RATIO MATHEMATICA 28 (2015) 31-43 ISSN:1592-7415

Influence of information on behavioral
effects in decision processes

Angelarosa Longo, Viviana Ventre
Dipartimento di Diritto, Economia, Management e Metodi Quantitativi

Università degli Studi del Sannio, Benevento, Italy

e-mail address ventre@unisannio.it

Abstract
Rational models in decision processes are marked out by many anoma-

lies, caused by behavioral issues. We point out the importance of infor-
mation in causing inconsistent preferences in a decision process. In a sin-
gle or multi agent decision process each mental model is influenced by the
presence, the absence or false information about the problem or about other
members of the decision making group. The difficulty in modeling these ef-
fects increases because behavioral biases influence also the modeler. Behav-
ioral Operational Research (BOR) studies these influences to create efficient
models to define choices in similar decision processes.

Keywords: Behavioral Operational Research, Intertemporal Choice, In-
formation in Decision Processes.

2000 AMS subject classifications: 91B16, 91B08, 91E10.

doi: 10.23755/rm.v28i1.26

1 Introduction
Some failures occur when dealing with traditional Discounted Utility (DU)

model from both normative and descriptive setting. Indeed, some studies, espe-
cially in psychology and neuroeconomics (a more specialized field of decision
neuroscience), point out anomalies that violate some axioms in the traditional
model (Sec. 2).

Bechara et al. [1] show positive effects of anomalies in intertemporal choices
and the use of hyperbolic delay discounting (declining as the length of the delay

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A. Longo and V. Ventre

increases) to represent inconsistent preferences. On the other hand, the negative
effects of emotions mainly stem from impulsivity. To properly describe individual
differences in intertemporal choices, derived from impulsivity and inconsistency,
behavioral economists have proposed the Q-exponential Delay Discount Function
and a Multiple Selves Model (quasi-hyperbolic discount model) (Sec. 3).

Mental models of each person, based on different assumptions and prefer-
ences, influence the effects of emotions (positives and negatives) and impulsivity.
To control impulsivity Strotz [11] proposed two strategies that might be employed
by a person who foresees how his preferences will change over time, and Thaler
and Shefrin [12] proposed a model in which the individual is treated as if he con-
tained two distinct psyches denoted as planner and doer (Sec. 4).

The information held by the agent plays an important role on the delineation
of his mental model. In a multi agent decision context all people involved have
their mental model and influence other mental models. Hence, in these strategic
decisions information about others and about the problem definitely influence the
final choice (Sec. 5). If there is no information about other players, as shown in an
experiment of Engelmann and Strobel [4], people weight their own decisions more
heavily than that of a randomly selected person from the same population (false
consensus effect). This happens in non-cooperative decision problems, not prop-
erly modeled in OR. Indeed, because false consensus effect and impulsivity not
always lead each agent towards the best strategy according to the theory of games,
so obtaining a common decision is only a chance (Sec. 6). On the contrary, when
all information is explicit people can consider the choices of others as more infor-
mative then their own (excess of consensus or overconfidence). An example is a
cooperative decision problem, modeled by OR with cooperative games, in which
final decision is based on mental models of the participants and their tendency to
overconfidence (Sec. 7).

However, the final decision is influenced not only by intrinsic characteristics of
every one, but also by the way in which information is passed: misunderstandings
and manipulations (above all for self-interest) change people’s reactions (Sec. 8).

At last, also the modeler is influenced by his mental models: creating a model
to predict a decision making process is itself a decision making process. A new
branch of research (BOR, Behavioral Operational Research) studies human im-
pacts of using OR models in decisional processes (Sec. 9).

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Influence of information on behavioral effects in decision processes

2 Effects of behavioral aspects: violations of tradi-
tional Discount Utility Model

Operational Research (OR) has modeled human behavior in intertemporal
choice in terms of DU model, which assumes an exponential temporal discount-
ing function and a constant discount rate: this represents the individual’s pure rate
of time preference. An important implication of constant discount rate and ex-
ponential discounting function is that a person’s intertemporal preference is time-
consistent.

