Discussion Paper No. 771

VISION AND FLEXIBILITY
IN A MODEL OF COGNITIVEDISSONANCE

Junichiro IshidaFebruary 2010

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Vision and Flexibility in a Model of Cognitive
DissonanceJunichiro Ishida
ISER, Osaka University
February 4, 2010

Abstract
This paper explores the consequences of cognitive dissonance, coupled with timeinconsistent preferences, in an intertemporal decision problem with two distinct goals:
acting decisively on early information (vision) and adjusting flexibly to late information(flexibility). The decision maker considered here is capable of manipulating information
to serve her self-interests, but a tradeoff between distorted beliefs and distorted actions
constrains the extent of information manipulation. Building on this tradeoff, the present
model provides a unified framework to account for the conformity bias (excessive relianceon precedents) and the confirmatory bias (excessive attachment to initial perceptions).

JEL Classification Codes: D03, D99.
Key Words: Cognitive dissonance, Vision, Flexibility, Conformity bias, Confirmatory bias.

 Correspondence to: Junichiro Ishida, Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan. E-mail address: jishida@iser.osaka-u.ac.jp.

“Wise men change their minds, fools never.”– from Zhouyi (“The Book of Changes”)“Not to amend a fault after you commit it, that is a true fault.”– from Analects of Confucius

1 Introduction
Suppose that you (e.g., CEO, constituency) are in search of someone (e.g., manager, politician) who, on your behalf, conducts some long-term project. Ideally, you would like yourdecision maker to achieve two distinct goals. First, time is precious and it is hence important
to exhibit a “vision” by acting decisively on early information before things unfold themselves. Second, as more information becomes available over time, it is also equally important
to be open-minded and “flexible” enough to adjust to new information without being prejudiced by any prior beliefs. The problem is that, while both vision and flexibility are clearly
indispensable for effective decision making, a body of literature in both social psychology
and behavioral economics suggests that they are indeed very rare to be found: on one hand,
we often rely excessively on precedents, instead of our own private information, and bias ourperceptions and behaviors towards the majority (the conformity bias);1 on the other hand,
we also often let our initial perceptions interfere too much with our decision making by misinterpreting subsequent evidence in favor of the initial perceptions (the confirmatory bias).2
In either case, we do not process information as objectively as an unbiased Bayesian learnerwould do, consequently resulting in all sorts of inefficient outcomes.3
1

One of the early experiments to show the conformity bias is provided by Asch (1951) who shows that anindividual conform to the judgments of the majority that are obviously incorrect.
2
A number of experiments, e.g., Ariely et al. (2003), document that our perceptions and valuations are
initially malleable but become imprinted and fairly stable after we are called upon to make an initial decision(the anchoring effect). Our notion of the confirmatory bias also implies that first impressions matter. See Rabin
and Shrag (1999) for psychological evidence on the confirmatory bias.
3
For instance, the lack of vision is often touted as a leading cause for business failures which occur ever sofrequently. The lack of flexibility is also salient, as exemplified by the two old Chinese proverbs in the opening
quotes.

1Given that the lack of vision and flexibility in dynamic decision making is so ubiquitous, it
is important to understand why our perceptions and behaviors are biased in such a systematicmanner. The main purpose of the paper is to provide a unified framework to account for boththe conformity bias (the lack of vision) and the confirmatory bias (the lack of flexibility) bybuilding on the theory of cognitive dissonance, coupled with time-inconsistent preferences,as an integral piece of the analysis.4 To this end, we consider a two-period setting where adecision maker must take some actions sequentially in an uncertain environment. In eachperiod, she can observe a free signal which partially reflects the state of nature: for clarity,
we refer to the signal observed in the first (second) period as the first (second) signal. Eachobserved signal is either informative or noisy depending on some factors beyond her control,
and when it is informative, its accuracy depends on her unknown ability type. Based on theavailable information, the decision maker makes an inference about the state of nature andtakes an appropriate action.
A critical aspect of this setting is that the decision maker does not know whether any
given signal is informative or noisy beyond its objective probability, which provides some leeway for her interpretation of the available information. While an unbiased Bayesian learnerwould update her belief based on this objective probability, we deviate from this convention
by allowing the decision maker to assign any probability (of the signal being informative)
to serve her self-interests. This information manipulation is not costless, however, because
any distorted beliefs would persist and later lead to distorted and less efficient choices of action.5 This tradeoff creates a tension within herself and constrains the extent of information
manipulation.
We attempt to capture this entire process by constructing a model of intrapersonal con4
The theory of cognitive dissonance asserts that people experience an uncomfortable feeling when holding
contradictory ideas or cognitions. To reduce dissonance, people change their beliefs and behaviors, often byinterpreting events or facts in a self-serving manner. For instance, it is well known that people tend to discover
flaws in evidence that conflicts with their self-interests but rely excessively on evidence that portrays them in agood light. For instance, several studies show that people tend to be more critical of the validity of tests on which
they failed (Wyer and Frey, 1983; Pyszczynski et al, 1985).
5
A case in point is an instance of workers in a hazardous job, as depicted in Akerlof and Dickens (1982). To
escape from the fear of injury, they have an incentive to believe that the job is actually safe, but in this state ofself-deception, they also often fail to wear required safety equipments – an apparently inefficient action. Thisinefficiency comes from the need for dissonance reduction: wearing safety equipments while believing that thejob is safe is apparently contradictory and hence puts them in the state of dissonance.

