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Rankings matter even when they shouldn't: bandwagone�ects in two-round elections
Vincent Pons (Harvard Business School)Clémence Tricaud (Ecole Polytechnique)
12 October 2017
Motivation
In indirect democracies, representatives vote on behalf of the people.In theory, their representativeness comes from being elected.
In practice, who gets elected depends on the behaviors of1 candidates/parties: decision to run, to strike an alliance2 voters: turnout, vote choice
In turn, voters and candidates' behavior depends on what they thinkothers will do
Understanding how political agents form their beliefs and make theirdecisions is key to understanding how democracy works
Research question
Polls and past results play an important role in informing voters andcandidates about others' preferences and strategy
This paper
I focuses on a speci�c piece of information: rankingsI isolates the impact of rankings (controlling for vote shares), using a
RDD in two-round elections
Rankings may a�ect behaviors, through
I coordinationI bandwagon
Research questions: How much do rankings matter and a�ectcandidates and voters' behaviors? Do their e�ects re�ect strategiccoordination or behavioral mechanisms?
Empirical strategy
2-round elections:
I Only one week between roundsI First round results work like a �super poll�: provide a (noisy) signal on
aggregate voters' preferencesI Up to 3 or 4 candidates can qualify for the 2nd round
Isolate the e�ect of 1st round rankings on 2nd round outcomes (running,winning, vote share)
I e�ect of being labeled 1st instead of 2nd (1vs2)I e�ect of being labeled 2nd instead of 3rd (2vs3)I e�ect of being labeled 3rd instead of 4th (3vs4)
Empirical strategy:
I RDDs on the vote share di�erence between the 1st and 2nd / 2nd and3rd/ 3rd and 4th
I Compare second round outcomes for candidates just below threshold(ranked 2nd (resp 3rd, 4th)) and just above (ranked 1st (resp 2nd, 3rd))
Contributions
1 Estimate the e�ects of rankings
I short time span (1 week) between 1st and 2nd rounds � helps isolatingthe direct e�ect of rankings on behaviors
I up to 3 or 4 candidates can qualify for the 2nd round � we canmeasure the e�ect of being labeled 1st, 2nd, or 3rd
I we �nd large e�ects of arriving 1st, 2nd, or 3rd in the 1st round onrunning and winning in the 2nd round
2 Disentangle underlying mechanisms
I we compare elections where 3 candidates or more quali�ed for the 2nd
round (and rankings can be used to coordinate) to elections where only2 candidates quali�ed (and there is no need for coordination)
I large e�ects even when only 2 candidates, driven by
F voters (bandwagon e�ect)F and candidates (the lower-ranked candidate often drops out when
she is of the same orientation as the other one)
Partial literature review
Rankings e�ects on voters' behavior
I 1vs2: Evidence of incumbency e�ects using RDD (e.g., Lee 2008;Eggers et al 2015)
F But cannot distinguish the e�ect of holding o�ce and candidatesselection e�ects from the e�ect of ranking
I 2vs3: Evidence showing that voters coordinate based on rankings
F Anagol and Fujiwara (2016): evidence of runner-up e�ect usingRDD across elections - but cannot fully isolate the coordinationmechanism from other things taking place between elections andfrom behavioral mechanisms
Rankings e�ects on parties/candidates' behavior
I In open-list systems, rankings in preference votes a�ect politicians'promotion within their party
F Folke et al. (2015) in Sweden and BrazilF Meriläinen and Tukiainen (2016) in Finland
Partial literature review
Evidence of behavioral e�ects
I Kiss and Simonovitz (2014): observational evidence of bandwagone�ects using 2-round elections
I Empirical and experimental work showing that voters are motivated inpart by a desire to vote for the winning candidate (Bartels 1985; Niemiand Bartels 1984)
I �Over-report for the winner� in post-electoral surveys (Wright 1993;Atkeson 1999)
I Models including voters' utility to vote for the winner (e.g., Hinich1981; Callander 2007, 2008)
Evidence of rank heuristic in other contexts
I Hartzmark (2014): e�ect of assets rankings on trading behaviorI Pope (2009): impact of hospital rankings on the number of patientsI Brankay (2012): e�ect of communicating rankings on employees' sales