However, decision neuroscience, whose goal is to integrate research in neu-
roscience and behavioral decision-making, highlights that there are a number of
behavior patterns that violate rational choice theory. Several empirical studies
on individual behavior, when discounting real or hypothetical rewards, stress the
existence of violations of the traditional discounting model [2].

Theory and algorithms of OR models are free of behavioral effects but as soon
as we use them in real life problem solving behavioral effects will be present.
Hence behavioral perspective is essential in decision analysis [6]. Research in
psychology has reported many types of cognitive and motivational biases as well
as heuristics which relate to human behavior and may significantly distort the de-
cision analysis generating inconsistent preferences in intertemporal choices. De-
lay effect, magnitude effect and sign effect are among the relevant anomalies in
intertemporal choice, we will deal with (see also [13]).

The delay effect. As waiting time increases, the discount rates tend to be higher
in short intervals than in longer ones. We can set out this effect as follows:

(x,s) ∼ (y,s) but (x,s + h) < (y,t + h), for y > x,s < t and h > 0

The magnitude effect. Larger outcomes are discounted at a lower rate than
smaller outcomes. This effect can be formulated as follows:

(x,s) ∼ (y,s) implies (ax,s) < (ay,t), for y > x > 0,s < t

and
(−x,s) ∼ (−y,s) implies (−ax,s) > (−ay,t)

The sign effect. Gains are discounted at a higher rate than losses of the same
magnitude. This anomaly implying that, changing the sign of an amount from
gains to losses, the weight of this amount increases:

(x,s) ∼ (y,s) implies (−x,s) > (−y,t) for y > x > 0 and s < t

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3 Effects of emotions: violations of traditional Dis-
count Utility model

In a series of studies (see, e. g., ([1], [3], [8])) using a gambling task, it
emerges that individuals with emotional dysfunction tend to perform poorly com-
pared with those who are endowed with intact emotional processes. Bechara et
al. [1] demonstrated that normal people possess anticipatory SCRs (Skin Conduc-
tance Response) – indices of somatic states – which represent unconscious biases
that are linked to prior experiences with reward or punishment and produce in-
consistent preferences. These biases alarm the normal subject about selecting a
disadvantageous course of action, even before the subject becomes aware of the
goodness or badness of the choice he is about to make. As a consequence there
is considerable agreement among psychologists and economists that the notion of
exponential discounting should be replaced by some form of hyperbolic discount-
ing, which can point out the delay effect (or present bias), that is the tendency of
the individuals to increasingly choose a smaller-sooner reward over a larger-later
reward as the delay occurs sooner in time.

Many authors proposed different hyperbolic discount functions, in which tem-
poral discount function increases with the delay to an outcome. One of these
proposed functions has the following form:

d(t) =

(
1

1 + αt

)β/α
where β > 0 is the degree of discounting and α > 0 is the departure from expo-
nential discounting. Hyperbolic discounting has been applied to a wide range of
phenomena, including consumption-saving behavior. Consistent with hyperbolic
discounting, people’s investment behavior exhibits patience in the long run and
impatience in the short run [13].

A second type of empirical support for hyperbolic discounting comes from
experiments on dynamic inconsistency. Studies and empirical evidences show that
delay effect can derive in preference reversal between two rewards as the time-
distance to these rewards diminishes. A hyperbolic discount model can clarify
this; in fact, hyperbolic time-preference curves can cross [11] and consequently
the preference for one future reward over another may change with time [13].

However, in some contexts individuals deprived of normal emotional reac-
tions might actually make better decisions than normal individuals, because of
the loss of self-control, as Damasio found when studying behavior of people with
ventromedial prefrontal damage [3]. Temptations are manifestations of loss of
self-control and in many cases induce disadvantageous behavior. Indeed, as far
as temptation increases the best long run interest of the problem solver conflicts

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Influence of information on behavioral effects in decision processes

with his short run desires, moreover impulsive behavior may fail to evaluate the
consequences of his behavior appropriately [13].

