IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 206 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 SHOULD THE UK HAVE BREXITED THE EUROPEAN UNION? Thomas L. Saaty Distinguished University Professor University of Pittsburgh Pittsburgh, Pennsylvania, USA E-mail: saaty@katz.pitt.edu Lirong Wei University of Science and Technology Beijing, China E-mail: weileerong@foxmail.com ABSTRACT This paper is an analysis of Brexit, and asked the question, “Should the UK have Brexited the European Union?” We use the Analytic Hierarchy Process (AHP) to model the decision based on Benefit-Opportunities-Costs and Risks (BOCR). The AHP structure considers various factors that may be taken into consideration from the perspective of the UK (Saaty, 1980). Questionnaires were used to obtain pairwise comparison judgments from experts and used to derive priorities for the factors and final decision to Brexit. The BOCR model results are combined in two ways. Both results show that the UK should remain a member of the EU. The referendum used showed the opposite result. The approach followed here can be used to educate people when voting on similar decisions. Keywords: Brexit; AHP; decision-making, Benefits, Opportunities, Cost, Risks, decision analysis, European Union, Eurozone 1. Introduction We believe that short of some kind of disaster and annihilation, the human race and its cultures are gradually drawing together from the agrarian age to villages, towns, cities, megacities and nations. This is despite much conflict and strife and great wars that have killed tens of millions of people. The European Union is a great and inspired step towards economic unity and in particular financial, social, and political unity. The world owes much to the English people for this increasing unity not only for the world wide language that draws humanity to communicate together, but also in regards to law and geographic dominance ranging from the United States, mailto:saaty@katz.pitt.edu mailto:weileerong@foxmail.com IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 207 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 Canada, Australia, New Zealand, and of course the United Kingdom itself to a unified India, despite the break up into Pakistan and Bangladesh. Is it beneficial to the UK and to the world at large in the long run that the UK has broken off from the European Union in its Brexit with dissent coming from Londoners, the Scottish and the Northern Irish people (Irwin, 2015; Moller & Oliver, 2014)? That is the question we wish to comprehensively and logically address in this paper. Of course, we need to consider the UK’s economic and political advantages and influence today in the hope that it will be a good decision for the future (Dagnis Jensen & Snaith, 2016). On June 23, 2016, the eligible voters in the UK voted on the EU referendum, "Should the United Kingdom remain a member of the European Union or leave the European Union?" The result of the vote was that the UK should leave the European Union; the breakdown of the votes by region is shown in Table 1 and Table 2. Table 1 Vote results of Brexit (23 June 2016) Results Votes % Leave 17,410,742 51.89% Remain 16,141,241 48.11% Valid votes 33,551,983 99.92% Invalid or blank votes 25,359 0.08% Total votes 33,577,342 100.00% Registered voters/turnout 46,501,241 72.21% *Source: Wikipedia of “United Kingdom European Union membership referendum, 2016” IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 208 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 Table 2 Results by voting areas in the United Kingdom Region Turnout Remain votes Leave votes Remain % Leave % England (with Gibraltar) 73.0% 13,266,996 15,188,406 46.62% 53.38% East Midlands 74.2% 1,033,036 1,475,479 41.18% 58.82% East of England 75.7% 1,448,616 1,880,367 43.52% 56.48% London 69.7% 2,263,519 1,513,232 59.93% 40.07% North East England 69.3% 562,595 778,103 41.96% 58.04% North West England 70% 1,699,020 1,966,925 46.35% 53.65% South East England 76.8% 2,391,718 2,567,965 48.22% 51.78% South West England & Gibraltar 76.7% 1,503,019 1,669,711 47.37% 52.63% West Midlands 72% 1,207,175 1,755,687 40.74% 59.26% Yorkshire and the Humber 70.7% 1,158,298 1,580,937 42.29% 57.71% Northern Ireland 62.7% 440,707 349,442 55.78% 44.22% Scotland 67.2% 1,661,191 1,018,322 62.00% 38.00% Wales 71.7% 772,347 854,572 47.47% 52.53% *Source: Wikipedia of “United Kingdom European Union membership