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Erschienen in: Public Choice 3-4/2017

18.05.2017

The ballot order effect is huge: evidence from Texas

verfasst von: Darren Grant

Erschienen in: Public Choice | Ausgabe 3-4/2017

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Abstract

Primary and runoff elections in Texas provide an ideal test of the ballot order hypothesis, because ballot order is randomized within each county and the state offers many counties and contests to analyze. Doing so for all statewide offices contested in the 2014 Democratic and Republican primaries and runoffs yields precise estimates of the ballot order effect across 24 different contests, including several not studied previously. Except for a few high-profile, high-information races, the ballot order effect is large, especially in down-ballot races for judicial positions. There, the empirical results indicate that going from last to first on the ballot raises a candidate’s vote share by nearly ten percentage points. The magnitude of this effect is not sensitive to demographic and economic factors.

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1
These ten studies are Alvarez et al. (2006), Brockington (2003), Chen et al. (2014), Ho and Imai (2006, 2008), Koppell and Steen (2004), Krosnick et al. (2004), Meredith and Salant (2013), Miller and Krosnick (1998), and Pasek et al. (2014). As discussed by Darcy and McAllister (1990), Miller and Krosnick (1998), and Ho and Imai (2008), early efforts had significant methodological problems, which these more recent studies have largely corrected. There is also a small U.S. literature on the effects of ballot order on the passing rates of propositions and bond issues. See Matsusaka (2016) for a review and recent evidence from propositions in California and Texas.
 
2
The number of votes rises substantially for the local contests that follow the state judicial positions on the ballot, suggesting that decision fatigue is not a major factor driving this roll-off.
 
3
The effort spanned 10 months and absorbed hundreds of man-hours. While most counties were prompt and professional in responding to these queries, a number of smaller counties required repeated callbacks in order to obtain the requested information.
 
4
Texas voters do not register by party labels, so all primaries are “open.” In most counties, one party’s primary will have many more contested races than the other, attracting crossover voters. Thus, in Republican-dominated counties, it is not unusual for Democratic-leaning voters to vote in the Republican primary, and vice versa. The results were very similar if the fraction of votes going to McCain or Obama replaced the log of the number of votes.
 
5
The demonstration now conducted for a three-candidate election can be extended by induction. Allowing the ballot order effect to differ across candidates yields the following system:
$$S_{1} = \alpha_{1} + \omega_{1} B_{1}^{1} + \varOmega_{1} B_{1}^{2} + \varepsilon_{1}$$
$$S_{2} = \alpha_{2} + \omega_{2} B_{2}^{1} + \varOmega_{2} B_{2}^{2} + \varepsilon_{2}$$
$$S_{3} = \alpha_{3} + \omega_{3} B_{3}^{1} + \varOmega_{3} B_{3}^{2} + \varepsilon_{3}$$
where ω and Ω represent the ballot order effects for the first and second positions on the ballot, and the subscripts 1, 2, and 3 refer to the three candidates in the election.
Assume an initial ballot order of 1, 2, 3. The following ballot order re-arrangements imply the following changes in total vote share, which must equal zero for elections to be zero-sum:
  • \(\begin{array}{*{20}l} {2, \, 1, \, 3{:}} \hfill & { -\upomega_{1} +\upomega_{2} +\Omega _{1} -\Omega _{2} = 0} \hfill \\ \end{array}\)
  • \(\begin{array}{*{20}l} {3, \, 2, \, 1{:}} \hfill & { -\upomega_{1} +\upomega_{3} = 0} \hfill \\ \end{array}\)
  • \(\begin{array}{*{20}l} {2, \, 3, \, 1{:}} \hfill & { -\upomega_{1} +\upomega_{2} +\Omega _{2} -\Omega _{3} = 0} \hfill \\ \end{array}\)
  • \(\begin{array}{*{20}l} {1, \, 3, \, 2{:}} \hfill & { -\Omega _{2} +\Omega _{3} = 0} \hfill \\ \end{array}\)
  • \(\begin{array}{*{20}l} {3, \, 1, \, 2{:}} \hfill & { -\upomega_{1} +\upomega_{3} +\Omega _{1} -\Omega _{2} = 0} \hfill \\ \end{array}\)
These restrictions together imply that ω1 = ω2 = ω3 and Ω1 = Ω2 = Ω3.
 