performance
Outline
1 Research question and strategy
2 Setting and empirical strategy
3 Main resultsImpact on winningImpact on runningImpact conditional on running
4 MechanismsImpact depending on political orientationsCoordination?Bandwagon e�ect?
5 Conclusion
6 Appendix
Outline
1 Research question and strategy
2 Setting and empirical strategy
3 Main resultsImpact on winningImpact on runningImpact conditional on running
4 MechanismsImpact depending on political orientationsCoordination?Bandwagon e�ect?
5 Conclusion
6 Appendix
French local and parliamentary elections
French parliamentary electionsI elect the representatives of the French Assembly (lower house of
Parliament)I 577 constituencies, elections every 5 years
French local electionsI elect the members of the department councilsI 101 departments divided in cantons, elections every 6 years
Voting rule
I 2 rounds separated by one weekI Quali�cation to 2nd round
F 1st and 2nd candidates in 1st round automatically qualify for 2nd roundF 3rd and lower-ranked candidates only qualify if their vote share is higher
than a threshold of registered citizens (5, 10 or 12.5%, depending onthe election year)
F quali�ed candidates can decide to withdraw from the race
I Plurality rule in 2nd round
Sample
Sample:
I 14 parliamentary elections: 1958 - 2017I 8 local elections: 1992 - 2015 (forthcoming: 1976, 1979, 1982, 1985
and 1988)I 18,000 races with two rounds:
F 6,335 parliamentary races (35%)F 11,665 local races (65%)
Elections we consider in the analysis:I 1vs2: elections with at least 2 candidates in the 1st roundI 2vs3: elections with at least 3 candidates in the 1st round, in which the
3rd candidate quali�es for the 2nd roundI 3vs4: elections with at least 4 candidates in the 1st round, in which the
4th candidate quali�es for the 2nd round
Number of close races in the 1st round (closer than 2pp)I 1vs2: 2,056I 2vs3: 1,458I 3vs4: 598
Descriptive statistics
Mean Sd Min Max Obs.
Panel A. 1 st round
Registered voters 32,782 29,708 282 200,205 18,000Turnout 0.634 0.123 0.094 0.919 18,000Candidate votes 0.611 0.120 0.093 0.894 18,000Number of candidates 6.9 3.3 1 48 18,000
Panel B. 2 nd round
Turnout 0.620 0.131 0.117 0.938 18,000Candidate votes 0.586 0.135 0.103 0.907 18,000Number of candidates 2.1 0.4 1 6 18,000
RDD Evaluation framework
Running variable for 1vs2 (resp. 2vs3, 3vs4)
Xi,d =
{votesharei − votesharei−1 if ranked 1st (resp. 2nd , 3rd)
votesharei+1 − votesharei if ranked 2nd (resp. 3rd , 4th)
Treatment variable
Ti,d =
{1 if Xi,d > 0
0 otherwise.
Non-parametric estimation: local linear regression (Imbens and Lemieux2008; Calonico et al. 2014, 2016)
Yi,d = α+ τTi,d + βXi,d + γXi,dTi,d + µi,d
RDD Evaluation framework
Optimal bandwidth �MSERD� from Calonico et al. (2014, 2016)I We test robustness to using �IK� method (Imbens and Kalyanaraman
2012) and using smaller bandwidths (MSERD:2)
Standard errors computed using Calonico et al. (2016) and clusteredat the race x year level
Identi�cation assumption
Identi�cation assumption: no sorting of candidates across thethreshold at the cuto� (de la Cuesta and Imai 2016)
Theoretical arguments:
I Information on 1st round vote's intentions in parliamentary and localelections is limited
