approval voting :

Approval Voting :Approval Voting :

JF LaslierJF Laslier

CNRS, PolytechniqueCNRS, Polytechnique

LogiCCC, Amsterdam 2010LogiCCC, Amsterdam 2010

Theory and Experiments

What is Approval Voting ?What is Approval Voting ?

A method for electing one candidate.A method for electing one candidate.

Each voter can vote for (“approve”) Each voter can vote for (“approve”) as many candidate he or she wishes.as many candidate he or she wishes.

The candidate with most approvals is The candidate with most approvals is elected.elected.

Introduction

Where does it come from ?Where does it come from ?

Long history, but not in use in Long history, but not in use in political elections.political elections.A lot of academic work after A lot of academic work after Steve Steve Brams and Peter Fishburn’s book in Brams and Peter Fishburn’s book in 19831983..Controversies in voting theory Controversies in voting theory community about sincerity.community about sincerity.

Introduction

Today’s TalkToday’s Talk

Survey of recent results.Survey of recent results.See a variety of methods to study See a variety of methods to study this topic.this topic.Check relation science/application.Check relation science/application.See forthcoming book See forthcoming book JFL and Remzi JFL and Remzi Sanver (Eds.) “Handbook on Approval Sanver (Eds.) “Handbook on Approval Voting”Voting”..

Introduction

Many facets of one object : Many facets of one object : 10 topics10 topics

1.1. History: ancient and modern.History: ancient and modern.2.2. Theory of dichotomous preferences.Theory of dichotomous preferences.3.3. Theory of voter’s strategic behavior.Theory of voter’s strategic behavior.4.4. Computational aspects.Computational aspects.5.5. Simulations exercisesSimulations exercises6.6. Laboratory experimentsLaboratory experiments7.7. Field experimentsField experiments8.8. Theory of electoral competitionTheory of electoral competition9.9. Meaning for individual and for societyMeaning for individual and for society10.10. Electing committeesElecting committees

Introduction

Today’s Talk: PlanToday’s Talk: Plan

1.1. Experimental observations.Experimental observations.

2.2. Voter’s behavior in theory.Voter’s behavior in theory.

3.3. Consequences for electoral Consequences for electoral competition.competition.

Introduction

1. Experiments1. Experiments

1.1. In situ experiments1.2. Laboratory experiments

1. Observations

1.1 1.1 In situIn situ observations observationsSCW council election, 1999, SCW council election, 1999, Brams and Brams and Fishburn, Saari, Laslier (SCW 2001, 2003)Fishburn, Saari, Laslier (SCW 2001, 2003)..

Presidential election, France, 2002, Presidential election, France, 2002, Balinski, Balinski, Laraki, Laslier and Van der StraetenLaraki, Laslier and Van der Straeten..

Presidential election, France, 2007, Presidential election, France, 2007, Baujard Baujard and Igersheimand Igersheim..

State election in Hesse, Germany , 2008, State election in Hesse, Germany , 2008, Allos-Ferrer and GranicAllos-Ferrer and Granic..

1.1 In situ obs.

In situIn situ obs. during political elections obs. during political elections

Participating has no direct consequence. Somehow similar to an opinion survey but:Uses the decorum and etiquette of true election: Open participation, anonymity and confidentiality. Different from pool surveys and laboratory. Presented as a scientific test of a voting rule, not an exit pool.

1.1 In situ obs.

Problems with the Problems with the in situin situ method methodNo control of the political supply. Similar to comparative analysis but no variation and thus no comparison !No control of the sample. Protocol imposes that the only selection is self-selection.Each observation is relatively poor: one anonymous ballot from a pooling station. No other individual characteristic known. (Baujard and Igersheim asked questionnaires.)Voter’s understanding. If the voting rule is complex, some voters may not know how the ballots will be counted.Potential ethical problems if a voter understands incompletely or even wrongly the voting rule, or the goal of the experiment.

1.1 In situ obs.

Voters completing the taskVoters completing the taskAll voters understand they are asked to make marks, give points, or chose adjectives. In many cases, sufficient to say “Do you understand ? YES ! ”Participants naturally understand the logic of addition: “give points, the candidate with the largest number of points wins.”A reasonable solution: to explain to the voters that they are not asked to evaluate the candidates but to give points to the candidates.No problem with Approval Voting.