Other evidences suggest that even relatively mild negative emotions that do
not result in a loss of self-control can play a counterproductive role among normal
individuals in some situations. When gambles that involve some possible loss are
presented one at a time, most people display extreme levels of risk aversion toward
the gambles, a condition known as myopic loss aversion. Shiv et al. [9] show that
individuals deprived of normal emotional reactions might, in certain situations,
make more advantageous decisions than those not deprived of such reactions; so
the lack of emotional reactions may lead to more advantageous decisions.

Inconsistent preference is the greatest contradiction of rational theory in in-
tertemporal choice. This behavior can be typically seen in psychiatric disorders
(alcoholism, drug abuse), but also in more ordinary phenomena (overeating, credit
card debt) [13]. Neuroeconomics has found that addicts are more myopic (have
large time-discount rates) in comparison with non-addicted population.

However, the preference for more immediate rewards per se is not always
irrational or inconsistent; addicts’ behavior is clinically problematic, but econom-
ically rational when their choices are time-consistent (if they have large discount
rates with an exponential discount function). But addicts also discount delayed
outcomes hyperbolically, suggesting the intertemporal choices of addicts are time-
inconsistent, resulting in a loss of self-control: they act more impulsively at the
moment of the choice, against their own previously intended plan. Moreover if
large discount rates are due to habitual drug intake, it is expected that discount
rates decreased after long-term abstinence.

Behavioral neuroeconomics and econophysical studies have proposed two dis-
count models, in order to better describe the neural and behavioral correlates of
impulsivity and inconsistency in intertemporal choice.

Q-exponential discount model. This function has been proposed and examined
for subjective value V (D) of delayed reward:

V (D) =
A

expq(kqD)
= A/[1 + (1 − q)kq]D

1
1−q

where D denotes a delay until receipt of a reward, A the value of a reward at
D = 0, and kq a parameter of impulsivity at delay D = 0 (q-exponential discount
rate) and the q-exponential function is defined as:

expq(x) = (1 + (1 − q))
1

1−q

The function can distinctly parametrize impulsivity and inconsistency [13].

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A. Longo and V. Ventre

Quasi-hyperbolic discount model. Behavioral economists have proposed that
the inconsistency in intertemporal choice is attributable to an internal conflict be-
tween “multiple selves” within a decision maker. As a consequence, there are (at
least) two exponential discounting selves (with two exponential discount rates) in
a single human individual; and when delayed rewards are at the distant future (> 1
year), the self with a smaller discount rate wins, while delayed rewards approach
to the near future (within a year), the self with a larger discount rate wins, result-
ing in preference reversal over time. This intertemporal choice behavior can be
parametrized in a quasi-hyperbolic discount model (also as a β − δ model). For
discrete time τ (the unit assumed is one year) it is defined as:

F(τ) = βδt (for τ = 1,2,3, . . .) and F(0) = 1 (0 < β < δ < 1)

A discount factor between the present and one-time period later (β) is smaller
than that between two future time-periods (δ). In the continuous time, the pro-
posed model is equivalent to the linearly-weighted two-exponential functions (gen-
eralized quasi-hyperbolic discounting):

V (D) = A[w exp(−k1D) + (1 − w) exp(−k2D)]

where w, 0 < w < 1, is a weighting parameter and k1 and k2 are two exponen-
tial discount rates (k1 < k2). Note that the larger exponential discount rate of
the two k2, corresponds to an impulsive self, while the smaller discount rate k1
corresponds to a patient self [13].

4 Mental models: self-control against impulsivity

Behavioral issues fit in each phase of the problem solving process, both if it
is a single agent decision process or a multi agent one. Every individual choice is
influenced by impulsivity and by all positive and negative biases derived from it.
The impulsive choices derived from mental models, which are informal models,
quickly constructed by problem solvers, which go on constantly during problem
solving.

Mental models help us to relate cause and effect, but often in a highly sim-
plified and incomplete way. They are always influenced by our preferences and
our personal experiences. So they can be extremely limiting. This explains why
emotions do not have always positive or negative effects on decision process and
why impulsivity generates sometimes positive and sometimes negative effects.