I Eggers et al. (2015) on RDD exploiting close races
Indirect empirical testsI Placebo tests on baseline variables
Placebo tests - political orientation
More
1st round vote shares
Outline
1 Research question and strategy
2 Setting and empirical strategy
3 Main resultsImpact on winningImpact on runningImpact conditional on running
4 MechanismsImpact depending on political orientationsCoordination?Bandwagon e�ect?
5 Conclusion
6 Appendix
Winning 1vs2: +7.6ppOutcome = 1 if runs in 2nd round and wins, 0 otherwise
Winning 2vs3: +8.9ppOutcome = 1 if runs in 2nd round and wins, 0 otherwise
Winning 3vs4: +1.1ppOutcome = 1 if runs in 2nd round and wins, 0 otherwise
Impact on winning
(1) (2) (3)Outcome Probability to win in the 2nd round
1vs2 2vs3 3vs4
Treatment 0.076*** 0.089*** 0.011(0.018) (0.015) (0.011)
Observations left 6,908 3,367 930Observations right 6,908 3,367 930Polyn. order 1 1 1Bandwidth 0.073 0.053 0.036Mean, left of threshold 0.446 0.054 0.008
More
Impact on winning
We �nd a strong impact of rankings on winning in the second round
This e�ect could come from
1 Impact on the probability to run in the second round (any quali�edcandidate can decide to drop out)
2 Impact on vote shares and on the probability to win the election,conditional on running
We now disentangle the two
Outline
1 Research question and strategy
2 Setting and empirical strategy
3 Main resultsImpact on winningImpact on runningImpact conditional on running
4 MechanismsImpact depending on political orientationsCoordination?Bandwagon e�ect?
5 Conclusion
6 Appendix
Winning & running 1vs2: +7.6 / +4.7pp
Winning & running 1vs2: +7.6 / +4.7pp
Winning & running 2vs3: +8.9/ +20.4pp
Winning & running 2vs3: +8.9/ +20.4pp
Winning & running 3vs4: +1.1 / +13.1pp
Winning & running 3vs4: +1.1 / +13.1pp
(1) (2) (3) (4) (5) (6)
Outcome 1vs2 2vs3 3vs4
Win Run Win Run Win Run
Treatment 0.076*** 0.047*** 0.089*** 0.204*** 0.011 0.131***
(0.018) (0.005) (0.015) (0.020) (0.011) (0.046)
Obs l 6,908 8,598 3,367 4,071 930 904
Obs r 6,908 8,598 3,367 4,071 930 904
Polyn. 1 1 1 1 1 1
Bdw 0.073 0.093 0.053 0.070 0.036 0.035
Mean 0.446 0.951 0.054 0.627 0.008 0.353
More
Outline
1 Research question and strategy
2 Setting and empirical strategy
3 Main resultsImpact on winningImpact on runningImpact conditional on running
4 MechanismsImpact depending on political orientationsCoordination?Bandwagon e�ect?
5 Conclusion
6 Appendix
Unconditional vs conditional e�ects
We are now interested in the impact of rankings conditional onrunning
I on vote shares: does the better ranked candidate attract more voters?Graphs
I on winning: is the candidate better ranked more likely to win,conditional on running?