2

flicts between the objective self and the subjective self. The objective self represents the rational side of the decision maker and is a forward-looking unbiased Bayesian learner, whereas
the subjective self represents the more instinctive and myopic side and cares about her selfimages (ego preferences). This framework then contains two sources of cognitive bias: on
one hand, the subjective self’s ego gives rise to an incentive to manipulate information topreserve her self-images; on the other hand, the difference in time horizon between the twoselves amounts to time-inconsistent objectives and the need to regulate future selves. With
these two forces at work, we obtain the following results.
The conformity bias (the lack of vision): The decision maker relies excessively on precedents
by discounting the first signal.
The confirmatory bias (the lack of flexibility): The decision maker exhibits excessive attachment to her initial choice of action, both by exaggerating the second signal if it is consistent
with the first signal and discounting it if it is inconsistent.
To see the underlying logic of the current model more clearly, we start with the second
period of the model where the decision maker has already accumulated some information.
The driving force of the confirmatory bias is the subjective self’s preference for better selfimages. As stated, the accuracy of each observed signal is dependent on the decision maker’s
ability. This means that if the second signal is consistent with the first one, chances arethat she has made the right observations. In this case, she has a reason to exaggerate theinformativeness of the second signal because that will boost her self-confidence. On theother hand, inconsistent signals are a bad news for the decision maker because this may
indicate the lack of ability on her part, placing her under the state of dissonance. To reduce
dissonance, she then downplays the importance of the second signal by simply disregarding
it as uninformative and unreliable. This result thus indicates that “first impressions matter”
in that the decision maker is prejudiced by the first signal, one way or the other, to the extent
that it is not warranted objectively. In either case, the decision maker lacks flexibility as she
fails to respond objectively to new information, consequently ending up with a biased viewof the world.

3

In contrast, the conformity bias concerns what happens in the first period. The underlying logic leading to this bias now stems partially from a self-control problem due to timeinconsistent objectives. To see how this bias arises, notice that while the decision maker’s
information processing in the second period is biased, its magnitude is heavily dependent
on the informativeness of the first signal. The magnitude is larger if she relies strongly on
the first signal and takes a clear stance. In contrast, if the decision maker regards the firstsignal as a complete noise containing no relevant information, the second signal provides
no information about her ability type whatsoever, and there arises no need to justify herself.
For a decision maker who is hampered by the self-control problem, therefore, discounting
the informativeness of the first signal and remaining rather ambiguous are a way to regulate
her future selves. In so doing, however, she fails to act decisively on early information andis hence unable to articulate her vision before things unfold themselves, which we take as
representing the lack of vision.6
The present setup allows us to identify several important factors that affect the way thedecision maker processes information over time and hence critical determinants of vision andflexibility. First, the key factor in this entire process is the extent to which the rational andfarsighted objective self can regulate the more instinctive and myopic subjective self. The lackof control over the subjective self, or the lack of willpower as we later define, is the source ofall behavioral biases in our model. A decision maker with weak willpower must compromise
more and consequently ends up with a more biased view of the world. In contrast, all sorts ofbiases disappear if the objective self has perfect control over the subjective self, which allows
the decision maker to rationally and objectively process information.
Another important factor is the decision maker’s self-confidence in her own ability, which
consists of two aspects: the level (the mean) and the fragility (the variance). The selfconfidence fragility is about how secure the decision maker feels about herself and measured
6
There are several papers which explicitly focus on the notion of vision. To name a few, Rotemberg andSaloner (2000) model vision as a bias which makes the manager favor one project over the other. Similarly,
Rotemberg and Saloner (1994) argue that a firm could be better off by committing to a specific business strategy.
Van den Steen (2005) also formalizes the notion of vision and shows that a leader with strong beliefs would
attract employees with similar beliefs. This sorting effect improves coordination within the firm, suggesting achannel through which strong vision can affect the firm’s performance. In this paper, we focus on a different
aspect of vision, defined as the ability to effectively utilize early information before things unfold themselves.

4

by the prior variance of the ability type, as perceived by the subjective self. The effect of theself-confidence fragility is complementary to the effect of willpower and generally works inthe same direction. If the decision maker is perfectly sure about her own ability, whatever
she observes does not change her assessment of herself, and the incentive to preserve selfconfidence disappears no matter how severe the self-control problem is. As she becomes lesssecure about herself, the need to preserve self-confidence intensifies, leading to all sorts ofbiased behavior.
In contrast, the effect of the self-confidence level, measured by the prior expectationof the ability type, is more complicated compared to the other two factors. In general, adecision maker with more self-confidence exhibits a lager bias in the second period in both
directions (both obsession and stubbornness) and hence is less flexible. This is because thosewith high self-confidence have more trust in the first signal, and the cost of biasing theinterpretation of the second signal is relatively low,7 indicating that high self-confidence per sedoes not necessarily leads to better and objective judgments. In contrast, the effect of the selfconfidence level on vision is less certain, as it could go either way. The logic is now partiallyreversed because the first signal is more reliable for those with high self-confidence and it
is relatively more costly for them to bias its interpretation. There is a countervailing effect,
however, since the second-period bias is larger for those with high self-confidence and theself-control problem is hence severer, given the same level of willpower and self-confidence
fragility. The overall effect is determined by this tradeoff but we argue that the first effect ismore likely to dominate the second. In light of this, we claim that high self-confidence makes
a decision maker less flexible while it tends to make her more visionary.
The paper proceeds as follows. In the remainder of this section, we briefly discuss related
literatures. Section 2 outlines the basic model of subjective information evaluation. Section
3 provides the main results of the paper, with special attention paid to the effects of selfconfidence and willpower. Finally, section 4 makes some concluding remarks.
7

To be more precise, this is because we consider a situation where the prediction ability is tested more in thefirst period. We explore more on this point later.

5

Related literature
The paper spans over several distinct areas, and there are accordingly several strands ofrelated literature. Among them, the paper is most closely related to Akerlof and Dickens(1982) in its motivation. In this seminal work, Akerlof and Dickens (1982) posit that: (i)people have preferences not only over states of the world, but also over their beliefs about
the state of the world; (ii) they also have some control over the beliefs; (iii) the beliefs
once chosen persist over time. The current analysis closely follows these premises in that we
consider a decision maker who is capable of deceiving herself and manipulating her belief inany way she can to serve her self-interests. Starting from these premises, however, the current
analysis builds on an entirely different analytical framework: we model a detailed process of
intrapersonal conflicts and extend it to a dynamic setting to see its dynamic implications.
Besides this, there is now a growing amount of interest on the manipulable nature ofour belief system. The importance of the self-serving nature of our belief system has also
gained some recognition among economists,8 and several attempts are made to capture thisseemingly robust human nature.9 Some early attempts to model belief distortions as a resultof optimized behaviors are provided by Benabou and Tirole (2002, 2004, 2006), Benabou(2008a, 2008b) and Brunnermeier and Parker (2005).10 These papers consider various cases
where an agent can manipulate her own memory or expectations, thereby explicitly looking
into the process of biased belief formation.11 The current paper intends to add to this line ofliterature: we view our main contribution in our specific way to apply the notion of cognitive
dissonance to the problem of dynamic information processing, which allows us to identify the8

