1. 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

2. 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.

3. Voting dec° Hyp. Decision Behaviour Non-EU Examples 2 Hypotheses considered here: - Preference for one candidate - Cost of voting - Probability of being decisive ε = ε 1 + ½ ε 2  ε 1 : equality if no vote  ε 2 : equality if vote Hypotheses NOT considered: - Taste for voting - Game theory solution  Individual decision framework

4. Voting dec° Hyp. Decision Behaviour Non-EU Examples 3 Owen& Grofman (84):

5. Voting dec° Hyp. Decision Behaviour Non-EU Examples 4 EU : V  A  (1-ε).C C Impossible since ε≈0 Paradox of not voting (PNV) Downs 57

6. 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

7. 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)...

8. 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

9. Voting dec° Non-EU Regret th. Prospect th. CC th. Examples 8 Ferejohn & Fiorina (74) Loomes & Sudgen (82) Regret theory : EU + regret V  A  4.0015 + 0.9997R(-1) + 0.0003 R(9) > 4.9985 + 0.9997R(1) + 0.0003 R(-9) H1, not H2: impossible

10. Voting dec° Non-EU Regret th. Prospect th. CC th. Examples 9 p w(p) 1 1 0 Kahneman & Tversky (79) Quiggin (82) Prospect theory : V  A  w(0.50015).9 - w(0.49985) > w(0.49985).10 H2, not H1: impossible

11. 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 Weighted average of : EU + objection V  A  µ.4.0015 + (1-µ).9 > µ.4.9985 + (1-µ).0, 0<µ≤1  µ<0.9003 H1 and H2: possible

12. 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

13. 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.

14. Voting dec° Non-EU Examples 13

15. THANK YOU for your attention ! Questions? Voting dec° Non-EU Examples 14