We cannot simply look at elections where the 2nd and 3rd (forinstance) are running
I selection issue: those who decide to run are not randomly chosenF the RDD does not imply that barely 2nd who run in the 2nd round are
similar to barely 3rd who do
We derive bounds on the e�ect on vote shares and on the probabilityof winning, conditional on running
Method: Bounds on winning 2vs3
T =
{1 for 2nd
0 for 3rd
R0,R1 : potential outcome indicators for running in the 2nd roundwhen T = 0 or T = 1 respectively
I We observe: R = TR1 + (1− T )R0
W0,W1 : potential outcome indicators for winning the 2nd round,conditional on running
I We observe: W = R[TW1 + (1− T )W0]
Key assumption: no �de�ers� (candidates who would run again after a3rd place but not after a 2nd place) => R1 ≥ R0
I Then, we can show:
E (W1R1 −W0R0|x = 0)︸ ︷︷ ︸RD effect on W
=
Prob(R1 > R0|x = 0)·︸ ︷︷ ︸RD effect on R
E(W0|x = 0,R1 > R0)︸ ︷︷ ︸Unobservable
+
Effect on win cond on being always−taker or complier︷ ︸︸ ︷E [W1 −W0|x = 0,R1 = 1] · E(R1|x = 0)︸ ︷︷ ︸
limx↓0E [R|x]
Hence, we get:
Effect on win cond on being always−taker or complier︷ ︸︸ ︷E [W1 −W0|x = 0,R1 = 1] =
1
E(R1|x = 0)︸ ︷︷ ︸limx↓0E [R|x]
[E(W1R1 −W0R0|x = 0)︸ ︷︷ ︸RD effect on W
− Prob(R1 > R0|x = 0)·︸ ︷︷ ︸RD effect on R
E(W0|x = 0,R1 > R0)︸ ︷︷ ︸Unobservable
]
Method: Bounds on winning 2vs3Computation of Lower and Upper bounds
We know:
I E (W1R1 −W0R0|x = 0), the RD e�ect on winning unconditional:0.089
I Prob(R1 > R0|x = 0), the RD e�ect on running: 0.204I E (R1|x = 0), the probability that a 2nd place runs at the threshold:
0.820
We make assumptions on the unobservable term
I i.e., probability that a complier would win if she ran after a close 3rd
place �nish (unobserved because compliers do not run after athird-place �nish, by de�nition)
Method: Bounds on winning 2vs3Computation of Lower and Upper bounds
Upper bounds : largest possible e�ect occurs if close 3rd placed complierswould never win
I Assume E [W0|x = 0,R1 > R0] = 0I we obtain 0.109
Lower bounds: assumes that 3rd placed compliers would have at most thesame proba of winning as 2nd place �nishers who run
I Assume E [W0|x = 0,R1 > R0] =Probability that a 2nd place wins atthe threshold = 0.144
I we obtain 0.065
Method: Bounds on winning 2vs3Bootstrapped standard errors
We use bootstrapping to compute the standard errors of the lower andupper bounds
1 Draw a sample from our data2 Compute the bounds as indicated above3 Redo steps 1/ and 2/ a very large number of times (10,000 for
instance)4 Estimate the standard error
We obtain:
I Upper bound: 0.109 (0.021)***I Lower bound: 0.065 (0.017)***
Bounds
1vs2 2vs3 3vs4
win vote share win vote share win vote share
Upper 0.076 0.036 0.109 0.124 0.024 0.079
s.e (0.026)*** (0.004)*** (0.021)*** (0.014)*** (0.024) (0.025)***
Lower 0.051 0.013 0.065 0.035 0.014 0.019
s.e (0.025)** (0.003)*** (0.017)*** (0.006)*** (0.019) (0.014)