A self-serving bias refers to a human tendency to make internal attributions for success and external attribution for failure. The study on this issue has yielded a voluminous literature; see, for instance, Zuckerman (1979).
See, for instance, Babcock and Loewenstein (1997).
9
Formal analyses which incorporate confirmation bias and explore its consequences include Rabin and Schrag(1999) and Compte and Postlewaite (2004). The approach of this paper is different, as we derive it as an
optimized behavior of divided selves, instead of assuming it and exploring its consequences.
10
Also, see Bracha and Brown (2009) and Mayraz (2009).
11
Several recent works also derive overconfidence, a type of self-serving bias, without explicitly assuming biased
information processing. Van den Steen (2004) argues that facing a choice of actions, people are more likely tochoose an action of which they overestimate the probability of success, and hence tend to be overoptimistic about
the current action that they choose. Santos-Pinto and Sobel (2005) consider a case where different individuals
hold different opinions about how skills combine to determine an ability level. In that setting, positive self-image
arises because they work more on a skill that is critical to their production function. Also, see Köszegi (2006) for
how a rational agent comes to hold an overoptimistic view of herself.

6sources of the two frequently cited cognitive biases and make a dynamic link between them.
We also provide an analytically tractable framework which allows us to intuitively relate thepresence of the biases to deep parameters of our cognitive process.
Whereas the confirmatory bias is deeply rooted in the self-serving nature of our belief
system, the conformity bias in our model stems from a type of self-control problem due totime-inconsistent objectives which results from the process of intrapersonal conflicts. In thissense, the paper is related to Carrillo and Mariotti (2000) and Benabou and Tirole (2002,
2004), among many others, who explore various aspects of self-regulation for individuals
with time-inconsistent preferences. In the present model, the self-control problem arises dueto the difference in time horizon between the two selves, where the myopic subjective self
gets in the way to obstruct the objective self to make a fully rational decision. The lack ofvision surfaces because taking an ambiguous stance early on is a way to reduce any concern
for protecting self-images and hence to regulate the future subjective self.
Besides these so-called “behavioral” aspects, the main thrust of the paper is the dynamic
nature of information acquisition. Works along this line include Prendergast and Stole (1996)
and Li (2007) who consider dynamic aspects of reputation concerns in signaling models. This
paper is especially related to Prendergast and Stole (1996) who consider a situation wherean agent signals his ability to acquire information and examine how that signaling incentive
changes over the course of his career. They show that the agent exaggerates information
when young and tends to become more conservative as he gets older. An important aspectof their model is that changing behavior from previous periods is costly because that signals
the lack of ability on his part. Our model shares this aspect, which is the driving force of
one side of inflexibility. Aside from this, however, there are several notable differences. First,
we consider a totally different setup, which allows us to focus on the flip side of inflexibility,i.e., exaggeration of favorable information.12 Second, while Prendergast and Stole (1996)
only consider static incentives (maximization of the current payoff), we explicitly consider
dynamic incentives to regulate the future selves, which results in the discounting of early12
In their model, the state space is extended on the real line and hence has no “extreme” points. In thisspecification, there is no way to exaggerate information in our sense.

7

information.

2 The model
Our optimization problem rests on the tradeoff between biased beliefs and biased actions,which stems from our inherent desire for coherence and consistency as suggested by thetheory of cognitive dissonance.

2.1 Setup
Consider a two-period model where a risk-neutral decision maker (DM) engages in somelong-term project. In each period, DM observes a signal, evaluates it and takes an action
based on the evaluation. The action chosen in each period yields a payoff which is realized
and received at the end of period 2. The value of the project depends on the action taken
in each period and the (time-invariant) state of nature  2 f0; 1g. The state of nature is notdirectly observable, and its prior distribution is given by

probf = 0g = probf = 1g = 0:5:
That is, each state occurs equally likely ex ante.
In this environment, DM’s job is to correctly predict the state and choose an appropriate
course of action accordingly. More precisely, let at 2 [0; 1℄ denote the action chosen in periodt = 1; 2. Given some realized state , the value of the project (for period t) is given by v (at )where v0 (a) =a2 and v1 (a) = (1a)2 . This specification implies that the actions are

ex ante symmetric in every respect. Given the action a and some belief  := probf = 1 javailable informationg, the expected value of the project is computed as

R(a; ) = (1 a)2 (1 )a2 :The first-order condition implies that the optimal action is a = .

2.2 Signals
At the beginning of each period, DM has a chance to observe a signal, which possibly contains
some information about the state of nature. The signal is either informative or noisy, and the8(objective) probability that any given signal is informative is ~ 2 (0; 1). When the signal isnoisy, it contains no information about the realized state, so thatprobfst =  j the signal is noisyg = 0:5; t = 1; 2:
When it is informative, on the other hand, the signal coveys some information about therealized state although its accuracy differs across periods. DM’s judgement ability is tested
more in period 1, and hence the accuracy depends more on her ability type, denoted by

 2 [0; 1℄:

probfs1 =  j the signal is informative; g = 1 +2  :The situation unfolds itself and becomes more predictable as time passes by, so that an informative signal in period 2 perfectly reflects the realized state:probfs2 =  j the signal is informative; g = 1:
It is perhaps worth emphasizing that the second signal contains information not just about
the realized state but also about the ability type, because DM with low ability is more likely
to observe inconsistent signals. The problem is that the informativeness of any given signal
is not known beyond its objective probability (which we refer to as the objective informativeness), and that provides some leeway for the decision maker’s interpretation.

