Strategic voting in run-off elections Jean-François L ASLIER (Ecole Polytechnique, France) Karine V...
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Transcript of Strategic voting in run-off elections Jean-François L ASLIER (Ecole Polytechnique, France) Karine V...
Strategic voting in run-off elections
Jean-François LASLIER (Ecole Polytechnique, France)
Karine VAN DER STRAETEN
(Toulouse School of Economics, France)
PRELIMINARY VERSION
Social Choice and Welfare, Moscow, July 21-24 2010
Run-off elections: definition
• On the first round, voters vote for one candidate.
- If one candidate gets more than 50% of the votes, he is elected.
- If not, the two candidates with the highest two numbers of votes proceed to a second round.
• On the second round (if any), voters vote for one candidate.
The candidate with the highest number of votes is elected.
Run-off elections: Properties• Rarely used in legislative elections, but quite
common in presidential elections
• Aggregate properties?
Duverger: Multiparty system (/ plurality where two parties dominate)
• Voter behavior?
- Duverger: sincere
- Cox: strategic (instrumental voters reasoning on pivot-events), three candidates only get votes
Are voters strategic?
• Our focus here.
• Why is it important?
Consequences on the party structure: affects the number of candidates receiving votes
Qualitative consequences on who gets elected
Ex.: Single-dimension politics with three candidates: a centrist Condorcet winner “squeezed” between a Condorcet loser on the left, and a rightist candidate.
With sincere voting, the rightist candidate wins; with strategic voting, the centrist may win.
Empirical evidence on strategic voting in runoff elections
• Election or survey data: pb = to compute strategic recommendation, one needs a lot of information about a voter’s preferences and beliefs
• Lab experiments data: Blais et al. (SCW, forth.)
- in a single-dimension five-candidate setting, voters neither (fully rational) strategic, nor sincere
- behavior best explained by a top-three heuristics, whereby voters vote for their preferred candidate among the three candidates expected to get the most votes
This talk
• Part 1: Typology of strategic reasoning
Describe possible patterns of strategic reasoning in run-off elections
• Part 2: Experiment
A lab experiment to test whether subjects are able to perform any of the patterns of the strategic reasoning
• Part 3: Analysis
Analysis of the experimental data with the help of the typology
Part 1: Typology of strategic reasoning in run-off elections
• Being strategic in run-off elections entails different kinds of reasoning, more or less complex.
• We propose here a typology of such types of reasoning, based on the different pivot-events in which the voter may happen to be
When is a voter pivotal on 1rst round?A voter is pivotal if other voters’ votes are such that
one of the following two conditions holds:
- Condition 1: one candidate receives an absolute majority minus one vote: by voting for this candidate, the voter can make him a 1rst-round winner
- Condition 2: no candidate gets an absolute majority and the vote margin between the 2nd and the 3rd ranked candidates is at most one vote: by voting for one of these candidates, the voter can make him be part of the run-off
When is a voter pivotal on 1rst round?A voter is pivotal if other voters’ votes are such that
one of the following two conditions holds:
- Condition 1: one candidate receives an absolute majority minus one vote: by voting for this candidate, the voter can make him a 1rst-round winner TYPE 1
- Condition 2: no candidate gets an absolute majority and the vote margin between the 2nd and the 3rd ranked candidates is at most one vote: by voting for one of these candidates, the voter can make him be part of the run-off
Condition 2: Run-off pivotAssume some candidate, say A is leading (with no
majority), followed by B and C at equality
If the voter votes for B: run-off (AB), with payoff u(A)+Pr[B wins/(AB)] × [u(B)-u(A)]
If votes for C: u(A)+Pr[C wins/(AC)] × [u(C)-u(A)]
If votes for any other candidate: run-off (AB) with probability ½ and a run-off (AC) with proba ½
→ Optimal decision: voting B or C, depending on the utility derived from the election of each candidate, and the relative strength of the follower candidates B and C in case of a run-off against leader A
If
Run-off pivot: comparing (AB) and (AC)If votes for B: u(A)+Pr[B wins /(AB)] × [u(B)-u(A)]
If votes for C: u(A)+Pr[C wins/(AC)] × [u(C)-u(A)]
Condition “equal strength”: Both followers are equally strong run-off candidates against A
Recommend.: Vote for the preferred follower TYPE 2
Condition “different strength”: One follower is a stronger run-off candidate against A
Recommend.: Vote for stronger run-off candidate if he is preferred to A TYPE 3
and for the weaker otherwise TYPE 4
Part 2: The experiment• Designed to test whether subjects follow the
strategic recommendations described above• Groups of 21 voters (students) acting as voters• Incentive structure mimics one-dimensional politics
with 3 or 5 candidates, with different candidate positions
Positions of the 21 voters
Left-right axis labelled from 0 to 20.