Mean 0.446 0.469 0.054 0.307 0.008 0.199
More
Outline
1 Research question and strategy
2 Setting and empirical strategy
3 Main resultsImpact on winningImpact on runningImpact conditional on running
4 MechanismsImpact depending on political orientationsCoordination?Bandwagon e�ect?
5 Conclusion
6 Appendix
Outline
1 Research question and strategy
2 Setting and empirical strategy
3 Main resultsImpact on winningImpact on runningImpact conditional on running
4 MechanismsImpact depending on political orientationsCoordination?Bandwagon e�ect?
5 Conclusion
6 Appendix
1vs2 - Same vs Di�erent orientation
We de�ne 6 political orientations: far-left, left, center, right, far-rightand other
1vs2 - Same vs Di�erent orientation
(1) (2) (3) (4) (5) (6)
Outcome Probability to run 1vs2 Probability to win 1vs2
Full Same Di� Full Same Di�
Treatment 0.047*** 0.307*** 0.002 0.076*** 0.290*** 0.043**
(0.005) (0.025) (0.003) (0.018) (0.041) (0.019)
Obs l 8,598 1,447 5,859 6,908 1,168 6,181
Obs r 8,598 1,447 5,859 6,908 1,168 6,181
Polyn. 1 1 1 1 1 1
Bdw 0.093 0.117 0.072 0.073 0.087 0.076
Mean 0.951 0.690 0.995 0.446 0.326 0.465
2vs3 - Same vs Di�erent orientation
2vs3 - Same vs Di�erent orientation
(1) (2) (3) (4) (5) (6)
Outcome Probability to run 2vs3 Probability to win 2vs3
Full Same Di� Full Same Di�
Treatment 0.204*** 0.561*** 0.063*** 0.089*** 0.197*** 0.046***
(0.020) (0.037) (0.021) (0.015) (0.031) (0.014)
Obs l 4,071 998 3,136 3,367 902 3,182
Obs r 4,071 998 3,136 3,367 902 3,182
Polyn. 1 1 1 1 1 1
Bdw 0.070 0.054 0.082 0.053 0.047 0.084
Mean 0.627 0.338 0.742 0.054 0.024 0.067
3vs4 - Same vs Di�erent orientation
3vs4 - Same vs Di�erent orientation
(1) (2) (3) (4) (5) (6)
Outcome Probability to run 3vs4 Probability to win 3vs4
Full Same Di� Full Same Di�
Treatment 0.131*** 0.370*** 0.039 0.011 0.017 0.004
(0.046) (0.075) (0.054) (0.011) (0.027) (0.008)
Obs l 904 260 685 930 278 637
Obs r 904 260 685 930 278 637
Polyn. 1 1 1 1 1 1
Bdw 0.035 0.042 0.036 0.036 0.046 0.032
Mean 0.353 0.313 0.350 0.008 0.016 0.003
Interpretation 1/3
The impacts on running and winning are largest when the candidatesare from the same political orientation
This may come from the fact thatI it makes coordination relatively more important and desirableI it makes rallying to the better ranked candidate less costly, whatever
the motive
We now investigate two possible mechanismsI coordinationI bandwagon
Outline
1 Research question and strategy
2 Setting and empirical strategy
3 Main resultsImpact on winningImpact on runningImpact conditional on running
4 MechanismsImpact depending on political orientationsCoordination?Bandwagon e�ect?
5 Conclusion
6 Appendix
1vs2 depending on the strength of the 3rd
Sample: 3rd is quali�ed
Gap = vote share 2nd - vote share 3rd in the 1st round
(1) (2) (3) (4) (5) (6)
Outcome Probability to run 1vs2 Probability to win 1vs2
Full Gap<5% Gap<2.5% Full Gap<5% Gap<2.5%
Rank 1st 0.080*** 0.100*** 0.145*** 0.076*** 0.090** 0.119**
(0.011) (0.016) (0.028) (0.027) (0.042) (0.050)
Obs l 2,492 1,648 774 2,845 1,290 893
Obs r 2,492 1,648 774 2,845 1,290 893
Polyn. 1 1 1 1 1 1
Bdw 0.063 0.100 0.080 0.074 0.074 0.095
Mean 0.915 0.892 0.844 0.436 0.397 0.367
More
2vs3 depending on 2+3 vote share
(1) (2) (3) (4) (5) (6)
Outcome Probability to run 2vs3 Probability to win 2vs3
Full 2+3<1 2+3>1 Full 2+3<1 2+3>1
Rank 2nd 0.204*** 0.279*** 0.183*** 0.089*** 0.013 0.107***
(0.020) (0.052) (0.021) (0.015) (0.011) (0.018)