1.1 In situ obs.

Voters using the voting ruleVoters using the voting ruleVoters may well understand how to complete the task, but fail to understand how ballots will be counted.For instance ballots in the form of preferences can be counted in many different ways. (See the whole Arrovian social choice !)But again: no problem with Approval Voting. Complex rules may be tested in the lab.

1.1 In situ obs.

Participation ratesParticipation ratesParticipation rates are very high compared to exit pools.Up to 92.4% in the small village of Gy-les-Nonains (France, 2002).A positive social event.Know from Gerber, Green, Larimer APSR 2008 that social pressure is a very important determinant of turnout. Positive social pressure seems high during these experiments, in particular in some places.

1.1 In situ obs.

Participation biasParticipation bias

We know that bias may be very important.Example: Inverse correlation between participation and vote for Le Pen at the official vote in Orsay, France 2002.Correcting these bias is possible (Laslier and Van der Straeten Revue Francaise de Science Politique 2004) by comparing different voting posts, but difficult.

1.1 In situ obs.

Lessons from Lessons from in situin situ experiments experiments (1/5)(1/5)

A. Public reaction to experimentation in political science. It is interesting to know how the public reacts to experimentation about politics and elections. In that respect, experiments are very successful. People are curious about it and ready to take part. Show very little hostility towards the idea of experimenting in politics.

1.1 In situ obs.

B. Understanding voting rules.

People who accept to take part in such an experiment understand the instructions, with one possible difficulty, in some cases, with incomplete ballots. But we do not learn from these experiments whether they understand the way ballots are counted. This is a problem for complex evaluative or ranking ballots; no problem for AV.

1.1 In situ obs.



C. Learning about voter behavior. The theory of how people vote under different voting rules is far from complete. One goal of the experiments should be to observe voters’ behavior at the individual level. The experimental elections in situ are not well suited for this goal because we cannot relate to the voter’s vote any personal characteristics: her/his true vote, her/his true ranking (or evaluation) of candidates, her/his social and economic characteristics...

1.1 In situ obs.


D. Learning about aggregate results. Many authors insist on the fact that different voting rules may yield different outcomes. Yet, little empirical evidence is provided to support this idea on large scale elections. After eliminating (important) sample bias Laslier and Van der Straeten, and Baujard and Igersheim have shown that:Approval voting and 0 − 1 − 2 range voting tends to favor consensus candidates.

1.1 In situ obs.


E. Learning about actual (French) politics. The low scores show that even elected candidates (Chirac, Sarkozy) do not have huge support in the population. Under AV, no candidate is approved by half of the electorate. More detailed information can be obtained on the structure of the political space. With AV we know how many voters approved each group of candidates. We can infer information on “correlations” between candidates.

1.1 In situ obs.

1.2. Laboratory observations1.2. Laboratory observations

1.2.1. The split majority case.1.2.2. The divided society case.1.2.3. The single-peaked case.

1.2 Laboratory obs.

1.2.1 1.2.1 The split majority case The split majority case (1/3)(1/3)

Forsythe, Myerson, Weber and Rietz, Forsythe, Myerson, Weber and Rietz, SCW 1993, IJGT 1996SCW 1993, IJGT 1996. .

Participants are voters, their Participants are voters, their payoffs depends only on the payoffs depends only on the elected candidate and the elected candidate and the participant type. participant type.

1.2 Laboratory obs. 1.2.1 Split Majority


The The split majoritysplit majority problem: problem: Incentive structure is defined by Incentive structure is defined by three groups in the electorate. One three groups in the electorate. One minority group and one majority minority group and one majority made of two groups. made of two groups.

Three candidates: the minority Three candidates: the minority supports one; the majority is split supports one; the majority is split between two others. between two others.



They demonstrate the importance They demonstrate the importance of of informationinformation (previous elections, (previous elections, pools)pools)

They show that one-round plurality They show that one-round plurality voting may elects the Condorcet voting may elects the Condorcet loser.loser.

They show that They show that AV and BordaAV and Borda tends to avoid electing the tends to avoid electing the Condorcet loser.Condorcet loser.