referendum, 2016” https://en.wikipedia.org/wiki/Gibraltar https://en.wikipedia.org/wiki/East_Midlands https://en.wikipedia.org/wiki/East_of_England https://en.wikipedia.org/wiki/Greater_London https://en.wikipedia.org/wiki/North_East_England https://en.wikipedia.org/wiki/North_West_England https://en.wikipedia.org/wiki/South_East_England https://en.wikipedia.org/wiki/South_West_England https://en.wikipedia.org/wiki/West_Midlands_(region) https://en.wikipedia.org/wiki/Yorkshire_and_the_Humber https://en.wikipedia.org/wiki/Northern_Ireland https://en.wikipedia.org/wiki/Scotland https://en.wikipedia.org/wiki/Wales IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 209 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 The overall result of the June 2016 vote was a narrow majority of 51.89% to 48.11% in favor of leaving the EU. We note that only London, Northern Ireland and Scotland are below the majority of 50%. 2. BOCR model In a complete analysis of a decision problem we usually consider the benefits (B), opportunities (O), costs (C) and risks (R) involved. For each control criterion of these B, O, C, and R, one derives priorities for the alternatives of a decision with respect to all the significant influences that cause some alternatives to have higher priority than others. One then combines the weights of the alternatives according to the weights of the control criteria of each of the B, O, C and R assessed in terms of strategic criteria (Wind & Saaty, 1980). Strategic criteria are very basic criteria used by individuals and groups to assess whether they should make any of the many decisions they face in their daily operations. Strategic criteria do not depend on any particular decision for their priorities but are assessed in terms of the goals and values of the individual or organization. Finally, one rates (not compares) the top ranked alternative for each B, O, C and R and uses the resulting weights to combine the values of each alternatives for the four merits and obtain the final answer in the form of priorities whose relative values are important for choosing the best alternative. The synthesized results of the alternatives for each of the four control B, O, C and R merits are combined, along traditional benefit to cost ratio analysis used in economics, to obtain a ratio outcome by taking the quotient of the benefits times the opportunities to the costs times the risks for each alternative (BO/CR), then normalizing the results over all the alternatives to determine the best outcome. This formula is only useful when one is certain that the relative measurements are commensurate, that is of the same order of magnitude. In other words it is meaningless to divide thousands of dollars for benefits, by pennies for costs; this is tantamount to dividing by numbers close to zero. There is another more reliable way to combine the B, O, C, and R that gives the total outcome. The top ranked alternative is rated (not compared) for each of the B, O, C and R with respect to strategic criteria that are needed to determine the merits of any decision. From this rating one then obtains normalized respective weights, b, o, c and r and computes the total outcome bB + oB − cC − rR for each alternative. In evaluating the benefits (opportunities), one responds to the question of dominance: which alternative contributes the most benefits (opportunities), whereas for costs (risks) one responds to the question which alternative costs (is subject to greater risks) more, which is opposite in sense of the benefits and opportunities and must be subtracted from them. It is known that the ranks obtained from ratio and total syntheses need not coincide. IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 210 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 3. Benefits, opportunities, costs and risks of Brexit– the Analytic Hierarchy Process (AHP) Four hierarchies (Figures 1-4) were developed: one for Benefits, Opportunities, Costs, and Risks (BOCR) to the UK of exiting from the European Union (EU). Each hierarchy results in priorities that sum to 1.000 for Leave or Not Leave. The priorities are derived from a group decision process. We administered an online survey to collect responses. The AHP questionnaire we used is shown in the Appendix. For each judgment in the questionnaire the respondent selected the dominant factor first, then decided how strongly more dominant the factor was using the 1-9 