Answers in which people report 80% confidence. Only 65% are correct. (Lichtenstein, Fischhoff & Phillips, 1982) Answers in which people report 80% confidence;

Answers in which people report 80% confidence. Only 65% are correct.

(Lichtenstein, Fischhoff

& Phillips, 1982)Answers in which people report 80% confidence; only 65% are correct.

Calibr

ation

line

(tru

e a

ccu

racy)

(confidence)

Overconfidence

Participants answer

“trivia” questions

Report confidence

(subjective probability)

of being correct

Instructed to be

calibrated

(sometimes with

incentives)

Introduction Example Results VariantsEvolutionModel

(confidence)

Interpretation:

overestimating

accuracy of private

information

Studied in many

papers (Oskamp,

1965; …)

Recent surveys:

Griffin & Brenner

(2004), Skala (2008)

Rational Explanations

Answers in which people report 80% confidence. Only 65% are correct.

(Lichtenstein, Fischhoff

& Phillips, 1982)Answers in which people report 80% confidence; only 65% are correct.

Calibr

ation

line

(tru

e a

ccu

racy)

(confidence)

Overconfidence


3

Motivation (1)

Existing economic models assume overconfidence

Directly (Odean, 98, Gervais & Odean, 01), Sandroni & Squintani, 07)

Positive utility from good self esteem (Compte & Postlewaite, 04;

Köszegi, 06; Weinberg, 09)

3

Strategic interaction overconfidence

Risk-averse principals prefer overconfident agents


4

Motivation (2)

Existing Evolutionary foundations for overconfidence:

Group selection (Bernardo & Welch, 01): improve aggregation of

information a few overconfident agents survive

Second-best outcome; compensates another bias (e.g., excess risk

aversion): Wang (91), Blume & Easly (92), Waldman (94)

4

Gene’s interest in diversification overconfidence

First-best outcome, individual selection, everyone is overconfident


555

Contents

Introduction

Motivating example

Model

Results

Evolutionary stability

Variants and Extensions

5


6

Related Phenomena

Better than average

Over-optimism about the future

Underestimating confidence intervals

Literature: Lichtenstein et al. (1982), Soll & Klayman (2004),

Teigen & Jorgensen (2005), Svenson (1981), Alicke & Govorun (2005),

Taylor & Brown (1988)

6

Experts


7

Motivating Example

7


8

Risk-averse venture capital CEO

manages investments in his area (chooses a

startup company)

Accepted guidelines Own judgment/intuition

failure success

q (positively correlated with others)

1-q

successfailure

pi (independentof others)

1-pi

Analyst 1 Analyst n


99

Model


10

Risk-averse Principal

g1 gi:[0,1][0,1] gn

Payoffs: Agent: 1 (success) / 0 (failure)

Principal: h(#successful agents)(h’>0, h’’<0)

Stage 1:principal chooses

bias profile

Stage 2:agentsreceive signals

Private: 0<pi<1~f(p) (evaluated as gi(pi)

Public: 0<q<1~f(q) (evaluated correctly)

pi (independentof others)1-q

failure success

q (positively correlated

with others) successfailure

1-pi

Accepted guidelines (aq) Own judgment (ap)Stage 3:agentschoose actions


Intuition

Agent – only cares if he succeeds:

Dominating strategy: Choose ap iff gi(pi)>q

Bias profile uniquely determines actions

Risk-averse principal – cares for total number of successes:

Tradeoff: higher expectation lower variance

Agents with q-<pi should choose ap

Chooses overconfident agents: g(p)=p+p


- correlation between agents that choose aq

Benchmark: =1

(all agents that follow aq succeed or fail together)

Comments

Why not using monetary incentives?

Risk-neutral stock owners informal mechanisms

Correlation


Technical assumption: decreasing absolute risk aversion

13

Results

13


14

Main Result

Unique optimal bias profile exists:

Homogenous profile: i gi=g

Represents overconfidence (g (p)>p, 0<p<1)

Induces the first-best payoff

Strictly better than any other profile

Depends only on h & fp

Asymptotic result (sufficiently many agents) 14

Details

Existence

Contrary

Uniqueness


Intuition

15

Comparative Statics (1)

principal I is more risk-averse than principal II

( , ’>0, ’’<0) hires more

overconfident agents: p , g*I(p)>g*II(p)

Intuition:

More risk-aversion

Principal cares more for variance (less for expectation)

More agents should follow ap (their judgment)

Agents should be more overconfident15

I IIh h


16


If (correlation) becomes larger the principal hires more

overconfident agents

Intuition:

