Rankings matter even when they shouldn't: bandwagon e … Files/PonsTricaud_Rankings_ebd424… ·...

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

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





5 Conclusion

6 Appendix

Winning 1vs2: +7.6ppOutcome = 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





5 Conclusion

6 Appendix

Winning & running 1vs2: +7.6 / +4.7pp

Winning & running 2vs3: +8.9/ +20.4pp

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





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]

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





5 Conclusion

6 Appendix

1vs2 - Same vs Di�erent orientation

We de�ne 6 political orientations: far-left, left, center, right, far-rightand other


(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


(1) (2) (3) (4) (5) (6)



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


(1) (2) (3) (4) (5) (6)



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





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)


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)


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





5 Conclusion

6 Appendix

1vs2 - 3rd NOT quali�edSample: elections where the 3rddoes NOT qualify

(1) (2) (3) (4) (5) (6)



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)


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)


Back

Run & Win - robustness

Method for selecting bandwidths: IK

(1) (2) (3) (4) (5) (6)



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)



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


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

Back

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)


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

Back

2vs3 depending on 2+3 vote share - Same orientation

(1) (2) (3) (4) (5) (6)


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

Back

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

Back

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

Back

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