1.2.2 1.2.2 The divided society case The divided society case (1/2)(1/2)

Altman, Baron and Kroll Altman, Baron and Kroll Journal of Journal of Conflict ResolutionConflict Resolution 2005 2005 studied the studied the ddivided societyivided society problem. problem.There are two groups, There are two groups, AA, , BB, in the , in the society, of equal size, and three society, of equal size, and three options.options.Two options, Two options, aa, , bb, clearly favor , clearly favor groups groups AA, , BB. The third option, . The third option, cc, is , is a second best for everyone, and a second best for everyone, and the social optimum.the social optimum.

1.2 Laboratory obs. 1.2.2 Divided Society

1.2.2 1.2.2 The divided society case The divided society case (2/2)(2/2)

The experiment is made on the The experiment is made on the internet (with no incentives) and in internet (with no incentives) and in the lab. the lab.

They show that AV, contrary to They show that AV, contrary to one-round plurality favors the one-round plurality favors the consensual outcomeconsensual outcome..

The reason is that some voters The reason is that some voters approve their second best.approve their second best.

1.2 Laboratory obs. 1.2.2 Divided Society

1.2.31.2.3 The single-peaked case The single-peaked case (1/6)(1/6)

Experiments by Experiments by Blais, Laslier, Blais, Laslier, Laurent, Sauger and Van der Straeten Laurent, Sauger and Van der Straeten (2008)(2008). .

Preference profile given by the Preference profile given by the one-dimensional euclidean modelone-dimensional euclidean model..

21 voters, 5 candidates.21 voters, 5 candidates.

1.2 Laboratory obs. 1.2.3 One-dimensionnal society

Single-peaked case Single-peaked case (2/6)(2/6) positions of the 5 candidatespositions of the 5 candidates

0 1 6 10 14 19 20

A B C D E

These positions remain the same These positions remain the same through the whole session.through the whole session.


Single-peaked case Single-peaked case (3/6)(3/6)

subjects’ positionssubjects’ positions

21 subjects in 21 positions: 1 voter in position 0, 1 voter in position 1, …, 1 voter in position 20.The distribution of positions is known to all voters.Positions are randomly assigned

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1 6 10 14 19


Single-peaked case Single-peaked case (4/6)(4/6) PayoffsPayoffs

Depend on the Depend on the distance between the distance between the subject’s position and the elected subject’s position and the elected candidate’s positioncandidate’s position on the axis. on the axis.

The smaller this distance, the higher the The smaller this distance, the higher the payoff.payoff.

Subjects receive Subjects receive 20 Euros minus the 20 Euros minus the distancedistance between the subject’s position between the subject’s position and the elected candidate’s position. (At and the elected candidate’s position. (At the end of the session, one election was the end of the session, one election was randomly drawn to determine payoffs.)randomly drawn to determine payoffs.)


Single-peaked case Single-peaked case (5/6)(5/6) winners (last two elections)winners (last two elections)

One One roundround

Two Two roundround

AVAV STVSTV

CC 52 %52 % 50 %50 % 100 %100 % 00

B or DB or D 48 %48 % 50 %50 % 00 100 %100 %

A or EA or E 00 00 00 00

totaltotal 4646 4646 1414 88


Single-peaked case Single-peaked case (6/6)(6/6) approval votingapproval voting

Strategic model: Strategic model: approve approve candidates who are candidates who are preferred to the preferred to the leader, compare leader, compare leader to main leader to main challenger.challenger.

Correct Correct predictionspredictions: : 1931/22051931/2205=88%.=88%.

Vote Vote = 1= 1

Vote Vote = 0= 0

PredPred=1=1

772772 183183 955 955 (.43)(.43)

PredPred=0=0

9191 11591159 1250 1250 (.67)(.67)

863 863 (.39)(.39)

1342 1342 (.61)(.61)

2205 2205 (1.)(1.)


Conclusions from Conclusions from lab. experimentslab. experiments

At the aggregate level: AV tends to At the aggregate level: AV tends to elect elect consensual outcomesconsensual outcomes and and Condorcet winnersCondorcet winners

At the individual level: the At the individual level: the strategic strategic theorytheory (best response to (best response to anticipations) works well.anticipations) works well.

No contradiction with No contradiction with sincere votingsincere voting..