Higher correlation

More aggregate risk from aq (following guidelines)

More agents should follow ap

Agents should be more overconfident

16


Correlation

17


Harder tasks (accurate signals are less likely) induce

more overconfidence

Hard-easy effect (Lichtenstein, et al., 1982; Moore & Healy, 2008)

Intuition:

Principal wants agents with the most accurate private signals to

choose ap

In an harder environment, each pi is more likely to be among the

most accurate

17


Overconfidence & Evolutionary Stability

18


19

g1

Each type induces a (possibly random)

bias function

Agentsreceive signals

Private: 0<pi<1~f(pi) (evaluated as gi(pi)

Public: 0<q<1~f(p) (evaluated correctly)

Which type will survivein the long run?

pi (independentof others)

1-q

failure success

q (positively correlated

with others) successfailure

1-pi

Conformity (aq) Own judgment (ap)Each agentmakes an important decision

Payoff (fitness): Agent: H (success) / L (failure)

gi:[0,1][0,1] gn

Evolutionary Model (Only Agents)


202020

Intuition

#offspring : product of the average fitness in each generation

The type that maximizes the geometric mean of the average

fitness prevails the population (large population, long run)

Evolutionary dynamics behaves as it were a risk-averse

principal with logarithmic utility:

h(#successful agents)=ln(average fitness)

Lewontin & Cohen (1969), Mcnamara (1995), Robson (1996)

20


212121

Results (1)

In the long run all agents are overconfident

Overconfidence level depend on the potential gain

D=(H-L)/L, fp

Explains finding such as Yates et al. (2002): Different societies

present different levels of overconfidence

21


222222

Results (2)

Larger D (more important decisions) induces more

overconfidence (Sieber, 1974)

Intuition: larger D more aggregate risk in aq more overconfidence

When g(p)~ 1, p is much smaller (for large D-s)

False certainty effect (Fischhoff et al., 1977) : people are often wrong

when certain in their private information

Results hold for any CRRA utility

22


23

Variants & Extensions

Social welfare

Risk averse agents

Agents as experts

Costly private signals

Bias w.r.t. the public signal

Choosing the number of agents

Underestimating variance

Underusing base rates23

Example

k alternatives

g* interpretation


363636

Summary

Explaining overconfidence as the result of diversification

Novel evolutionary foundation of overconfidence and its

observed properties (1st best, no other bias, no group selection)

Demonstrate why principals prefer overconfident agents in

some strategic interactions

E.g., CEO and analysts in a venture capital

36

Future Research


373737

Future Research

Applying the model to voting / career-motivated experts

Noisy signals about the quality of the candidates

Each voter (also) wishes to vote correctly

Social planner wishes that most voters vote correctly

Requires relaxing a few technical assumptions:

Non-risk-averse principal (e.g., step functions in voting)

(Ex-ante) asymmetric agents

Small number of agents

More general signaling systems (p1,…,pk; q1,…,qk)37


Optimal g in the CRRA Case (with perfect correlation)

51


Hard-Easy Effect(Lichtenstein,

Fischhoff & Phillips,

1982)

Calibr

ation

line

(tru

e a

ccu

racy)

(confidence)

Hard tasks

Easy tasks

565656

Related Literature (Models of Overconfidence)

Conflict with future selves (Bénabou & Tirole ,QJE 2002)

Positive emotions improve performance / utility: Compte & Postlewaite (AER 2004), Köszegi (2006), Weinberg (2009)

Taking credit for lucky successes (Gervais & Odean, 2001)

Apparent overconfidence due to unbiased random errors Van Den Steen (AER 2004), Moore (2007), Benoit & Dubra (2008)

Influence of overconfident agents Odean (JoF 1998), Sandroni & Squintani (AER 2007)

Evolutionary foundations: Bernardo & Welch (2001), Blume & Easly

(1992), Wang (1991), Waldman (AER 1994)56


57

g1 gi:[0,1][0,1]

gn

Stage 1:principal chooses

bias profile

Stage 2:agentsreceive signals

Private: pi~f(pi) (evaluated as gi(pi)

Public: q~f(p) (evaluated correctly)

pi (independentof others)1-q

failure success

successfailure

1-pi

Accepted guidelines (aq) Own judgment (ap)Stage 3: agentschoose actions

q

failure success

Common lottery

1 q 1 qIndependent lotteries


Total successprobability: q

Documents

Answers in which people report 80% confidence. Only 65% are correct. (Lichtenstein, Fischhoff & Phillips, 1982) Answers in which people report 80% confidence;