute for which no scale to measure exists. Thus, each individual has its own scale in mind. However, if there were a scale to measure the attribute, relative measurement would provide an answer in relative terms. For example, consider that we want to measure the weight of three cantaloupes, C1, C2 and C3, but we do not have a weight scale with us. So, we get two cantaloupes, C1 and C2, one in each hand and we try to feel which one is heavier. We do that with each pair of cantaloupes, (C1, C2), (C1, C3) and (C2, C3). We cannot compare all of them at once. Each pairwise comparison gives us an estimate of relative heaviness, but how do we decide which one is heaviest? If we decide that between C1 and C2, C2 is heaviest, then we can compare C2 and C3 and we are done. Suppose that C2 is the heaviest of the three cantaloupes, so we buy C2. However, our result did not give us an estimate of how much heavier C2 is than the other two cantaloupes. If the store were to give us the actual weights of the cantaloupes, w1, w2 and w3, we could estimate, when we compared C1 and C2 balancing them on our hands, which one is heavier with the ratio w1/w2 or w2/w1. It is easiest to estimate how much heavier the heavier one is, as a function of the lighter one, than vice versa. This is equivalent to what is known in psychometrics as fractionation and multiplication. If we arrange these comparisons in a matrix form, we have: 1 2 3 1 1 1 1 1 2 3 2 2 2 2 1 2 3 3 3 3 3 1 2 3 C C C w w w C w w w w w w C w w w w w w C w w w                   (A.1) Note that in Equation A.1 we took the ratio of the weights. The result is a number without units. It is an absolute number. On the other hand, had we taken the differences, e.g., w1 - w2, if the weight is given in pounds, the difference will be in pounds. Thus, taking the ratio to estimate the weight does not need a scale unit. All we need to do is estimate in absolute terms how much heavier one is than the other one. The next step is to obtain from the ratio comparisons i j w w       the relative weights of the objects. Relative weights would be 1 2 3 1 2 3 1 2 3 1 2 3 , , w w w w w w w w w w w w            . It turns out that if we multiply the first column by w1, the second by w2, and the third one by w3, and sum across the rows we get: IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 388 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 1 2 3 1 1 1 1 11 2 3 1 2 3 2 2 2 2 1 2 3 2 1 2 3 3 3 3 1 2 33 3 1 2 3 3 3 3 C C C w w w C ww w w w w w w w w C w w w w w w w w w w w w wC w w w w                                    . Thus, we recover the weights by dividing each value by the sum of all the values, and this would yield the relative weights of the objects: 1 2 3 1 2 3 1 2 3 1 2 3 , , w w w w w w w w w w w w            In real life, we may not know the weights, but we may be able to guess them by assigning a positive number. For example, we could have the following matrix: 1 2 3 1 2 3 1 1 / 1 1 / 1 / 1 C C C C a b C a c C b c          . (A.2) In matrix notation, entry, e.g., (1,2), represents the row number = 1, and the column number = 2. Note that the entries in the positions (1,1), (2,2) and (3,3) are now 1, the result of dividing a positive number by itself. The entries in the transposed positions, i.e., the transposed entry of (1,2) is the entry in the (2,1) position, are the reciprocal of the original entries, e.g., if entry (1,2) is a then the entry (2,1) is 1/a. Now the entries of the matrix of pairwise comparisons are educated guesses of the underlying ratios of the weights we seek. To estimate the relative weights, (Saaty 1980) proposed a first order approximation by first normalizing to unity each of the columns, and then averaging the resulting rows. For the matrix given in (A.2) we would have: IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 389 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 / (1 ) / ( 1 ) / ( 1) 1 / 1 (1 / ) / (1 ) 1 / ( 1 ) / ( 1) 1 / 1 / 1 (1 / ) / (1 ) (1 / ) / ( 1 ) 1 / ( 1) {[1 / (1 )] [ / ( 1 )] [ / ( 1)]} / 3 {[(1 / ) / (1 ) [ a b c a b c a b c a b c a b a b a a b b c a c a a c b c b c b c a b c a a b b c a                                              1 1 1 1 1 / ( 1 )] [ / ( 1)]} / 3 {[(1 / ) / (1 )] [(1 / ) / ( 1 )] [1 / ( 1)]} / 3 c a b c a c b c b c a b c                      . The mathematical model that provides the solution to our estimation problem is known as a principal eigenvalue problem. We refer to the reader to (Saaty 1977) for details of this model. The importance of this model lies with the fact that now we can estimate relative measures for intangible attributes. (Saaty 1977) used the absolute scale given in Table 1 to estimate the pairwise comparisons. Remember that the scale in Table 1 is an estimate. If actual measurement were available, we could use those to compute the relative weights. Table 1 Fundamental scale Intensity of Importance Definition Explanation 1 Equal Importance Two activities contribute equally to the objective 3 Moderate importance Experience and judgment slightly favor one activity over another 5 Strong importance Experience and judgment strongly favor one activity over another 7 Very strong or demonstrated importance An activity is favored very strongly over another; its dominance demonstrated in practice 9 Extreme importance The evidence favoring one activity over another is of the highest possible order of affirmation 2, 4, 6, 8 Reciprocals of above Intermediate values between the two adjacent judgments If activity i has one of the above nonzero numbers assigned to it when compared with activity j, then j has the reciprocal value when compared with i When compromise is needed Rationals Ratios arising from the scale If consistency were to be forced by obtaining n numerical values to span the matrix IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 390 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 The first experiment performed to try to validate perception with the fundamental scale of Table 1 was the optics experiment (Saaty 1977). Four objects were placed at the following distances measured in yards from a light source: 9, 15, 21, 28. In normalized form these distances are 0.123, 0.205, 0.288, 0.384. Next, two independent sets of judges were asked to estimate pairwise comparisons of the brightness of the objects, labeled in increasing order according to their nearness to the source where the judges were located. The result was two pairwise comparison