6
For multi-candidate races, a test of the joint hypothesis of ballot order randomization across all candidates in the same contest also is presented, when feasible. Fisher’s exact test is computationally intensive, however, so it rarely executed herein for races with more than three candidates. Full results for all candidates in multi-candidate races can be found in Table A2 in the Online Appendix.
 
7
Assume two, two candidate races; across the state the “establishment” candidate is clearly favored in the ballot order in Race 1 (but not necessarily Race 2). Let F1 be a dummy variable indicating whether this candidate is listed first on the ballot (and F2 indicate the same for Race 2). Then, in Race 1, P(F c 1  = 1) = 1/2 + Zc/2, where Z is a latent indicator variable indicating whether the county chair favors the establishment candidate in determining ballot order. If this candidate is listed second on county c’s ballot, Zc = 0. If they are listed first, P(Zc = 1) = 2 − 1/E(F1), with the expectation taken across all counties.
Suppressing controls for simplicity, the vote share of the establishment candidate in Race 2 is Sc = α + ωF c 2  + (φZc + εc), where the unobserved term φZc reflects potential bias introduced when county party chairs’ favoritism in determining ballot order is related to that candidate’s popularity in that county. Then:
$$E\left( {S_{c} |F^{1} = 0,F^{2} = 0} \right) = \alpha$$
$$E\left( {S_{c} |F^{1} = 1,F^{2} = 0} \right) = \alpha + {\varphi }\left[ {2 - 1/E\left( {F^{1} } \right)} \right]$$
$$E\left( {S_{c} |F^{1} = 0,F^{2} = 1} \right) = \alpha + \omega$$
$$E\left( {S_{c} |F^{1} = 1,F^{2} = 1} \right) = \alpha + \omega + {\varphi }\left[ {2 - 1/E\left( {F^{1} } \right)} \right]$$
Therefore, E(S|F1 = 1, F2 = 1) − E(S|F1 = 1, F2 = 0) = E(S|F1 = 0, F2 = 1) − E(S|F1 = 0, F2 = 0) = ω. Thus, the regression Sc = α + ωF c 2  + λF c 1  + δXc + εc yields unbiased estimates of ω. It is used in obtaining the bracketed estimates in Table 4.
 
8
This information was brought to the author’s attention by Paul Hastings, manager of the Rick Green campaign, shortly after the primary. Mr. Hastings generously volunteered (without conditions) preliminary ballot order data, taken from the website described below; these data were checked for accuracy and supplemented by the author. Vote shares come from the Texas Secretary of State.
 
9
The imbalance would be smaller when ballot order is rotated systematically across similarly sized jurisdictions, as in the studies discussed in Sect. 2. Because this procedure is less decentralized, however, it is unlikely to be adopted in Texas.
 
10
Paul (Rick) Green was listed first in 121 (112) of the 233 counties for which ballot order was known, or 51.9% (48.1%). Chi-squared tests could reject neither the null of equal proportions (p = 0.56) nor the null that Paul Green's being listed first was unrelated to the independent variables described in the text (p = 0.59). However, Paul Green was listed first on the ballot in 62% of the votes cast across the state. Even subtracting two standard errors from the point estimate, the implied advantage for Paul Green was 2.15% of the vote.
 
11
The address is https://​webservices.​sos.​state.​tx.​us/​candidate-filing/​cf-report.​aspx. Most, though not all, chairs did enter candidates in ballot order. Although the statutory language implies that such information should be archived, it was not done for the March 2016 cycle. Doing so would provide additional accountability and a valuable database in the event of lawsuits.
 
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Metadaten
Titel
The ballot order effect is huge: evidence from Texas
verfasst von
Darren Grant
Publikationsdatum
18.05.2017
Verlag
Springer US
Erschienen in
Public Choice / Ausgabe 3-4/2017
Print ISSN: 0048-5829
Elektronische ISSN: 1573-7101
DOI
https://doi.org/10.1007/s11127-017-0454-8

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