Strotz proposed two strategies that might be employed by a person who fore-
sees how his preferences will change over time [11]:

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Influence of information on behavioral effects in decision processes

1) The “strategy of precommitment”: a person can commits to some plan of
action;

2) The “strategy of consistent planning”: an individual take into account future
changes in the utility function and reject any plan that he will not follow
through. His problem is then to find the best plan among those she will
actually follow.

Hyperbolic discounting predicted a number of mechanisms of self-control.
However, the hyperbolic model, as well as the exponential one, is only a special
case of interpreting reality. Common sense highlights how people, when are in
front of identical short term opportunities, perform only sometimes self-control,
independently of the use of one’s Strotz strategy. In the setting of Multiple Selves
Models, to control impulsivity, Thaler and Shefrin proposed a “planner-doer”
model which draws upon principal agent theory [12]. They deal with an individ-
ual as if he contained two distinct psyches: one planner, which pursue longer-run
results; and multiple doers, that are concerned only with short-term satisfactions,
so they care only about their own immediate gratification (and have no affinity
for future or past doers). For example, consider an individual with a fixed income
stream, where which has to be allocated over the finite interval (0,T). The planner
would choose a consumption plan to maximize his utility function

V (Z1,Z2, . . . ,ZT) subject to
t∑
t=1

ct ≤ Y

in which is a utility function of consumption level in t.
On the other hand, an unrestrained doer 1 would borrow Y − y1 on the cap-

ital market and therefore choose c1 = Y ; the resulting consequence is naturally
c2 = c3 = · · · = cT = 0. Such action would suggest a complete absence of
psychic integration. The model proposes two instruments that the planner can use
to control the behavior of the doers:

(a) he can impose rules on the doers’ behavior, which operate by altering the
constraints imposed on any given doer;

or

(b) he can use discretion accompanied by some method of altering the incen-
tives or rewards to the doer without any self-imposed constraints [13].

5 Role of information in decision process
In many decision processes the information held by the agent and the way

in which they are represented play an important role, above all in multi agent

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A. Longo and V. Ventre

decision problems, in which all the people involved have their intrinsic mental
models, intentions, expectations and cultural habits, and emotions of each agent
can be contagious and influence group behavior, modifying their mental models.

In this process the way the interaction and communication is carried out be-
comes important and has an effect on the dynamics of the problem solving pro-
cess. An OR process can get opposite results depending on the way the phe-
nomenon is described and how the questions are phrased and graphs used. This
can influence the behavior and preferences of the participants. As a result, we
need to pay attention to the way we communicate.

In a multi agent decision model the influence of communication depends, first
of all, on whether the information is absent or present.

6 False consensus effect for lack of information in a
non-cooperative decision problem

As observed in social psychology, people with a certain preference tend to
make higher judgments of the popularity of that preference in others, compared
to the judgments of those with different preferences. This empirical result has
been termed the false consensus effect. Consequently, as pointed out in several
experiments, in a multi agent decision problem each decision maker overestimates
his own opinion.

However, this effect becomes more pervasive when people lack necessary data
to base their judgments [10] about the choice of other members of their own group,
there are influences in opposite direction to a false consensus effect, while results
of experiment are in line with a false consensus effect in all groups in which the
information were implicit. This shows that most subjects are unwilling or unable
to use information that is not handed to them on a silver platter [4].

As a consequence, in multi agent decision problem without information about
others members and about the problem, the false consensus effect produces partial
objectivity and incomplete impartiality [10].

Mathematical instrument used to describe strategic interactions, as a multi
agent decision problem, is the theory of games, and a non-cooperative game can
be assimilated to situations in which information about decision of other members
of decision group is absent, so implicit. In this kind of interaction it is not possible
to implement some precommitment to control the doer’s actions (the impulsive
part that represents the effects of emotions), as a consequence it is not possible to
recognize the best choice on a rational base [7].