2.3 Information processing and belief formation
There are two unknowns in this model, the ability type  and the state of nature  , and abelief must be formed on each of them. Although DM knows nothing more than the fact thatany given signal is informative with probability ~ , we here consider a situation where she
can deceive herself and subjectively assigns the informativeness to each observed signal ina self-serving manner. Let t 2 [0; 1℄ denote the subjective informativeness of the observed
signal, i.e., the subjective assessment of the probability that the signal observed in period t is
informative.13 While there are potentially many ways to capture this aspect, we model DM
13

The important point is that this informativeness is exogenous and, more importantly, independent of DM’sability type, so that it is not ego-threatening. Our stance here is that the accuracy of each signal depends on

9

as a multi-layered self with divided interests between the objective self (cognition) and thesubjective self (affect).14
The objective self:

The objective self represents a rational side of DM who is forward-

looking and processes information in an objective manner as conventionally assumed. The
objective self derives utility from the outcome of the project and is hence interested in knowing the true state of nature. Given some informativeness (g1 ; g2 ), let1 (s1 ; g1 ) := probf = 1 j s1 ; g1 g; 2 (s1 ; s2 ; g1 ; g2 ) := probf = 1 j s1 ; s2 ; g1 ; g2 g;denote the beliefs about  where gt 2 f t ; ~ g: we say that a belief is unbiased when gt = ~and compromised when gt = ~ . We also assume that the objective self knows the true valueof  with precision, which is denoted by .
When evaluating her expected payoff, the objective self uses the unbiased belief. Assuming that the objective self does not discount the future,15 the expected (total) payoff for theobjective self in period 1 is hence given by

tO (at ) = R(at; ~t ) + E [R(a2 ; ~2 ) j s1 ; 1 ℄;where ~1 := 1 (s1 ; ~ ) and ~2 := 2 (s1 ; s2 ; ~ ; ~ ) denote the unbiased beliefs. The expectation
here is taken over possible second-period signals. Similarly, the expected payoff in period 2is2O (a1 ; a2 ) = R(a2 ; ~2 ):The subjective self: The subjective self represents a more primitive and instinctive side of
DM who is myopic and, with imperfect knowledge about herself, cares about her self-images(ego preferences). To be more precise, the subjective self postulates that her ability type ismany factors, including those that are not ego-threatening: for instance, the accuracy is most likely to dependon environmental factors that are purely external to DM. This informativeness is a formal representation of thoseexternal factors that are not ego-threatening.
14
One of the first attempts to model an individual with divided selves is provided by Thaler and Shefrin (1981).
Recent attempts to model divided selves are provided by Lowenstein and O’donoghue (2005) and Fudenberg andLevine (2006). For a different approach, see Brocas and Carrillo (2008) who model the brain as a hierarchicalorganization.
15
The assumption is strictly for simplicity, as the role of the discount factor, even if it is introduced, is fairly
straightforward.

10

drawn from some distribution F with mean  :=RR

dF and variance 2 := 2 dF 2 .16 We

take that the prior mean reflects DM’s initial self-confidence level while the variance reflects
its fragility: we say that DM is more secure about her self-images when  2 is smaller andclose to zero.
When estimating her ability type, the subjective self uses the subjective informativeness.
Define1 (s1 ; 1 ) := E [ j s1 ; 1 ℄; 2 (s1 ; s2 ; 1 ; 2 ) := E [ j s1 ; s2 ; g1 ; g2 ℄;as the belief about  . Being myopic, the subjective self totally disregards the value of the
project which realizes in the future and instead cares only about the immediate gain, i.e., her
self-images at each moment.17 The subjective self’s payoff in each period is thus simply givenbytS = 1 (s1 ; 1 ); tS = 2 (s1 ; s2 ; 1 ; 2 ):2.4 The intrapersonal conflict
The subjective informativeness is chosen so as to maximize the overall payoff t , which isdefined as a weighted average of tS and tO :t = tS + tO :Here,> 0 is a parameter which measures the strength of DM’s willpower: she is regarded

as possessing strong willpower to regulate herself (or the subjective self) whenis smalland close to zero. Note that this parameter conflates two fundamentally distinct elements:
the weight given to the subjective self (which determines the severity of time inconsistency)
and the strength of ego preferences. The parameteris hence a concept which encompasses

these two aspects that happen to play the same role in this particular setup.
16This specification implies that the subjective self’s prior mean coincides with its true value, although there
is no strong reason why this must be so. While we make this assumption mainly for analytical tractability, we
argue that this is also realistic because actual ability and self-confidence are generally positively correlated, e.g.,
Stankov and Crawford (1996). In Appendix B, we relax this assumption to show that our main insights can beobtained even if the prior mean deviates from the true value.
17
The current specification means that the subjective self cares only about the mean of the ability estimate but
not about the variance. If the subjective self prefers a more (less) accurate estimate for some reasons, that tends
to raise (lower) both 1 and 2 .

11Formally, we divide each period into two stages and suppose that DM goes through thefollowing two-stage process:Stage 1 (the information-processing stage): Upon observing st , the objective and subjective
selves assign t to it so as to maximize the overall payoff t . The subjective informativenesschosen in this stage then yields a compromised belief about the state of nature.
Stage 2 (the action stage): The objective self chooses the optimal action based on the compromised belief.
Being the only one to care about the outcome of the project, an action in each period is chosendeliberately by the objective self.18 This choice is made, however, based on the compromised
belief because, once t is imprinted, deviating from that produces cognitive dissonance. Thismeans that, although DM can freely choose any t , that will become a part of her perception and influence the subsequent choice of action: in this particular sense, the beliefs areinternally consistent and coherent.
This internal process eventually amounts to a constrained optimization problem in eachperiod. In period 2, taking (s1 ; s2 ) and1 as given,max
2 = 2 (s1 ; s1 ; 1 ; 2 ) + R(a2 ; ~2 );2subject to

a2 = 2 (s1 ; s2 ; 1 ; 2 ):Let

2 (s1 ; s2 ; 1 ) denote the optimal solution to this problem which possibly depends on(s1 ; s2 ) and 1 . Then, in period 1, taking s1 as given,max
1 = 1 (s1 ; 1 ) + R(a1 ; ~1 ) + E [R(a2 ; ~2 ) j s1 ; 1 ℄;1
subject to

a1 = 1 (s1 ; 1 ); a2 = 2 (s1 ; s2 ; 1 ; 2 (s1 ; s2 ; 1 )):18

One can regard Stage 1 as an automatic process which operates at a subconscious level and is inaccessible
to consciousness. In contrast, Stage 2 may be regarded as a controlled process though which deliberate andconscious choices are made. See Camerer et al. (2005) for the distinction between automatic and controlled
processes in neural functioning.