Obs l 4,071 600 3,398 3,367 674 2,736
Obs r 4,071 600 3,398 3,367 674 2,736
Polyn. 1 1 1 1 1 1
Bdw 0.070 0.050 0.073 0.053 0.060 0.053
Mean 0.627 0.552 0.641 0.054 0.006 0.065
More
Interpretation 2/3
Mixed evidence that local coordination plays a role in candidates'behavior
I Impact on running 1vs2 stronger when the 3rd is closer to the 2nd
candidateI But impact on running 2vs3 not stronger when coordination may help
the 2nd to win over the 1st
More robust evidence that voters use rankings to coordinate on thetop 2 More
I Impact on winning 1vs2 stronger when the 3rd is closer to the 2nd
candidateI Impact on winning 2vs3 stronger when coordination may help the 2nd
to win over the 1st
Outline
1 Research question and strategy
2 Setting and empirical strategy
3 Main resultsImpact on winningImpact on runningImpact conditional on running
4 MechanismsImpact depending on political orientationsCoordination?Bandwagon e�ect?
5 Conclusion
6 Appendix
1vs2 - 3rd NOT quali�edSample: elections where the 3rddoes NOT qualify
(1) (2) (3) (4) (5) (6)
Outcome Probability to run 1vs2 Probability to win 1vs2
Full Same Di� Full Same Di�
Rank 1st 0.018*** 0.208*** -0.000 0.076*** 0.183*** 0.065***
(0.004) (0.041) (0.001) (0.022) (0.057) (0.023)
Obs l 5,623 458 3,753 4,856 593 4,540
Obs r 5,623 458 3,753 4,856 593 4,540
Polyn. 1 1 1 1 1 1
Bdw 0.104 0.089 0.073 0.087 0.122 0.090
Mean 0.982 0.792 1.000 0.463 0.408 0.468
1vs2 - 3rd NOT quali�edSample: elections where the 3rddoes NOT qualify
(1) (2) (3) (4) (5) (6)
Outcome Probability to run 1vs2 Probability to win 1vs2
Full Same Di� Full Same Di�
Rank 1st 0.018*** 0.208*** -0.000 0.076*** 0.183*** 0.065***
(0.004) (0.041) (0.001) (0.022) (0.057) (0.023)
Obs l 5,623 458 3,753 4,856 593 4,540
Obs r 5,623 458 3,753 4,856 593 4,540
Polyn. 1 1 1 1 1 1
Bdw 0.104 0.089 0.073 0.087 0.122 0.090
Mean 0.982 0.792 1.000 0.463 0.408 0.468
1vs2 - 3rd NOT quali�edSample: elections where the 3rddoes NOT qualify
(1) (2) (3) (4) (5) (6)
Outcome Probability to run 1vs2 Probability to win 1vs2
Full Same Di� Full Same Di�
Rank 1st 0.018*** 0.208*** -0.000 0.076*** 0.183*** 0.065***
(0.004) (0.041) (0.001) (0.022) (0.057) (0.023)
Obs l 5,623 458 3,753 4,856 593 4,540
Obs r 5,623 458 3,753 4,856 593 4,540
Polyn. 1 1 1 1 1 1
Bdw 0.104 0.089 0.073 0.087 0.122 0.090
Mean 0.982 0.792 1.000 0.463 0.408 0.468
Bounds absent the 3rd
1vs2 absent the 3rd
Win Vote share
Upper bound 0.076 0.019Boot. s.e (0.028)*** (0.005)***Lower bound 0.066 0.010Boot. s.e (0.028)** (0.004)***Mean 0.463 0.499
Interpretation 3/3
The e�ects on running and winning 1vs2 remain strong even if there is noneed for coordination (3rd candidate not quali�ed)
I Evidence that dropouts are not only driven by local coordinationI Evidence of bandwagon e�ect: desire to vote for the winner More
The impact on vote share indicates that the bandwagon e�ect concerns onlya relatively small fraction of voters
But in the context of close races, their behavior has a large impact onelection results
I it increases the chance of victory of the 1st by ∼7pp relatively to the2nd
This could come from
I mobilization: less voters turning out when they realize their favoritecandidate is ranked 2nd
I �switching�: voters voting for the 1st instead of the 2nd
I next step: use data at the polling station level to disentangle the two
Conclusion
We �nd strong e�ects of rankings on 2nd round outcomesI e�ects on candidates' entry decisionI e�ects on candidates' probability to win
The e�ect on running is mainly driven by alliances among parties fromthe same political orientation
Voters' behavior is at least partly driven by a behavioral mechanism:�desire to vote for the winner�
Next stepsI assess the magnitude of mobilization and switching mechanismsI include two-round elections outside France, especially US jungle
primaries
THANKS!
