EL DEBATE EN CUANTO A LA IMPARTICIÓN DE JUSTICIA

I estimate the size of rational order eects in two ways. The rst method is described here, the second method is more structural and is described further below. Both methods provide similar results.

Method 1: In my model, behavioral voters do not create a relationship between per- centiles q and conditional order eects b(q).23 _{But as seen in the previous section, rational} 23_{If one were to assume dierent (or more sophisticated) behavioral theories, my quantitative estimates}

of strategic ballot order eects could change as a result - in both directions, up or down. One could use estimation strategies similar to the tests implemented in the following section to allow for more sophisticated behavioral voting.

order eects create an increase in order eects b(q) for high vote share percentiles q.24 _Since

I do not observe the percentile cuto for where rational order eects exist, I need to estimate this cuto. I do this by estimating the percentile cuto beyond which e conditional order eects become hill-shaped, as that shape can only be caused by rational order eects. I then compare order eects on both sides of the cuto to estimate a lower bound on rational order eects.

To do this, I rst run a regression of vote share on various controls such as incumbency, month, year, and county dummies, whether the election is an open seat election (no incum- bent), and whether the oce is for 4 years or shorter. After partialling out the eects of these controls on vote share τkj,25I compute conditional order eects b(q) using the adjusted

vote shares. However, to compute b(q) directly, I need to discretize q into 100 bins.

I rst run a non-linear least-squares estimation where I estimate a cuto ¯q given the following equation

b(q) = (a0+ a1q + a2q2) · 1{q < ¯q} + (a00 + a01q + a02q2} · 1{q ≥ ¯q}.

Given the estimate of ¯q, I then compute the dierence β in order eects between percentiles below and above this cuto using the regression equation

b(q) = β · 1{q ≥ ¯q} + ε.

My estimate of rational order eects is then β · (1 − ¯q).26 _{I estimate standard errors by}

bootstrapping this procedure 1,000 times.

Table 2.4.2 lists the results. I estimate the cuto to be around the 50-th percentile for most specications (1) - (3). Rational order eects are 1.29%∗ _{in my main specication (1),} 24_{Since rational order eects decrease for very high vote share percentiles in my model, this method would}

provide a lower bound on rational order eects.

25_{I only do this for the dependent variable, as the independent variable is binary and I use it to construct}

ballot order eects. However, no regressors are signicant when regressing ballot position on the control variables.

26_{Alternatively, one could use the estimated coecients of the rst stage to estimate strategic order eects,}

which accounts for 48%∗ _{of all order eects. Similarly, I nd a share of 1.4% behavioral}

voters, which is very similar to what I estimate in the structural estimation below. The estimates change little when also using smaller elections with at least 196 votes (2), when using only school-related elections (3), or when considering the dierence between single- vote and multi-vote elections to determine the cuto. However, I estimate a substantially dierent cuto value for elections other than school elections, which then leads to dierent estimates of rational order eects as well (4).

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

VARIABLES % Vote Share Vote Share Vote Share Vote Share Vote Share

β · ¯q: Strategic order eects 1.29* 1.24* 1.57* 0.69 1.47*

(0.757) (0.749) (0.926) (0.793) (0.821)

Strategic share 48* 46* 57** 23 54**

(25.4) (24.5) (28.5) (20.6) (26.6)

λ: Behavioral order eects 1.40 1.46 1.18 2.31** 1.23

(0.889) (0.916) (1.092) (1.057) (0.860)

¯

q: Cuto 52** 54** 43 77*** 56**

(25.44) (24.47) (28.54) (20.61) (27.14)

Scenario Voters > 196 School elections No school +multi-vote elections

Excluded 1% and 100% Yes Yes Yes Yes Yes

Observations 1,638 1,701 1,008 630 5,175

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Method 2: I use the theoretical model described in the previous section to estimate the size of rational order eects in three-candidate and four-candidate single-vote and multi-vote elections. To do this, I rst draw mean utilities for candidates U from a standard normal distribution U ∼ N(0, 1). Given these mean utilities, I use a logit model to determine how many voters prefer a candidate with mean utility Uj over a candidate with mean utility Uk,

P (uij > uik) =

exp(Uj/µ)

exp(Uj/µ) + exp(Uk/µ)

,

where µ denotes the scale parameter of the logit distribution.

I use the relationship between P (·) and U to compute vote shares. Recall that in single- vote elections, strategic voters only maximize utility between the top-two candidates. It is thus sucient to dene preferences over candidate pairs to determine strategic vote shares.

Behavioral voters always vote for the rst-listed candidate, their behavior does not depend on the preference distribution in single-vote elections.

As before, let λ denote the share of behavioral voters. I use a Method of Moments approach to estimate the two parameters µ and λ, i.e., I match moments generated by the model given some values of the parameters to the respective moments generated by the data. I compute standard errors by bootstrapping the procedure 200 times.

Let me discuss the identication of the parameters. I use conditional order eects b(q) in single-vote elections for all percentiles to estimate the share of behavioral voters in the electorate. First, strategic voters do not create order eects for candidates with vote shares in low percentiles in single-vote elections or (almost) none in multi-vote elections, so order eects for these elections identify the share of behavioral voters. The variation of order eects for larger percentiles identies the preference parameter as these order eects must come from strategic voter, which only occur if vote shares are suciently close for behavioral voters to change the election outcome - and the vote share distribution is determined by preferences. For example, if behavioral voters would never change the election outcome, i.e., the vote share distribution would imply that vote shares are far apart from each other, we would not get any strategic order eects and thus no curvature of total order eects.

I estimate the preference parameter µ to be ˆµ = 0.503, CI90=[−1.13, 0.7] . In three-

candidate elections, this value implies with the logit specication the following preferences: on average, 76% of voters prefer the candidate with the highest mean utility over the one with the second-highest mean utility (and similarly the 2nd over the 3rd); and 90% prefer the candidate with the highest mean utility over the one with the lowest mean utility.

Results, three-candidate elections: I estimate the share of behavioral voters to be ˆ

λ = 1.73%∗∗∗, CI95= [0.05, 2.42],

which is comparable to my previous estimate of behavioral voters in three-candidate elections and to the share of behavioral voters in two-candidate elections as shown below. Given this

share of behavioral voters, I estimate that rational order eects b − λ account for around ˆ_{b − ˆλ = 52.7%}∗∗∗_{, CI}

95= [38.5, 109]

of all order eects. Note that this uses the estimated share of total order eects in the model.27