If we analyze a non-cooperative multi agent decision problem like the tradi-
tional prisoner’s dilemma, on one temporal interval and with only two alternatives,

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Influence of information on behavioral effects in decision processes

we note that the agents achieve common decision, and this is the best strategy, be-
cause each doer wants to obtain the higher advantage which is the same and, for
the false consensus effect, each one thinks that other make the same. The doer
of each prisoner will choose the strategy of “do not confess”. In the traditional
version of the game, the police arrest two suspects (A and B) and interrogate them
in separate rooms. Each can either confess, thereby implicating the other, or keep
silent. In terms of years in prison the payoff for each strategy are these:

Agent A
Confess (C) Do not confess (NC)

Agent B
Confess (C) 5,5 10,0
Do not confess (NC) 0,10 1,1

According to the theory of games, given this set of payoffs, in absence of
information there is a strong tendency for each to confess (optimal decision in
terms of Pareto), implying two rational players with consistent preferences. This
creates the paradoxical situation that rational players lead to a poorer outcome
than irrational players. Actually, when each player has to choose the best strategy
every doer drives his agent to make decision that leads him a greater advantage,
believing that the other will do the same due to the effect of the false consensus.
Consequently, the decision made by each leads to optimal decision in terms of
Pareto, because both have the same utility function and both doers choose the
only action that is the best strategy.

However, it is just a coincidence that the two players have achieved a common
strategy. In other types of non-cooperative problems this can not happen, with the
result that you will never achieve a joint decision without a prior agreement, if
there is no information. Consider, for example, a multi agent decision problem
in which the agents set to save money to realize a common purchase. Even agent
has a fixed income, YA and YB and a nonnegative level of saving, SA and SB. The
planner of each agent choose the best strategy which maximize his utility function
of saving (thinking for future), but the present doer of each agent wants to obtain
the highest advantage now, so it would consume Y and therefore choose= 0, with
a degree= 1. Indeed, the doers are impulsive, each one assigns weight= 1 to one
preference and weight= 0 to all the others, thinking that everybody will make in
the same way for effect of false consensus. In this case it is not possible obtain a
common decision.

The plan made in advance by a group of agents (to realize a common purchase)
is not feasible if they don’t set some rule or some method to alter the incentives
for the doers. This type of problem can be represented in the following scheme:

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A. Longo and V. Ventre

Agent A
Save (S) Do not save (NS)

Agent B
Save (S) 10,10 5,5
Do not save (NS) 5,5 -10,-10

where the payoff represent the utility of each agent for each strategy.
According to the rational choice, the Nash equilibrium coincides with the best

strategy (S,S). However false consensus effect and impulsivity lead each agent to
the worst equilibrium, because utility functions of the agents are different among
them (each agent prefers consumptions to savings). This causes the lack of con-
sensus on a common decision.

In conclusion, in a non-cooperative multi agent decision problem, there are
two situations:

1) the doers of each agent have the same preference and they will reach a
common decision that is given by the unanimous choice (doers don’t affect),

2) the doers have different preferences and do not assign any weight to the
other preferences, so it is not possible to aggregate the preferences. Hence,
we can affirm that in a non-cooperative decision problem it is only a chance
obtaining a common decision.

7 Excess of consensus in a cooperative decision prob-
lem

According to Engelmann and Strobel’s experiment there is no false consensus
effect if representative information is highly prominent and retrievable without
any effort. On the contrary, there is a significant effect in the opposite direc-
tion, indicating that subjects consider others’ choices more informative than their
own [4]. This is the overconfidence o “groupthink”, a psychological phenomenon
which can occur in highly trained cohesive groups. Hence, in the extreme case
in which all is known in decision making process, the interplay between differ-
ent subjects involves anyway other behavioral effects, as the excess of consensus,
apart from influence of mental models and all behavioral effects of each individ-
ual.

In the OR field this kind of decision making process can be modeled with
cooperative games where the rationality of the equilibrium choice is saved by the
possibility of making an agreement among agents, which represents a pure rule
to maintain self-control at later time in Thaler and Shefrin’s model. Moreover
with an arrangement the agents have explicit information about the choices of

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Influence of information on behavioral effects in decision processes

other members, so the lack of false consensus effect is in line with the result of
Engelmann and Strobel’s experiment. However, only the decision of one member
will prevail, and this is influenced by the strength of each mental model. An
example of cooperative game is a coordination game, when players choose the
strategies by a consensus decision making process [7].