matrices: 1 2 3 4 1 2 3 4 1 1 2 2 3 3 4 4 1st Trial 2nd Trial 1 5 6 7 1 4 6 7 1 / 5 1 4 6 1 / 4 1 3 4 1 / 6 1 / 4 1 4 1 / 4 1 / 3 1 2 1 / 7 1 / 6 1 / 4 1 1 / 7 1 / 4 1 / 2 1 C C C C C C C C C C C C C C C C                         The relative brightness from the trials was: Relative brightness Relative brightness (1st trial) (2nd trial) 0.61 0.62 0.24 0.22 0.10 0.10 0.05 0.06 There is a law in optics known as the inverse square law that states that the brightness of an object located at a distance from a source of light is inversely related to the square of the distance of the object to the source of light. Table 2 gives the inverse square law of the four objects considered. Table 2 Inverse square law of optics Note that after applying the inverse square law of optics to the distances, the relative values (6 th column of Table 2) are very close to the estimates of relative brightness obtained in the two trials. There are many experiments like this that support the idea that Normalized Distance 1/Distance2 Distance2 1st Trial 2nd Trial 9 0.01234568 0.607 0.61 0.62 15 0.00444444 0.218 0.24 0.22 21 0.00226757 0.112 0.10 0.10 28 0.00127551 0.063 0.05 0.06 IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 391 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 judgments could be used to estimate in relative terms the importance of intangibles in decision making. In measurement theory, when a set of objects, or alternatives in general, are compared, they must always be compared with respect to one criterion and only one criterion at a time. No comparison can take place without a criterion in mind. When multiple criteria are involved, we must compare the alternatives with respect to each of the criteria. What makes relative measurement so interesting is that we can now combine the relative scales because they are all measured in the same units. Since the criteria may not be equally important one could think about using a weighted average of the different relative scales. There are different opinions as to how to combine the different scales obtained from each criterion, but if one is careful when defining the criteria so that they do not overlap in meaning, the weighted average is usually a good estimate. This is known as hierarchical synthesis because instead of criteria and alternatives, one could think of criteria, sub- criteria, sub-criteria of sub-criteria and so on, all the way down the hierarchy to the alternatives that usually occupy the bottom level of the hierarchy. The top level of the hierarchy is the goal. A logical extension of the Analytic Hierarchy Process is the Analytic Network Process (Saaty 1996). Instead of considering hierarchies as in Figure A.1, we consider a network of relations between the criteria, the sub-criteria, the alternatives, and so on as in Figure A.2. An important characteristic of networks is that they allow for feedback between clusters. Figure A.1. A Hierarchy Figure A.2. A network For example, when comparing a diagnostic procedure for a disease, alternative procedures need to be prioritized with respect to, for example, accuracy, simplicity, logistics, invasiveness and so on. But, to select a procedure we need to assign priorities to the criteria. However, each procedure could perform better under different criteria. There may be statistics that tell us, for a given procedure, under which criterion it performs better. This would be equivalent to comparing the criteria or attributes of the procedures Goal Criteria Sub-criteria Alternatives Criteria Sub-criteria Alternatives IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 392 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 under each alternative. This is a feedback loop from the cluster of alternatives to the cluster of criteria. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 393 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 APPENDIX B: DEFINITIONS Cluster – a grouping of nodes that share a similar class within the AHP / ANP model. Collectors – this category of gun owner tends to possess them for the potential appreciation in value. They may display their guns and could have many in their possession. Enthusiasts – these are generally people who feel an affinity with guns. Gun shop owners - Dealers Historical reenactment – this category may have weapons for recreating battles such as Gettysburg, may participate in demonstrations such as Veteran’s Day parades, or take part in filming. Hunters – there are a variety of types of hunters. For instance, a bird hunter might prefer a shotgun, whereas a deer hunter might prefer cartridge. There are some hunters that prefer black-powder, whereas some others may prefer high-power. Some hunters hunt for recreation, whereas others hunt to supplement their food. We do not separate the various types of hunters, but recognize there is a variety. Law enforcement – these individuals will often be issued a service weapon, but may also have personal weapons that they may decide to carry while working and may also carry while off-duty. Node – an individual unit or member of a cluster that shares some characteristic of the other members within the cluster of the AHP / ANP model. Paramilitary – these individuals may possess weapons for the purpose of serving in a militaristic type of organization which is not government backed or supported. Private citizens – homeowners, personal protection, automobile. Private security guards – these individuals are typically contracted out through a firm to cover banks, buildings, and other locations. They may be required to own their own gun though their employer may provide one. Retired and active duty military – military members may have basic weapons training but may also have advanced weapons training. These individuals may have a variety of types of weapons. Shooting – paper fixed targets, skeet, and pop-up. Survivalists – these individuals may purchase weapons with the idea of needing them should social structures and services fall into disarray. IJAHP News and Events: Guiora, Minutolo, Vargas/Report on an Analytic Network Process (ANP) model to estimate the benefits, opportunities, costs and risks (BOCR) that gun policies and violence prevention interventions have on legal users of firearms International Journal of the Analytic Hierarchy Process 394 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.909 APPENDIX C: ACRONYMS AHP – Analytic Hierarchy Process ANP – Analytic Network Process