Why do rational people vote

in large elections with costs to vote?

Serge Blondel (GRANEM Univ. Angers & INH, CES)

Louis Lévy-Garboua (CES University Paris 1)

IAREP-SABE 08 Rome

Voting dec°

Non-EU

Examples

1

This result has not changed the behavior of people for who voting is a citizen obligation because this is the foundation

of a democracy.

American presidential election Bush-Gore:

each vote in Florida has counted.This issue is very rare, but this elcetion has recalled that it is possible.

We will study here the vote as a decision, as an alternative to abstention.

Voting dec°

Hyp.

Decision

Behaviour

Non-EU

Examples

2

Hypotheses considered here: - Preference for one candidate- Cost of voting - Probability of being decisive ε = ε1 + ½ ε2

ε1 : equality if no vote ε2 : equality if vote

Hypotheses NOT considered:- Taste for voting- Game theory solution Individual decision framework

Voting dec°

Hyp.

Decision

Behaviour

Non-EU

Examples

3

Owen& Grofman (84):

Voting dec°

Hyp.

Decision

Behaviour

Non-EU

Examples

4

EU : V A (1-ε).C < ε.(B-C) ε.B > CImpossible since ε≈0

Paradox of not voting (PNV) Downs 57

N o t d e c i s i v e D e c i s i v e

V i c t o r y D e f e a tq 1 - q - ε ε

A B 0 0

V B - C - C B - C

Voting dec°

Hyp.

Decision

Behaviour

Non-EU

Examples

5

Observed behaviours:- People do vote- The rate of participation increases with

the stake of the election- The rate of participation increases with

the uncertainty of the election

Ile-de-France - 2001

45%

50%

55%

60%

65%

70%

75%

45% 50% 55% 60% 65% 70% 75%

Rate of participation

Per

cen

tage

sco

re o

f th

e w

inn

er

Voting dec°

Non-EU Regret th.

Prospect th.

CC th.

Examples

6

=> non-EU theories (Starmer 2000): related to the previous results, not the PNV.

Paradoxes and anomalies of EU:- Gambling and insurance (Friedman &

Savage, 1948) - Allais paradox (Allais, 1953)- Preference reversal phenomenon

(Lichtenstein & Slovic, 1971)- Reflection effect (Kahneman & Tversky,

1979)...

Voting dec°

Non-EU Regret th.

Prospect th.

CC th.

Examples

7

Two hypotheses ignored by EU:H1: utility depends of the outcome

and the outcome in the alternative decision

H2: ε should be overestimated

N= 30 millions and q=50% => ε = 0.03%We pose:- B = 10- C = 1

N o t d e c i s i v e D e c i s i v e

V i c t o r y D e f e a t4 9 . 9 8 5 % 4 9 . 9 8 5 % 0 . 0 3 %

A 1 0 0 0

V 9 - 1 9

Voting dec°

Non-EU Regret th.

Prospect th.

CC th.

Examples

8

Ferejohn & Fiorina (74)Loomes & Sudgen (82)

Regret theory : EU + regretV A 4.0015 + 0.9997R(-1) + 0.0003 R(9) > 4.9985 + 0.9997R(1) + 0.0003 R(-9)

H1, not H2: impossible

N o t d e c i s i v e D e c i s i v e

V i c t o r y D e f e a t4 9 . 9 8 5 % 4 9 . 9 8 5 % 0 . 0 3 %

A 1 0 ( + 1 ) 0 ( + 1 ) 0 ( - 9 )

V 9 ( - 1 ) - 1 ( - 1 ) 9 ( + 9 )

Voting dec°

Non-EU Regret th.

Prospect Prospect th.th.

CC th.

Examples

9

N o t d e c i s i v e D e c i s i v e

V i c t o r y D e f e a t4 9 . 9 8 5 % 4 9 . 9 8 5 % 0 . 0 3 %

A 1 0 0 0

V 9 - 1 9

p

w(p)

1

10

Kahneman & Tversky (79)Quiggin (82)

Prospect theory :V A w(0.50015).9 - w(0.49985) >

w(0.49985).10

H2, not H1: impossible

Voting dec°

Non-EU Regret th.

Prospect th.

CC th.

Examples

10

Cognitive consistency theory – Lévy-Garboua 99: decision in two steps

1/EU maximisation 2/ Focus on the objection to EU

N o t d e c i s i v e D e c i s i v e

V i c t o r y D e f e a t4 9 . 9 8 5 % 4 9 . 9 8 5 % 0 . 0 3 %

A 1 0 0 0

V 9 - 1 9

Weighted average of : EU + objectionV A µ.4.0015 + (1-µ).9 > µ.4.9985 + (1-µ).0 , 0<µ≤1

µ<0.9003

H1 and H2: possible

Voting dec°

Non-EU Regret th.

Prospect th.

CC th.

Examples

11

General problem:V A µ.(εB-C) + (1-µ).(B-C) > 0

Prob (V A):- Increases with B- Decreases with C - Increases with ε- Decreases with µ

An “objection” to this theory: ε has a negligeable influence on the criterion. The impact of ε is marginal in relation with B,

C and µ. The weight of the objection is independent

from ε

N o t d e c i s i v e D e c i s i v e

V i c t o r y D e f e a tq 1 - q - ε ε

A B 0 0

V B - C - C B - C

Voting dec°

Non-EU Regret th.

Prospect th.

CC th.

Examples

12

V A µ.(εB-εC-(1-ε)C) + (1-µ).(B-C) > 0

(1-µ(1-ε)).(B-C) + µ.(1-ε)(-C) > 0

“w(1-ε)” “w(ε)”

The cognitive consistency theory explains the PNV and also the main paradoxes and anomalies of EU with only one extra parameter.

Voting dec°

Non-EU

Examples

13

THANK YOU for your attention !Questions?

Voting dec°

Non-EU

Examples

14