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

Disclaimer. Don't rely on these old notes in lieu of reading the literature, but they can jog your memory. As a grad student long ago, my peers and I collaborated to write and exchange summaries of political science research. I posted them to a wiki-style website. "Wikisum" is now dead but archived here. I cannot vouch for these notes' accuracy, nor can I say who wrote them.

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.


The Test

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."

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Coate, Stephen (author)Conlin, Michael (author)Moro, Andrea (author)Political TheoryVotingTurnoutAltruism

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