On β-Plurality Points in Spatial Voting Games

Let V be a set of n points in mathcal R d , called voters . A point p ∈ mathcal R d is a plurality point for V when the following holds: For every q ∈ mathcal R d , the number of voters closer to p than to q is at least the number of voters closer to q than to p . Thus, in a vote where each v ∈ V votes for the nearest proposal (and voters for which the proposals are at equal distance abstain), proposal p will not lose against any alternative proposal q . For most voter sets, a plurality point does not exist. We therefore introduce the concept of β-plurality points , which are defined similarly to regular plurality points, except that the distance of each voter to p (but not to q ) is scaled by a factor β , for some constant 0< β ⩽ 1. We investigate the existence and computation of β -plurality points and obtain the following results. • Define β * d := {β : any finite multiset V in mathcal R d admits a β-plurality point. We prove that β * d = √3/2, and that 1/√ d ⩽ β * d ⩽ √ 3/2 for all d ⩾ 3. • Define β ( p, V ) := sup {β : p is a β -plurality point for V }. Given a voter set V in mathcal R 2 , we provide an algorithm that runs in O ( n log n ) time and computes a point p such that β ( p , V ) ⩾ β * b . Moreover, for d ⩾ 2, we can compute a point p with β ( p , V ) ⩾ 1/√ d in O ( n ) time. • Define β ( V ) := sup { β : V admits a β -plurality point}. We present an algorithm that, given a voter set V in mathcal R d , computes an ((1-ɛ)ċ β ( V ))-plurality point in time O n 2 ɛ 3d-2 ċ log n ɛ d-1 ċ log 2 1ɛ).

A comparison of zero and minimal intelligence agendas in Markov Chain voting models

Emergent behavior in repeated collective decisions of minimally intelligent agents -- who at each step in time invoke majority rule to choose between a status quo and a random challenge -- can manifest through the long-term stationary probability distributions of a Markov Chain. We use this known technique to compare two kinds of voting agendas: a zero-intelligence agenda that chooses the challenger uniformly at random, and a minimally-intelligent agenda that chooses the challenger from the union of the status quo and the set of winning challengers. We use Google Co-Lab's GPU accelerated computing environment, with code we have hosted on Github, to compute stationary distributions for some simple examples from spatial-voting and budget-allocation scenarios. We find that the voting model using the zero-intelligence agenda converges more slowly, but in some cases to better outcomes.

On the Distortion Value of Elections with Abstention

In Spatial Voting Theory, distortion is a measure of how good the winner is. It has been proved that no deterministic voting mechanism can guarantee a distortion better than 3, even for simple metrics such as a line. In this study, we wish to answer the following question: how does the distortion value change if we allow less motivated agents to abstain from the election? We consider an election with two candidates and suggest an abstention model, which is a general form of the abstention model proposed by Kirchgässner. Our results characterize the distortion ¨ value and provide a rather complete picture of the model.

A Clustering Approach for Characterizing Voter Types: An Application to High-Dimensional Ballot and Survey Data

Large-scale ballot and survey data hold the potential to uncover the prevalence of swing voters and strong partisans in the electorate. However, existing approaches either employ exploratory analyses that fail to fully leverage the information available in high-dimensional data, or impose a one-dimensional spatial voting model. I derive a clustering algorithm which better captures the probabilistic way in which theories of political behavior conceptualize the swing voter. Building from the canonical finite mixture model, I tailor the model to vote data, for example by allowing uncontested races. I apply this algorithm to actual ballots in the Florida 2000 election and a multi-state survey in 2018. In Palm Beach County, I find that up to 60 percent of voters were straight ticket voters; in the 2018 survey, even higher. The remaining groups of the electorate were likely to cross the party line and split their ticket, but not monolithically: swing voters were more likely to swing for state and local candidates and popular incumbents.

Demographic Moderation of Spatial Voting in Presidential Elections

Using multiple large national surveys, we investigate how the relationship between policy-based ideology and vote choice in presidential elections differs across demographic groups. Specifically, we consider three key demographic characteristics: race, education, and gender. We find that large differences exist in the way ideology relates to presidential vote for voters from different racial groups. By contrast, we find quite small differences in this relationship when separating voters by education level. Perhaps most surprisingly, whereas men are on average more conservative than women, the relationship between ideology and presidential vote is estimated to be almost exactly the same for the two genders. The large sample sizes we employ allow for relatively precise estimation of these relationships even among our various demographic subsamples and these findings hold similarly across several recent presidential elections.

The polarization dynamics of electoral reforms

Electoral reforms affect legislative outcomes by influencing incumbent legislators’ behavior, new entrants’ behavior, and the probability that incumbents are replaced with new entrants. Empirical work on electoral reforms and polarization has focused on new entrants’ behavior. We employ a simple decision theoretic framework with partial incumbent policy persistence and spatial voting to examine the three channels jointly. We show that a reform designed to encourage ideological moderation produces larger effects on polarization when the reform is implemented than when it is removed. The key insight is that implementing a moderation-inducing reform generates a set of challengers who are more likely to defeat incumbents while the incumbents are more likely to win reelection when the reform is removed. We then empirically examine how elections and legislative polarization respond to unlimited PAC contributions in state legislatures. Examining incumbents’ decisions to stand for reelection, the electoral performance of incumbents who do run, and partisan polarization, we find empirical support for our predictions.