12In what follows, the entire process is described as if DM singlehandedly solves this constrained problem. Other than the interpretation detailed just above, this setup yields a wide
variety of interpretations as to the structure behind it. In any event, though, the bottom lineis the tradeoff between distorted beliefs and distorted actions and any structure that can (atleast partially) capture this aspect can suffice for our purposes.19

3 Optimal information processing
3.1 Preliminary
Before we move on, we first describe in some depth how the beliefs are formed in this model.
First, the objective self must form a belief about the state of nature t . Given some informativeness g1 , the best estimate of  in period 1 is obtained as

1 + g1  :(1)
2
Due to the symmetric nature of the states, 1 (0; g ) = 1 1 (1; g ) for any g . Since the states
are symmetric, we shall hereafter focus on s1 = 1 without loss of generality. The manipulable
1 (1; g1 ) =range of the belief is depicted in figure 1.
[Figure 1]
With an additional signal in period 2, the belief about  is updated and given by2 (1; 1; g1 ; g2 ) =(1 + g2 )(1 + g1)
(1 + g2)(1 + g1)2((1 g2 )(1 g1) + (1 + g2 )(1 + g1)) = 2(1 + g1 g2) :(2)

2 (1; 0; g1 ; g2 ) =(1 g2 )(1 + g1)
(1 g2)(1 + g1) :=2((1 + g2 )(1 g1) + (1 g2 )(1 + g1))2(1 g1 g2)(3)

To ease notation, defineC (g1 ; g2 ) := 2 (1; 1; g1 ; g2 ) and I (g1 ; g2 ) := 2 (1; 0; g1 ; g2 ):The manipulable range of the belief is depicted in figure 2.
19

For instance, we could model this process as an intrapersonal game (or bargaining) between the two selves.
An advantage of the current specification over potential alternatives is its greater tractability, as it leads to aclosed-form solution for the second-period problem. In any case, we would expected to reach similar conclusions
as long as a model captures the tradeoffs considered here.

13

[Figure 2]
Being uncertain about her own ability, on the other hand, the subjective self must forma belief about  . The inference is only relevant in period 2 because one signal conveys no
information about  . The beliefs in period 2 are obtained as2 (1; 1; 1 ; 2 ) =R1
1 2 0R (1 + )dF + (11
1 2 0 (1 + )dF + (11 2 ) =  + 1 2 E [2 ℄ ;1 + 1 21 2)

(4)

2 (1; 0; 1 ; 2 ) =R1
1 2 0R (1 )dF + (11
1 2 0 (1 )dF + (11 2 ) =  1 2 E [2 ℄ :1 1 2
1 2)(5)

Similarly as above, defineC ( 1 ; 2 ) := 2 (1; 1; 1 ; 2 ) and I ( 1 ; 2 ) := 2 (1; 0; 1 ; 2 ):Notice that C >  > I for any

1 2 > 0 and 2 > 0, i.e., consistent signals are a good news

for DM while inconsistent signals are a bad news.

3.2 Flexibility: the second-period problem
In period 2, DM observes an additional signal, which may nor may not be consistent withthe first signal. DM’s flexibility, which is defined as the ability to respond rationally andobjectively to new information, is tested in this situation. When DM is prejudiced by the firstsignal and fails to respond objectively to the second signal, the consequent action is distorted
and becomes necessarily inefficient. Here, we examine when and to what extent DM exhibits
this type of behavioral bias.
In period 2, DM observes s2 and assigns the subjective informativeness to it, taking (s1 ; s2 )and

1 as given. Choosing 2 then yields a compromised belief 2 (s1 ; s2 ; 1 ; 2 ), which corre-

sponds to the action chosen by the objective self. The optimization problem is thus defined
as

max
2

2 (s1 ; s2 ; 1 ; 2 ) + R(2 (s1 ; s2 ; 1 ; 2 ); 2 (s1 ; s2 ; ~; ~ )):The first-order condition is given by

2
 2

2 = 0;2(2 (s1 ; s2 ; 1 ; 2 ) 2(s1 ; s2 ; ~; ~))  2
14

assuming that there exists an interior solution. The solution is obtained as a function of

1 anddenoted as 2 (s1 ; s2 ; 1 ). Given some optimal belief 2 (s1 ; s2 ; 1 ), we refer to b2 (s1 :s2 ; 1 ) :=2 (s1 ; s2 ; 1 ) ~2 (s1 ; s2 ; ~ ; ~ ) as the optimal bias as perceived by the objective self. We takethis as a measure of flexibility where DM is less prejudiced and hence more flexible when thebias is smaller.
When the signals are consistent, this condition becomes

1 2(1 + 1 2 )22(2 ~C ) (11 + ( 1 ) )2 = 0;
1 2

where ~C := C (~ ; ~ ). The optimal belief C in this contingency as a function of

1 is given

by

2 1
1 ( 1 )2 :C ( 1 ) ~C =It follows from this that C > ~C for any

1 > 0, meaning that DM exaggerates her informa-tion even more when the observed signals are consistent.
Similarly, when the signals are inconsistent, this condition becomes(1

1 2 + (2
1 2 )2

~I )1 ( 1 )2 = 0;
(1 1 2 )2where ~I := I ( 1 ; ~ ). The optimal belief I as a function of

I ( 1 ) ~I =which again implies that I > ~I for any

1 is then given by2 1
1 ( 1 )2 ;1 . This means that DM undervalues the second

signal and instead favors the first one in order to justify her prior stance. Note also thatthe optimal bias is symmetric, i.e., b2 (1; 0; 1 ) = b2 (1; 1; 1 ) for any

1 . Define b2 ( 1 ) :=b2 (1; 0; 1 ) = b2 (1; 1; 1 ), which can be seen as a measure of DM’s flexibility.