Turnout in close races
General balance test
Back
Win - robustness
Method for selecting bandwidths: IK
(1) (2) (3)Outcome Probability to win in the 2nd round
1vs2 2vs3 3vs4
Treatment 0.076*** 0.093*** 0.011(0.018) (0.012) (0.012)
Observations left 7,026 4,661 813Observations right 7,026 4,661 813Polyn. order 1 1 1Bandwidth 0.074 0.089 0.030Mean, left of threshold 0.449 0.053 0.006
Win - robustness
Method for selecting bandwidths: MSERD divided by 2
(1) (2) (3)
Outcome Probability to win in the 2nd round1vs2 2vs3 3vs4
Treatment 0.065*** 0.080*** 0.013(0.024) (0.021) (0.015)
Observations left 3,696 1,889 548Observations right 3,696 1,889 548Polyn. order 1 1 1Bandwidth 0.036 0.026 0.018Mean, left of threshold 0.455 0.060 0.006
Back
Run & Win - robustness
Method for selecting bandwidths: IK
(1) (2) (3) (4) (5) (6)
Outcome 1vs2 2vs3 3vs4
Win Run Win Run Win Run
Treatment 0.076*** 0.047*** 0.093*** 0.211*** 0.011 0.123***
(0.018) (0.004) (0.012) (0.018) (0.012) (0.033)
Obs l 7,026 13,187 4,661 4,689 813 1,396
Obs r 7,026 13,187 4,661 4,689 813 1,396
Polyn. 1 1 1 1 1 1
Bdw 0.074 0.164 0.089 0.089 0.030 0.084
Mean 0.449 0.950 0.053 0.614 0.006 0.321
Run & Win - robustness
Method for selecting bandwidths: MSERD divided by 2
(1) (2) (3) (4) (5) (6)
Outcome 1vs2 2vs3 3vs4
Win Run Win Run Win Run
Treatment 0.065*** 0.044*** 0.080*** 0.183*** 0.013 0.132**
(0.024) (0.007) (0.021) (0.027) (0.015) (0.063)
Obs l 3,696 4,675 1,889 2,401 548 534
Obs r 3,696 4,675 1,889 2,401 548 534
Polyn. 1 1 1 1 1 1
Bdw 0.036 0.047 0.026 0.035 0.018 0.018
Mean 0.455 0.954 0.060 0.635 0.006 0.368
Back
Vote share 1vs2Outcome: 0 if the candidate is not running
Vote share 2vs3Outcome: 0 if the candidate is not running
Vote share 3vs4Outcome: 0 if the candidate is not running
Back
Conditional e�ects - additional testExample for 2vs3
We ask for which values of the unobservable term the e�ect issigni�cantly di�erent from 0
To do so we:I create a variable equal to the numerator: Zλ = WR − λRI for every possible value of the unobservable λ ∈ [0; 1]I and take it as outcome variable in our RDD
We then ask for which values of λ the estimate is signi�cantlydi�erent from 0
The e�ect is signi�cantly di�erent from 0 for any λ ≤ 31%
Assuming λ = 31% amounts to assuming that close 3rdcandidateswho do not run would have won the election in 31% of the cases ifthey had run
This is unlikely, given that close 2nd candidates who run win in only14% of the cases, and close 3rd candidates who run win in only 5% ofthe cases.� we can be con�dent that the e�ect on winning conditional onrunning is signi�cant and positive
1vs2 2vs3 3vs4
win vote share win vote share win vote share
λ threshold 0.88 0.64 0.31 0.46 0.00 0.19
Mean for T=1 0.53 0.48 0.14 0.36 0.02 0.22
Mean for T=0 0.45 0.47 0.05 0.31 0.01 0.20
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1vs2 depending on the strength of the 3rd- Same orientation
Sample: 3rd is quali�ed