fundamental scale (Saaty, 1977, 1986). The questionnaire was sent to 90 experts who attended the ISAHP2016 in London and came from the UK. They are all AHP decision making experts; however, not all of them are familiar with the Brexit. Therefore, in our study we used the judgments of four knowledgeable experts who completed the questionnaire. The consistency of judgments was examined for each expert and found to be adequate. Next, we calculated the geometric mean of each judgment from these experts and entered the combined judgment into the Super Decisions model. The alternatives of the decision are as follows: leave the EU or remain a member of the EU. We constructed the model using the Super Decisions software and inputting the judgments of diverse experts to compute the priorities. Figure 1. Benefits hierarchy IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 211 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 Figure 2. Opportunities hierarchy ECONOMIC 1) Result in trade barriers between UK and EU 2) Loss of British stocks 3) Loss of investments 4) Recession in economy 5) Sterling fall 6) Loss of the biggest trading partner POLITICAL 1) Reduce UK influence on EU 2) Harder to keep close foreign-policy links with EU 3) Loss of tax revenue from leaving SECURITY 1) Loss of access to EU assets database and surveillance records 2) Increase the difficulty of tracing the international criminal SOCIAL 1) Can no longer travel freely 2) Loss of technological collaboration with EU Figure 3. Costs hierarchy Opportunities to UK Allow the UK to make its own trade deals Allow the UK to design its own regulations Leave the EU Remain a member of the EU IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 212 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 ECONOMIC 1) Decline of financial services industry 2) Decline of law firms industry 3) London may no longer be finance center of Europe 4) Risks of diminishing investment from EU 5) US and UK ties may weaken POLITICAL 1) Diminish UK influence in world affairs 2) Harder to keep close foreign-policy links with EU 3) Risk of losing the UK's prosperity 4) Risk of Scotland leaving the UK SECURITY 1) Cause much possible collateral damage to UK’s security 2) Potential risk for conflict with EU 3) Weaken border control through EU police cooperation SOCIAL 1) Negative for health service 2) Loss of EU food protection 3) Unemployment rate may rise Figure 4. Risks hierarchy The results for the four hierarchies are summarized in Table 3. The idealized results in the final column to the right are obtained from each relative priority by dividing each by the largest value. For the Benefits we have relative values that sum to 1 of Leave (0.82) and Remain (0.18). Dividing each by 0.82 we obtain the ideal values of Leave (1.00) and Remain (0.22). IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 213 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 Table 3 Priorities derived from the four hierarchies Factors Priorities Relative (Ideal) B e n e fi ts Economic 0.250 Benefit the fishing industry (able to land more fish) 0.119 Leave the EU 0.82 (1) Remain a member of the EU 0.18 (0.22) Free the UK from EU regulations and bureaucracy 0.555 No longer pay more into EU than receive 0.064 Save billions of pounds in EU membership fees 0.262 Political 0.655 Allow the UK to better control immigration 0.833 Relive conflict among British Conservatives 0.167 Social 0.095 Reduce pressure on public services, housing and jobs 0.200 Improve self-confidence of the British 0.800 O p p o rt u n it ie s Allow the UK to design its own regulations 0.800 Leave the EU 0.83 (1) Remain a member of the EU 0.17 (0.20) Allow the UK to make its own trade deals 0.200 C o st s Economic 0.103 Result in trade barriers between UK and EU 0.184 Leave the EU 0.86 (1) Remain a member of the EU 0.14 (0.16) Loss of British stocks 0.190 Loss of investments 0.154 Recession in economy 0.150 Sterling falls 0.083 Loss of the biggest trading partner 0.239 Political 0.231 Reduce UK influence on EU 0.117 Harder to keep close foreign-policy links with EU 0.614 Loss of tax revenue from leaving EU enterprises 0.268 Security 0.624 Loss of access to EU assets database and surveillance records 0.833 Increase the difficulty of tracing the international criminal 0.167 Social 0.042 Can no longer travel freely 0.250 Loss of technological collaboration with EU 0.750 R is k s Economic 0.153 Decline of