Proposition 1 The optimal second-period bias is always positive and given byb2 ( 1 ) =For any given2 1
1 ( 1 )2 :1 , the bias is increasing in , 2 and . Moreover, the bias is increasing in 1 .
15

P ROOF: Most of the proposition is self-evident from the discussion made thus far. We only

1 . This is the case if
2 (1 + ( 1 )2 )(1 ( 1 )2)2 > 0;show that the optimal bias is increasing in(6)

which always holds.
Q.E.D.
Several remarks are in order. First, the optimal second-period bias is always positive,
meaning that DM biases her decision in the direction of the first signal (the anchoring effect).
There are two sides to this biased information processing. When the observed signals are
consistent, DM overreacts to the second signal, becoming rather obsessive about her initialstance. As a flip side, when the observed signals are inconsistent, she downplays the importance of the second signal and sticks stubbornly with her initial stance. In either case,with imperfect willpower> 0 and imperfect knowledge about herself 2 > 0, DM in gen-eral exhibits a degree of inflexibility as she fails to respond rationally and objectively to new
information.
Second, taking

1 as given, the size of the bias depends on attributes such as the self-

confidence level and fragility as well as the strength of willpower. The effects of the selfconfidence fragility and the strength of willpower are identical and relatively straightforward.
The bias is smaller when DM is more secure about herself and/or she has strong willpower
to regulate herself: in fact, when DM is perfectly secure about herself ( 2 = 0) or has perfect
willpower (= 0), the intrapersonal conflict disappears and she exhibits no bias whatso-

ever.20 What is more interesting but intuitively less straightforward is perhaps the effect of
the self-confidence level. The analysis reveals that DM who has more confidence in herself
is less likely to reverse her prior decisions and hence more prone to exhibiting inflexibility
in both ways. This suggests that although high ability itself is helpful in making good judgements, high self-confidence is often an obstacle to making objective decisions. This result
20

As an alternative interpretation, the self-confidence fragility can be taken as reflecting how the predictability of the underlying environment is related to DM’s ability. For instance, if the accuracy of the first signal isless ability-intensive and related only weakly to  , not much is revealed about her ability type. The situation
corresponds to a case with a smaller  2 .

16

comes from the fact that the accuracy of the first signal is more sensitive to ability than thatof the second signal. Since DM with high self-confidence trusts her first observation morethan that with low self-confidence, the cost of biasing the interpretation of the second signal
is lower in a relative sense. This biases her information processing in order to protect her
self-images, making inflexibility more of a problem for DM with high self-confidence.
Finally, it is important to note that the optimal bias is also a function of an endogenous
choice variablecreases as

1 . The bias is larger when DM puts more stock in the first signal and de-

1 decreases, meaning that vision and flexibility are substitutes. In particular, when

1 = 0, i.e., DM believes that the first signal is not at all informative, nothing she observes
undermines her self-confidence, and there is hence no need to bias her decision making inorder to justify herself. This aspect gives rise to critical dynamic interactions, because the objective self in period 1 can reasonably control the subjective self in period 2 by disregarding
the first signal and remaining rather ambiguous. This is precisely the problem faced by DMin period 1, which we will next turn to.

3.3 Vision: the first-period problem
The prediction ability is tested more in period 1, as the accuracy of the first signal depends
positively on DM’s ability. In this setting, vision is defined as the ability to respond rationallyand objectively to early information before things unfold themselves. The key factor at thisstage is the presence of time-inconsistent objectives, which stems from the difference in time
horizon between the two selves. The objective self knows that her second-period prediction
will be biased, to the detriment of her own interests, to accommodate the subjective self’s ego
preferences. The objective self thus has an incentive to minimize this bias, if it is possible atall. There is indeed a way to achieve this because, as we have seen, the optimal bias in period
2 depends positively on the informativeness of the first signal

1 . Disregarding the first signal

frees the future self from any concern about her self-images and allows her to react moreobjectively to the second signal, thereby minimizing the prediction bias which works against
the objective self’s interests.21 There is of course a cost associated with it, because a failure
21

Alternatively, exhibiting a vision (by placing a larger weight on the first signal) is a commitment to limit theset of available future choices. The current framework thus naturally and endogenously gives rise to the tradeoff17

to objectively utilize the first signal generally results in an inefficient action in period 1. The
optimal bias in period 1 is determined by this tradeoff.
Since
choice of

1 and 2 are intertemporally linked, DM can influence her future self through the
1 . The objective self’s expected payoff in period 2 as a function of 1 is given by22O2( 1 ) = 1 +2~  C ( 1 ) + 1 2~  I ( 1 );where

C ( 1 ) := R(C ( 1 ); ~C ) = ~C (1 C ( 1 )) (1 ~C )C ( 1 );
I ( 1 ) := R(I ( 1 ); ~I ) = ~I (1 I ( 1 )) (1 ~I )I ( 1 ):Upon observing s1 = 1, DM’s problem in period 1 is defined asmax
1 + R(1 (1; 1 ); 1 (1; ~)) + O2 ( 1 ):Notice that the myopic subjective self has nothing at stake in period 1, so that the problem isstrictly about how the objective self regulates the future subjective self.
Define ~1 := 1 (1; ~ ) and b1 ( 1 ) := 1 (1; 1 )~1 where we take b1 as a measure of DM’s

vision: the larger b1 is, the more visionary she is.22 The first-order condition is then given by

1 + 1 + ~ 2  C + 1 ~ 2  I = 0:2b1( 1 ) 

2 
2 
1

1

1

(7)

Since

C Id==2b2 ( 1 ) C ; 1  1d1(7) can be written asb1 ( 1 ) = R( 1 )b2 ( 1 );whereR( 1 ) :=

dC
d 1
1
 1

2
( 1 )2 ) ;= 2 (1 (1 +( 1 )2)2

between commitment and flexibility, like the one analyzed in Amador et al. (2006) and some others.
22
Evidently, there is a right degree of vision, i.e., more vision is not necessarily better. DM indeed takes anexcessively strong stance when b1 > 0 although, as we will see later, this would not occur in equilibrium.