1.2 Laboratory obs.

2. Theory of individual voting2. Theory of individual voting

2. Theory of voting

Theory of individual votingTheory of individual voting

Main controversies about “sincere”, “honest”, and “strategic” voting.Controversy useless since strategic voting is sincere under AV except in some (strange!) circumstances.

2. Theory of voting

Sincere votingSincere votingSincerity defined following Brams-Fishburn and others: If I approve a and I strictly prefer b to a then I also approve b.Leaves as many possibilities as candidates Sincere and undominated voting still leaves too many possibilities for predictions (Brams, Sanver 2008).

2. Theory of voting

Strategic votingStrategic votingStrategic voting defined as rational response to belief.Problem if belief exact: often, everything is a best response, and moreover:DeSinopoli, Dutta and Laslier (IJGT 2006) found examples of stable equilibria with insincere voting and examples with Condorcet-inconsistency.

2. Theory of voting

Myerson-Poisson modelMyerson-Poisson modelOne needs refinements and careful study of pivotal events (Myerson Weber APSR 1993).Myerson (JET 2002) introduced specific uncertainty on the number of voters called Poisson voting games and studies large electorates.Nunez (2009) provides examples of Condorcet-inconsistency in AV Myerson-Poisson equilibrium.

2. Theory of voting

Strategic voting: the Leader rule Strategic voting: the Leader rule (1/5)(1/5)

Laslier (J. Th. Pol. 2009) considers large electorates with:Small probability of material mistake when recording each vote.Voters neglect 3-way ties in front of 2-way ties.

2. Theory of voting


Result:Result:Individual behavior = response to the anticipated relative scores.Approve the candidates you prefer to the leading candidate c1.

Approve c1 herself by comparison with the main challenger c2.

2. Theory of voting


This behavior produces a sincere ballot.It is obtained by lexicographic maximization (hierarchical reasoning). Plausible / cognitive psychology.It well explains individual behavior in lab experiments.

2. Theory of voting


Equilibrium results if there is a Condorcet winner :There exist one and only one equilibrium.The equilibrium is pure (and strict). The Condorcet winner is elected. The score of any other candidate is its majoritarian score against the winner.The winner is the only candidate approved by half of the voters.

2. Theory of voting


Equilibrium result if there is no Condorcet winner :There is no pure equilibrium.

2. Theory of voting

3. Theory of electoral competition3. Theory of electoral competition

3.1. Classical model: exogeneous candidates.

3.2. Citizen-candidate model.

3. Electoral compet.

3.1. Classical electoral competition 3.1. Classical electoral competition (1/3)(1/3)

Framework :Set X of policies, or political positions.Set C of candidates.Voters have preferences over policies.Candidates choose positions x(c)Voters vote, one candidate elected.Candidates only want to be elected.

3.1 Classical elect. compet.


Result 1Result 1 (Laslier and Maniquet 2010) :

If x* is a Condorcet winner policy, then the situation in which all candidates choose x* is a equilibrium of the electoral competition game. If x* is a strict Condorcet winner then the equilibrium is strict.



Result 2Result 2 (Laslier and Maniquet 2010) :

In the single-peaked model: (i) The situation in which all parties choose the median policy is a strict equilibrium of the electoral competition game. (ii) It is the only equilibrium.


3.2. Citizen-candidate model 3.2. Citizen-candidate model of electoral competition of electoral competition (1/2)(1/2)

Framework :Framework :Electoral competition similar to the classical one but: At the first stage, each citizen chooses whether or not to enter the electoral race as a candidate at a >0 cost.Candidates are thus policy-motivated.

3.2 Citizen-candidate model

3.2. Citizen-candidate model 3.2. Citizen-candidate model of electoral competition of electoral competition (2/2)(2/2)

Results (Results (Dellis and Oak GEB 2005, Dellis 2009Dellis and Oak GEB 2005, Dellis 2009):):

In a single-peaked preference model, equilibria in relatively sincere strategies and without spoiler candidates always generate outcomes close to the median voter. Approval voting satisfies Duverger’s Law in the sense that there are at most two winning positions.

3.2 Citizen-candidate model

Merci de Merci de votre attention.votre attention.

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approval voting :

Documents

approval voting

situ experiments1

voting theory community

voters behavior

voting rulevoters

taskall voters

situ methodno control

presidential election