financial services industry 0.207 Leave the EU 0.87 (1) Remain a member of the EU 0.13 (0.15) Decline of law firms industry 0.208 London may no longer be finance center of Europe 0.288 Risks of diminishing investment from EU 0.179 US and UK ties may weaken 0.119 Political 0.307 Diminish UK influence in world affairs 0.737 Risk of losing the UK's prosperity 0.085 IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 214 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 Risk of Scotland leaving the UK 0.177 Social 0.219 Negative for health service 0.752 Loss of EU food protection 0.197 Unemployment rate may rise 0.051 Security 0.322 Cause much possible collateral damage to UK’s security 0.189 Potential risk for conflict with EU 0.054 Weaken border control through EU police cooperation 0.757 A summary of the idealized priorities shown in Table 3 are given in Table 4. Table 4 Idealized priority vectors for Leave the EU or Remain in the EU Benefits (B) Opportunities (O) Costs (C) Risks (R) Leave the EU 1.00 1.00 1.00 1.00 Remain in the EU 0.23 0.20 0.16 0.15 We structured the hierarchy of strategic criteria shown in Figure 5 from the media coverage of voter concerns and prioritized the factors through the usual pairwise comparison process. The priorities of the strategic criteria thus derived are shown in Table 5. Figure 5. The strategic criteria IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 215 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 Table 5 Overall priorities of strategic criteria Economic 0.098 Trade/Business 0.089 Financial Market 0.012 Political 0.244 Immigration 0.225 Regulations 0.028 Social 0.036 Education 0.148 Health 0.019 Job 0.423 Travel 0.054 Security 0.622 We then created Table 6 for rating the benefits, opportunities, costs and risks of this decision. It has one column for every lowest level of strategic criteria. We defined intensities for the scale of very high (0.42), high (0.26), medium (0.16), low (0.1), and very low (0.06). Their priorities were derived by making judgments on pairs of intensities in the usual pairwise comparison matrix, asking how much one intensity was preferred to the other. We evaluated the impact of the highest valued alternative in each of the four hierarchies on the strategic criteria in the ratings table shown in Table 6. In every one of the four hierarchies the highest priority alternative was to Remain in the EU. We selected the appropriate impact for that alternative each cell in Table 5. As an example, for the top leftmost cell (Benefits, Education), we asked what intensity the beneficial impact of leaving would have on Education and concluded it would have a Medium impact, so Medium was entered in the cell. Because it was the highest value alternative in every hierarchy we rated Remain in the EU across every row. The overall priorities for benefits (b = 0.291), opportunities (o = 0.224), costs (c = 0.243) and risks (r = 0.242), are shown outlined in red in Table 6. Table 6. Priorities for b, o, c, r, from the ratings table 4. Results We obtained the overall priorities shown in Table 7 in two ways using the multiplicative formula BO/CR and the additive-negative formula bB+oO-cC-rR. The vectors B, O, C, and R are from Table 4 and the b, o, c, r priorities are from Table 6. We see that “Remain in the EU” is dominant (in bold type) using either formula and is the best alternative. IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 216 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 Table 7 Overall final results Results Alternatives B b=(0.291) O o=(0.224) C c=(0.243) R r=(0.242) BO/CR bB+oO- cC-rR Leave the EU 1 1 1 1 1 0.029 Remain in the EU 0.218 0.2 0.158 0.147 1.892 0.034 *B, O, C and R (the respective columns above)are the priority vectors for the two alternatives; b, o, c and r are the priorities derived by rating against the strategic criteria . 