18

Proposition 2 The optimal first-period bias is always negative. The bias is increasing in ,and  2 and disappears as they tend to zero, whereas it is decreasing in  if

1 4(~ )2 3(~ )4 > 0:Moreover,1 = 0 (the complete lack of vision) if  is sufficiently small.

P ROOF: See Appendix.

The optimal first-period bias is always negative, in contrast to the second-period bias,
where DM biases her prediction towards her prior mean (excessive reliance on precedents)and strategically settles for an ambiguous initial stance in order to allow her future self to act
more flexibly. This is taken as a sign of the lack of vision. As in period 2, the bias is increasinginand  2 , because the need to regulate the future self is simply larger. This indicates that

DM fails to articulate her vision when she is insecure about herself and/or lacks willpower toregulate herself.
It is, on the other hand, more complicated to see how a change in  affects
hand, an increase in  enlarges the second-period bias for any given
marginal gain of lowering

1 . On one

1 , which raises the

1 . On the other hand, there is also a countervailing effect. To see

this, recall that an increase in  tends to make DM more inflexible in period 2 because withthe first signal being more accurate, the cost of disregarding the second signal is relatively
small. As can be imagined, the situation is totally reversed in period 1: the cost of disregarding the first signal is now larger for DM with high self-confidence. While the optimal bias
could go either way due to this tradeoff, it is decreasing in  when ~ is sufficiently small,23
because the second-period bias becomes negligibly small, and the need for self-regulation
diminishes in this case. Then, since the cost of disregarding the first signal is larger, thefirst-period bias becomes smaller for DM with high self-confidence who articulates a clearer
vision.
The effect of the self-confidence level can also be seen from an alternative perspective.
Notice that, as  ! 0, the choice of

1 becomes totally irrelevant, because the signal is not2

The bias is in fact decreasing in  for all [0; 1℄ if ~ < 
0:464. Of course, this is only a sufficientcondition, indicating that the bias is decreasing in  for a wider range of parameter values.
23

19

informative anyway, no matter how she interprets it: in other words, there is little Bayesian
updating when there is little information. Since the cost of biasing the interpretation isvanishingly small, there is no reason to assign any positive informativeness to the first signal.
As the proposition indicates, the optimal response is the complete lack of vision ( 1 = 0) forDM with sufficiently low self-confidence. When that happens, DM totally disregards early
information and does not make up her mind until things become sufficiently clear.

3.4 The overall impact on flexibility
In section 3.2, we have discussed how the second-period bias b2 varies in response to changes
in parameters such as ,  2 and  when

1 is exogenously given and fixed. Since 1 itself

is a function of those parameters, however, indirect effects through1 must also be taken

into account to fully understand the overall impact on flexibility. As suggested, vision andflexibility are substitutes in that when one goes up, the other must go down. Changes in
exogenous parameters also affect the relative value of vision and flexibility, as captured byR( 1 ), thereby yielding some indirect effects. Although our primary focus is on the direct
effects, we here briefly discuss the overall impact of exogenous parameters on the degree of
flexibility.
or  2 . Since these two parameters yield

We first examine the impact of changes inexactly the same effect, we focus on changes in . As we have seen, an increase in

1 and, taking 1 as given, also 2 . At the same time, though, a change inraisesalso changes

the relative value of vision and flexibility. While the bias increases up to some point with anincrease in , the cost of inflexibility rises as

becomes sufficiently large. Oncereachessome point, therefore, the first-period bias becomes less of a concern, and DM attempts tominimize the second-period bias by decreasingof changes in

1 towards zero. This indicates that the impact(or  2 as well) on the second-period bias is non-monotonic, where the bias

disappears whenis either too small or too large.

Second, the impact of changes in Æ is relatively straightforward. Because it yields nodirect effect on the second-period bias, we only need to look at the indirect effect though

1 . As we have seen, an increase in Æ decreases 1 away from ~ . This in turn monotonically20decreases the second-period bias, making DM more flexible.
Finally, the impact of changes in  is somewhat more complicated, because the direct
effect can in principle go either way. As we have seen, though, the second-period bias isdecreasing in  for a wide range of parameter values. In that case, we can obtain an unambiguous prediction because both the direct and indirect effects work in the same direction.
For a sufficiently low value of , DM is perfectly flexible although it comes at the expense of
the complete lack of vision. An increase in  then unambiguously raises the second-period
bias, where DM becomes less and less flexible. We can thus summarize this finding as follows: while high self-confidence per se makes DM more visionary, it makes her less flexible inthat she sticks excessively to her initial stance.

4 Conclusion
The paper sheds light on two important aspects of dynamic decision making – vision andflexibility – and provides a framework to illustrate the workings behind these seemingly
contradictory notions. As the misalignment of incentives is a typical source of inefficientdecision making in organizations, the driving force of the model is the misalignment of incentives within oneself. In the present model, two distinct sources of intrapersonal conflicts
are merged into a single framework: on one hand, the objective and subjective selves differ
in their objectives, which eventually forces DM to bend the truth to protect her ego; on theother hand, the two selves also differ in their time horizon, thus leading to time-inconsistentobjectives and, as a direct consequence, a type of of self-control problem. Our model provides a unified framework to account for both the conformity bias and the confirmatory bias
in dynamic decision making.
As a final note, since we set up a tightly specified model to obtain clear predictions,
there are some obvious limitations of the analysis. One such limitation is the fact that weonly consider a two-period model. Although the two-period framework is just sufficient
to illuminate the two cognitive biases of our interest, an extension to a multi-period setup
would certainly yield a richer set of dynamic implications. We expect, however, that similar21

properties would eventually emerge in that framework.24 To see this, consider a three-periodcounterpart. First, in the last period, DM still has an incentive to exaggerate consistentsignals and discount inconsistent ones, although the meanings of consistent/inconcistent are
now history-dependent.25 This provides an incentive to discount the signal in the first period
to mitigate this bias. This extension to a multi-period setup, however, adds a new dimension
to the problem in the second period where both of these forces are present. It would behighly interesting to see how these opposing forces balance out in this intermediate period.