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
Positions of the candidates
(EL) L C R (ER)
Profile I / 4 11 13 /
Profile I bis 1 4 11 13 20
Profile II / 3 8 15 /
Profile II bis 0 3 8 15 20
The payoffs • Depend on the distance between the subject’s
position and the elected candidate’s position on the axis.
• The smaller this distance, the higher the payoff.• Subjects receive 20 euros minus the distance
between the subject’s position and the elected candidate’s position.
• (At the end of the session, one election was randomly drawn and used to determine payoffs.)
Timing of a session• Explain the incentive structure and the voting rule• Series of four elections where positions of the
candidates and voters’ preferences remain constant; after each election, the results of the election are publicly announced
• After each series of 4 elections is completed, voters draw a new position, and the profile of candidates is changed
• Complete information setting = distribtuion of voter positions is known, as well as candidate positions
• So far, 5 sessions in Paris
Part 3: Analysis Computation of the strategic recommendation • For each voter in each election, compute her best
response against other voters’ votes.
• Assumptions:
- Utility = payoff
- Beliefs = The voter correctly anticipates other voters’ behavior, but assumes some possible (small) mistakes – “trembling hand assumption”, that yields unique strategic predictions even when the election is not so close that a single vote can indeed make a difference
Does the strategic recommendation coïncide with actual vote?
• Preliminary results
• Focus on three candidates elections
• Does the strategic recommendation coïncide with actual vote? Yes in 68% of the cases
Performance of the strategic model by type
• Does the performance of the strategic model vary across types?
• For each voter in each election, trace which type of reasoning the voter needs to make to decide for which candidate to cast a vote
Performance of strategic model by type
Type Type 1 Type 2 Type 3 Type 4
Condition Direct pivot
Run-off pivotEqual strengthL or C leaders
Run-off pivot≠ strengthR leaderC preferred to R
Run-off pivot≠ strength M leaderR preferred to C
Nb of cases 314 178 159 42
Among which % of correct predictions
80% 65% 62% 12%
Performance of the sincere model of individual behavior
• The strategic recommendation coïncides with actual vote in 68% of the cases
• To be compared with the sincere behavioral model, whereby voters simply vote for the candidate yielding the highest payoff if elected, which correctly predicts vote in 76% of the cases
Conclusion
• In a lab experimental setting, we test strategic voting in run-off elections
• In the three-candidate setting, little strategic voting is observed
• Some recommendations of the strategic model are followed: e.g. “Vote for a candidate that might be a first-round winner”
• But others are not: e.g. “Vote for a weak candidate which might be more easily defeated”
Next steps
• Extend the analysis to the five-candidate elections
• Run more sessions (5 more in Montreal are scheduled)
• Correlate strategic voting with measures of cognitive skills
Typology of strategic reasoningType 1 Type 2 Type 3 Type 4
Direct pivot Run-off pivot
Equal strength
Run-off pivot
≠ strength
Stronger challenger preferred to leader
Run-off pivot
≠ strength
Leader preferred to stronger challenger
Vote for leader if preferred to first follower
Vote for the preferred follower
Vote for the stronger run-off challenger
Vote for the weaker run-off challenger
Typology in profile IType 1 Type 2 Type 3 Type 4
Direct pivot Run-off pivotEqual strength
Run-off pivot≠ strengthStronger challenger preferred to leader
Run-off pivot≠ strengthLeader preferred to stronger challenger
Any configuration
mM~C
Cm~M
Mm~C
Mm~C
Vote for the leader if he is preferred to immediate follower
m supporters vote C
M supporters vote M
C supporters vote m (or M if C leader & m least preferred candidate)
m and C supporters vote C
M supporters vote m
Performance of strategic model by typeType Type 1 Type 2 Type 3 Type 4Condition Direct pivot Run-off pivot
Equal strengthm or C leader
Run-off pivot≠ strengthM leader,C preferred to M
Run-off pivot≠ strength M leaderM preferred to C
Nb of cases 314 178 159 42
Among which % of correct predictions
80% 65% 62% 12%
Nb of cases where strategic rec. sincere
231 159 81 0
Among which % correct 93% 70% 93% /
Nb of cases where strategic rec. non sincere
83 19 78 42
Among which % correct 46% 21% 31% 12%