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Elections with Multiple Positive and Negative Votes

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We investigate the performance of a voting procedure in which voters cast multiple votes, with some votes positive and some negative. The procedure is a variant of the “D21” method proposed by Janeček (2016). The setting is the 2018 Czech Republic presidential election. Evidence is provided through a survey of secondary school students asked to cast ballots in both single- and multi-vote election experiments. Using the survey data, we estimate a spatial voting model to uncover ideological positions of candidates and respondents. Results suggest that the multi-vote procedure may limit the success of extreme candidates in elections.

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  1. These include rank-order voting schemes, the Condorcet criterion, approval voting, and others. Mueller (2003) and Nurmi (1983) describe many of these alternative schemes.

  2. Boehm (1976) was an early proponent of negative voting. Alcantud and Laruelle (2014), Yilmaz (1999), and Baharad and Nitzan (2016) also propose schemes with negative voting.

  3. The voting procedure applied in this study did not impose the D21 requirement of the 2:1 ratio of positive to negative votes.

  4. Analysis of the second wave survey data produced results that were qualitatively similar to those obtained with the first. Results of that analysis are provided in an online appendix.

  5. The original sample included 304 students, but three were eliminated because their ballots reported either zero votes or more than three votes, violating the election rules.

  6. Poole and Rosenthal recover spatial locations of the choices voted upon as well as the locations of the legislators. In our model, we similarly recover the locations of candidates (the choices) and those of the voters. Logit and probit models assume different distributions for the model error terms, but this is not normally a matter of importance.

  7. In the Poole-Rosenthal applications, there are only two choice options available to legislators. Vote probabilities depend on the distances of the candidate from each of the two options.

  8. This does not presuppose that these candidates were extreme, as the range for positions of other candidates is not restricted. For example, other candidates could have had estimated positions near 1000 or − 1000.

  9. The 2018 Czech election was seen as a battle “between authoritarianism and liberal democracy, between east and west,” where Zeman, a pro-Russian politician represented authoritarianism and east, while Drahos, a pro-EU academic with no prior political experience was a pro-west liberal (Cameron 2018).

  10. Fully accounting for all of these issues would be very difficult. There are no off-the-shelf econometric models that are strictly appropriate.

  11. As we have noted, our functional form imposes a lower bound on voter utilities. A consequence is that when distances between candidates and voters become very large, additional changes in distance have negligible marginal impacts on utility and extreme voter positions are not well-identified.


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Correspondence to Tanya Gibbs.

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Tanya Gibbs, former Chief Research Officer, Institute H21, Prague, Czech Republic

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Gibbs, T., Chappell, Jr., H.W. Elections with Multiple Positive and Negative Votes. Homo Oecon 38, 37–47 (2021).

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