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Coate, Conlin, and Moro: The performance of the pivotal-voter model in small-scale elections

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Coate, Conlin, and Moro. 2006. The performance of the pivotal-voter model in small-scale elections: Evidence from Texas liquor ref.

In Brief

The researchers test how well the pivotal voter model explains turnout in small-scale elections using data from the Texas liquor referenda. While the model predicts turnout fairly well, it predicts closer electoral outcome than are observed. The expressive voter model actually outperforms the pivotal voter model in predicting the results.


  • Pivotal voter model--citizens are motivated to vote by the chance that they might swing the election
  • Intensity model--assumes citizens vote to express their preferences and that their expressive payoffs are higher the more intensely they feel about an issue. (Expressive voting)

The Test

  • They use data from 366 local liquor referenda in Texas from 1976-1996.
  • Because of computational constraints, the authors will use only 144 cases of referenda that can be considered "small", having less than 900 voters (called "in sample" observations). 222 elections are considered large, called "out of sample" observations.
  • Liquor referenda elections are held separately from other elections so the only reason to go to the polls is to vote on the proposed change in liquor law. They never overlap with the election of officials.
  • Controlled for the fraction of Baptists in the population between small and large jurisdictions, the fraction of elections held on the weekend between small and large, and the type of proposed restrictions (which across both small and large groups are almost always beer and wine referenda, which permit only the sale of beer and wine, and off-premise referenda, which allow the sale of alcohol off bar premises)
  • Turnout is substantially lower in larger districts to begin with, 24% of eligible voters as opposed to 54% in smaller districts. When plotted, turnout is seen to decreases sharply from 80% in small jurisdiction to about 20% as the jurisdiction size increases to about 500 voters. Also, elections in small districts are less likely to be close. The average winning margin in small jurisdictions is 16%, compared to 4.6% in large.

Goal is to provide inference on the coefficients for the parameters of the model using the data on election outcomes in Texas liquor referenda. The four parameters are the supporters' benefit 'b', the opposer's loss 'x'; the probability that a citizen is a supporter 'u'; and the upper bound of the uniform cost distribution 'c'. The authors will consider how changes in the values of the coefficients of the parameters will impact the outcome predicted by the model.

Testing two things. 1. How well the pivotal voter model explains total turnout and 2. The closeness of the referenda outcome.


A table with the results for each parameter coefficient value are on Page 19 for the pivotal voter model and page 23 for the expressive voter model.

  1. The pivotal voter model does well to predict total turnout
    • Based on the parameter calculation from the in sample data, the model is relatively accurate in predicting the average voter turnout of 0.54.
  2. The model predicts much closer results than are seen in the data
  3. Based on the coefficient outcomes from the small scale election data, when applied to larger jurisdictions, the pivotal voter model under predicts total turnout.
    • the pivotal voter model predicts an average of 0.14 turnout in large districts, while actual turnout in large districts is 0.24
  4. When compared to a simple alternative model based on expressive voting, the expressive model does a much worse job predicting turnout (under predicts for small jurisdictions and over predicts for large), but predicts closeness just as well as the more sophisticated pivotal voter model. If we allow for the possibility that citizens in smaller communities have a stronger desire to express themselves, say due to a stronger sense of community, the expressive model performs better.
    • Why does it pivotal voter model not predict closeness as well? Because in the Pivotal voter model we would not predict, ceteris paribus, that groups with different sizes display significant differences in the closeness of the election. The logic of the pivotal voter model is that results will be a certain closeness regardless of jurisdiction size, whereas the intensity model is not driven by the desire to influence the outcome.

Comments and Criticisms

Can it be both motivations acting simultaneously? That is, can we have pivotal motivations that that 75% effect our decision to vote, and if that approaches some close cutoff level, only then do we consider our expressive non instrumental goals (or vice versa).

For example, I may consider if my vote will be pivotal in a liquor referenda, and though my belief may not approach my cut-off level for voting, it is close enough to it that I can no consider my expressive gains. In other words I consider the two sequentially and have brink-points to consider the other motivation that are lower in value to the actual full value needed to motivate a vote.

Do you buy their theory about why the intensity model predicts closeness better? Do voters in small communities have stronger desires to express themselves? "If we allow for the possibility that citizens in smaller communities have a stronger desire to express themselves, say due to a stronger sense of community, the expressive model performs better."