Consider the classic example of coordination game: the “battle-of-the sexes”.
In this game an engaged couple must choose what to do in the evening: the man
prefers to attend a baseball game and the woman prefers to attend an opera. In
terms of utility the payoff for each strategy is as follows:

Man
Opera (O) Baseball (B)

Woman
Opera (O) 3,1 0,0
Baseball (B) 0,0 1,3

In this example there are multiple outcomes that are equilibriums: (B,B) and
(O,O). However both players would rather do something together than go to
separate events, so no single individual has an incentive to deviate if others are
conforming to an outcome. In this context, a consensus decision making process
can be considered as an instrument to choose the best strategy in a coordination
game. A common final decision is achievable only if the man and the woman
have explicit information, then only if there is cooperation [7]. If we follow the
Thaler and Shefrin’s model, we can analyze choices in a cooperative game in
this way: at period-one the planner of each agent states his preference, which
is the best strategy because the planner wants to maximize his utility function.
Then, the influence of doers, that want to obtain an immediate gratification, can be
avoided, because agents can enforce contracts through parties at period-one, what
eliminate the problem of loss of self-control, because they eliminate all choices.
However, only one will maximize his utility function and this is not known in
advance because it depends on the different strength of each mental models.

8 Strategic communication modify behavioral effects
In a multi agent decision problem, information held by the participants can be

wrong for two causes, not independent of each other:

1) misunderstandings and

2) manipulations.

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A. Longo and V. Ventre

In the first case, the different reaction of people at the same problem with the
same information do not reflect people’s lack of cognitive abilities but the way the
situation is described in the communication. In the second case, there is the will to
misrepresent the problem for self-interest, from one member of the group. Human
cognitive processes relate strongly to motivational issues which interplay between
people in social contexts. Self-interest is the primary cause of biases especially
in participatory processes with multiple stakeholders. Self-interest is the driver
of strategic behavior, which produce above all priming and framing effects. As
a result, some biases can be unintentional consequences of cognitive limitations,
others can be motivated by omissions or over or under emphasization of aspects,
strategically or not [6].

9 BOR: Behavioral Operational Research
In considering the behavioral effects we should take a humble approach and

accept the fact that we are not likely be able to produce a “perfect” model but
still could find one that is useful. However, modeling is not about models only,
but it matters how we choose the models and how we work with the models [6].
Creating a model to manage or solve problems is a process composed of many
phases and human behavior moderates each stage of the process and mediates the
progression through stages [5]. Hence the behavioral lens needs to be integrated
in the practice of OR as an additional perspective. Behavioral Operational Re-
search (BOR) considers the human impact on the process of using operational
research (OR) methods in problem solving and decision support as well as using
OR methods to model human behavior [6].

Not only decision makers but also modelers are subject to cognitive and mo-
tivational biases and the way the decision problems are framed. Moreover, the
cumulative effects of biases in a modeling process can also result in path depen-
dency (a phenomenon where the order in which steps are taken in the modeling
process can have an impact on the resulting model). In large models the initial
modeling choices can be very hard to change later and these can have a crucial
impact on the path the modeling process will proceed. The loss aversion effect in
decision making can also have an effect on modeling in general. Theoretically it
can be equivalent to use and label variables as losses or gains but in the interpre-
tation of the model results there can be a difference. A somewhat related effect is
the so called action bias where people choose to foster improvement rather than
prevent deterioration [6]. Also communication is an important part of modeling.
The modeler should not only be focused only on the perfection of the accuracy
of the model, the process and communication counts a lot too. Modelers should
recognize the possibility of strategic behavior of the participants. Such behavior

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Influence of information on behavioral effects in decision processes

can mean, for example, the misrepresentation of preferences or data in an envi-
ronmental participation process. Finally, also modelers are guided by self-interest.
The purpose for which the model is developed is reflected in the parameters and
scales as well as in the level of detail used. There is not a single valid model fitting
every purpose [6]. Hence biases exist in each aspect of a problem solving process
and in each phase of modeling of these processes, however finding ways to avoid
them is an open research field.

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