5. Conclusion The conclusion of this study is that Remain in the EU would have been the best outcome, though it flies in the face of the actual vote which was to Leave the EU. In this study we aimed to predict the best outcome. Whether it really was the best outcome will need to be determined a few years hence as the dust settles. Any decision can be viewed in two ways: what is most likely to occur and what is the best outcome. Frequently they are not the same. Although this study cannot be considered definitive, the outcome of this exercise leaves one to seriously wonder about citizens voting Yes or No. This is a habit that we practice inherited from the past with no way to measure the intangibles involved or determine their importance. There is a talk today about France and Austria also thinking of leaving the EU, and among others, the Japanese have complained about the large investment they have made in the UK as part of the EU. They say this Brexit decision amounts to significant losses to them now in a message issued on the eve of the G20 summit in China in September 2016. The document entitled “Japan’s Message to the UK and EU” warns of dire consequences for “the interests of the world” if an open Europe cannot be maintained. There has not been very strong advocacy for our approach about how to examine the subject carefully before resorting to a Yes-No kind of vote on the outcome as was done in the United Kingdom (Dhingra et al., 2016). Expert opinion and the strength of the judgments should play an important role in making such decisions that have global consequences and involve multi-criteria kind of thinking. Feelings and intuition may not be adequate to obtain the right result. IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 217 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 REFERENCES Dagnis Jensen, M., & Snaith, H. (2016). When politics prevails: the political economy of a Brexit. Journal of European Public Policy, 1-9. doi: http://dx.doi.org/10.1080/13501763.2016.1174531 Dhingra, S., Ottaviano, G. I., Sampson, T., & Reenen, J. V. (2016). The consequences of Brexit for UK trade and living standards. The Centre for Economic Performance, The London School of Economics and Political Science. Irwin, G. (2015). BREXIT: the impact on the UK and the EU. Global Council: London. Available online at: http://www. globalcounsel. co. uk/system/files/publications/Global_Counsel_Impact_of_Brexit_June_2015. pdf. Möller, A., & Oliver, T. (2014). The United Kingdom and the European Union: what would a “Brexit” mean for the EU and other States around the World? European and global perspectives. DGAPanalyse. Saaty, T. L., & Vargas, L. G. (2012). The possibility of group choice: pairwise comparisons and merging functions. Social Choice and Welfare, 38(3), 481-496. doi: 10.1007/s00355-011-0541-6 Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234-281. doi: http://dx.doi.org/10.1016/0022- 2496(77)90033-5 Saaty, T.L. (1980). The Analytic Hierarchy Process. New York: McGraw-Hill. Doi: http://dx.doi.org/10.1080/00137918308956077 Saaty, T. L. (1986). Axiomatic foundation of the analytic hierarchy process. Management Science, 32(7), 841-855. doi: http://dx.doi.org/10.1287/mnsc.32.7.841 Saaty, T. L. (1996). The Analytic Network Process. Pittsburgh: RWS Publications. Wind, Y., & Saaty, T. L. (1980). Marketing applications of the Analytic Hierarchy Process. Management Science, 26(7), 641-658. doi: http://dx.doi.org/10.1287/mnsc.26.7.641 http://dx.doi.org/10.1080/13501763.2016.1174531 http://dx.doi.org/10.1016/0022-2496(77)90033-5 http://dx.doi.org/10.1016/0022-2496(77)90033-5 http://dx.doi.org/10.1080/00137918308956077 http://dx.doi.org/10.1287/mnsc.32.7.841 http://dx.doi.org/10.1287/mnsc.26.7.641 IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 218 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 APPENDIX I Should the UK have Brexited the European Union? This is a questionnaire of the AHP Benefits-Opportunities-Costs-Risks model to evaluate "Should the UK have Brexited the EU?" There are five parts to the questions as can be seen below. Please do the pairwise comparison of all the criteria using the 1-9 dominance scale of absolute numbers: 9 - Extremely 8 Very strongly to extremely 7 - Very strongly 6 - Strongly to very strongly 5 - Strongly 4 - Moderately to strongly 3 - Moderately 2 - Equally to moderately 1- Equally Click ""NEXT" at bottom of the page to begin. *Required IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 219 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 220 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 221 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 222 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 IJAHP: Article: Saaty, Wei/ Should the UK have Brexited the European Union? International Journal of the Analytic Hierarchy Process 223 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.415 (You can get the complete questionnaire at https://goo.gl/forms/DGdba9TpRkQ757rK2)