Appendix A: Proof of Proposition 2
Since

1 
= ;
 1 2
C I2 (1 + ( 1 )2 )== 1  1(1 ( 1 )2 )2 ;the first-order condition becomes( 1 ~)2 + 2 1 2 (1 + ( 1 )2) = 0:
4
1 ( 1 )2 (1 ( 1 )2)2
DefineD( ; 2 ; ; 1 ) :=4( 2 )2(1 + ( 1 )2) 1 ;2 (1 ( 1 )2 )3

so that the optimal informativeness is obtained as the following fixed point:1=~

D( ; 2 ; ; 1 ):

1 < ~ . The properties of 1 depend on how D respondto changes in exogenous parameters such as ,  2 and .
It is immediately clear from this that24

Of course, the equilibrium properties depend crucially on the minute details of the information structure,especially how the accuracy of each signal is related to the ability type. A sensible specification in a T -period
setup might have prob st =  the signal is informative;  = t + (1 t )(1 +  )=2 where t is aligned in a
non-decreasing order, i.e., 1 T
T 1 ::: 1 0. The current two-period setup is a special case of thiswith 1 = 0 and 2 = 1.
25
More precisely, they depend both on the history of observed signals and associated choices of informativeness.

f



j



 



22

g

We now examine how

1 responds to changes in , 2 and . It is easy to see that

D= > 0, implying that 1 is decreasing and the size of the bias is hence increasing in.

By the same logic, one can show that the size of the bias is increasing in  2 . The effect of is, on the other hand, more complicated. To see this, note that D= < 0 if

( 1 )2 (1 ( 1 )2) (1 + ( 1 )2)(1 4( 1 )2 ) < 0:which can be written as

1 4( 1 )2 3( 1 )4 > 0:
Since we already know that

1 < ~ , a sufficient condition for this is

1 4(~ )2 3(~ )4 > 0:
When this condition holds, the size of the bias is decreasing in .
Finally, we show that1 ! 0 as  ! 0. This is relatively straightforward sincelim D( ; 2 ; ; 1 ) = 1;

!0

for any

1 > 0. An interior solution thus fails to exist and the optimal choice is bounded at

1 = 0.
Q.E.D.

Appendix B
In the main body of the analysis, we have assumed that the subjective self’s prior expectationof the ability type coincides with its true value. This assumption not only makes the analysis
more tractable but also allows us to obtain more realistic implications since actual ability
and self-confidence are generally positively correlated.26 In principle, though, there is noconvincing reason why the prior mean must coincide with the true value. Here, we relax
this assumption to show that the main results of the paper basically go through with thisalteration to the baseline model.
Our comparative static results regarding changes in  are also valid to the extent that actual ability andself-confidence are positively correlated.
26

23

Since the subjective self is totally disinterested in period 1, the first-order condition inperiod 1 is virtually identical, so that similar conclusions would follow if the basic properties
in period 2 were to hold. Now suppose that the subjective self’s prior mean is fixed at S
which may or may not coincide with . With this differing prior, the first-order condition inperiod 2 is modified as2(2 ~C ) (11 + ( 1 ) )2 = 0;
1 2

(8)

2 1
1 ( 1 )2 = 0;
+
(


~
)
2
I
(1 1 2 )2
1 2 S ) 2

(9)

2 1
(1 + 1 2S)2for consistent signals and(1for inconsistent signals. It is evident from these that the same conclusions hold in this case as
well: consistent signals are exaggerated while inconsistent ones are discounted, and the bias
disappears as! 0 or 2 ! 0.

What remains to be seen is the impact of

1 on the optimal bias. To see this, from (8), we

obtain2 ~C = dC ( 1 ; 2 )2 b2 ( 1 ):where

dC ( 1 ; 2 ) :=1 + 1 2 :1 + 1 2 S

We need to show that the optimal bias is increasing in

1 . Taking 2 as a constant, it suffices

to show thatdb( S) b + d db2 > 0;C 
2dC db2 + dC 2 = 2dC 2
 1
d1(1 + 1 2 S)2 2 C d 1
which can be written as

2 1 2( S) + 1 + ( 1 )2 > 0:
(1 + 1 2S)2 1 ( 1 )2This condition holds if

2 1 2 ( S) > 1 , 2  > 1 ( S)2 :1 2
1 2(1 + 1 2 S)224

Similarly, it follows from (9) that

2 ~I = dI ( 1 ; 2 )2 b2 ( 1 ):wheredI ( 1 ; 2 ) :=1
1

1 2 :
1 2 S

1 , it suffices to show thatdb
(S ) b + d db2 > 0;I 
b2 + dI 2 = 2dI 2
2dI d 1
d1(1 + 1 2 S)2 2 I d 1

To show that the optimal bias is increasing inwhich can be written as

2 1 2(S ) + 1 + ( 1 )2 > 0:
(1 1 2S)2 1 ( 1 )2With some algebra we obtain(2 1 2(S ))(1 ( 1 )2 ) + (11 2 S )2 (1 + ( 1 )2 ) > 0;

which is further simplified to2 1 2 ( 1 )2(2S + ) + (1 + ( 1 2 S)2 )(1 + ( 1 )2 ) 2 1 2  > 0:This condition holds since

1 + ( 1 )2 > 2 1   2 1 2 :This shows that the optimal bias in period 2 is increasing in

1 even when the subjective

self’s prior mean diverts away from the true value. This property gives rise to the same selfcontrol problem as discussed in the main body, leading to qualitatively similar conclusions.

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0:5

1+~
2

1+
2

Figure 1: The manipulable range of the belief when s1 = 1 ( = 0:5, ~ = 0:5).

s2 = 0s2 = 1

0:5

1+ 1 
2

Figure 2: the manipulable range of the belief when s1 = 1 ( = 0:5, ~ = 0:5,29

1 = 0:8).