Gap = vote share 2nd - vote share 3rd in the 1st round
(1) (2) (3) (4) (5) (6)
Outcome Probability to run 1vs2 Probability to win 1vs2
Full Gap<5% Gap<2.5% Full Gap<5% Gap<2.5%
Rank 1st 0.358*** 0.402*** 0.524*** 0.332*** 0.475*** 0.476***
(0.041) (0.057) (0.061) (0.055) (0.063) (0.097)
Obs l 559 282 216 592 331 174
Obs r 559 282 216 592 331 174
Polyn. 1 1 1 1 1 1
Bdw 0.065 0.070 0.108 0.069 0.085 0.076
Mean 0.645 0.602 0.463 0.301 0.185 0.198
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2vs3 depending on 2+3 vote share - Same orientation
(1) (2) (3) (4) (5) (6)
Outcome Probability to run 2vs3 Probability to win 2vs3
Full 2+3<1 2+3>1 Full 2+3<1 2+3>1
Rank 2nd 0.561*** 0.642*** 0.529*** 0.197*** 0.006 0.266***
(0.037) (0.064) (0.044) (0.031) (0.020) (0.040)
Obs l 998 267 723 902 280 689
Obs r 998 267 723 902 280 689
Polyn. 1 1 1 1 1 1
Bdw 0.054 0.069 0.050 0.047 0.074 0.048
Mean 0.338 0.249 0.367 0.024 0.016 0.026
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Campaign expenditures
The impacts we �nd on vote shares and on the probability of winning,conditional on running, could be driven by
1 Voters' choices : more votes going to the candidate better ranked2 Parties/candidates' campaigning: the candidate better ranked receives
more contributions and intensi�es her campaign
We argue that mechanism 2/ is unlikely to drive our results in this setting
I only 1 week between the two roundsI small (or no) e�ects of rankings on campaign expenditure and
contributionsI which may be driven by the e�ects on running
We take as outcome:
I the total amount spent and received by each candidate for the givenelection (it includes both rounds)
I divided by the number of registered citizensI sample: parliamentary elections from 1993, local elections from 2008
(forthcoming: 1992, 1994, 1998, 2001 and 2004)
Campaign expenditures
(1) (2) (3) (4) (5) (6)
Outcome 1vs2 2vs3
Run Expend. Contrib. Run Expend. Contrib.
Treatment 0.027*** -0.003 -0.004 0.075 0.091*** 0.092***
(0.005) (0.012) (0.014) (0.050) (0.033) (0.035)
Obs l 3,785 3,271 3,068 407 460 490
Obs r 3,785 3,271 3,068 407 460 490
Polyn. 1 1 1 1 1 1
Bdw 0.118 0.098 0.090 0.033 0.039 0.042
Mean 0.972 0.547 0.566 0.841 0.402 0.410
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Learning?
Can our results be alternatively explained by updating/learning fromvoters?
I voters who take rankings as a signal of quality and update their beliefs
In Bayesian learning models, voters look at vote shares and there is nodiscontinuity in the rankings (e.g., Knight and Schi� 2000)
Rankings could still be a quality signal in case of limited informationI however we �nd even stronger e�ects in races that receive greater
coverage (parliamentary elections)I next step: look at press coverage to see if rankings are over-reported
compared to closeness/vote sharesF �rst look at it suggests that press tends to report closeness of the race
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