Party System Compactness: Measurement and Consequences

An important property of any party system is the set of choices it presents to the electorate. In this paper we analyze the distribution of parties relative to voters in the multidimensional issue space and introduce two measures of the dispersion of the parties in the issue space relative to the voters, which we call measures of the compactness of the parties in the issue space. We show how compactness is easily computed using standard survey items found on national election surveys. Because we study the spacing of the parties relative to the distribution of the voters, we produce metric-free measures of compactness of the party system. The measures can be used to compare party systems across issues, over time within countries, and across countries. Comparing the compactness of party systems across countries allows us to determine the relative amount of issue choice afforded voters in different polities. We examine the compactness of the issue space and test the impact it has on voter choice in four countries: the United States, the Netherlands, Canada, and Great Britain. We demonstrate that the more compact the distribution of the parties in the issue space on any given issue, the less voters weight that issue in their vote decision. Thus we provide evidence supporting theories suggesting that the greater the choice offered by the parties in an election, the more likely it is that issue voting will play a major role in that election

An experimental study on learning about voting powers

We investigate experimentally whether subjects can learn, from their limited experiences, about relationships between the distribution of votes in a group and associated voting powers in weighted majority voting systems (WMV). Subjects are asked to play two-stage games repeatedly. In the second stage of the game, a group of four subjects bargains over how to divide fixed amount of resources among themselves through theWMV determined in the first stage. In the first stage, two out of four subjects in the group, independently and simultaneously, choose from two options that jointly determine the distribution of a given number of votes among four members. These two subjects face a 2 × 2 matrix that shows the distribution of votes, but not associated voting powers, among four members for each outcome. Therefore, to obtain higher rewards, subjects need to learn about the latter by actually playing the second stage. The matrix subjects face in the first stage changes during the experiment to test subjects' understanding of relationships between distribution of votes and voting power. The results of our experiments suggest that although (a) many subjects learn to choose, in the votes apportionment stage, the option associated with a higher voting power, (b) it is not easy for them to learn the underlying relationships between the two and correctly anticipate their voting powers when they face a new distribution of votes.experiment, learning, voting power, bargaining

An experimental study on learning about voting powers

We investigate experimentally whether subjects can learn, from their limited experiences, about relationships between the distribution of votes in a group and associated voting powers in weighted majority voting systems (WMV). Subjects are asked to play two-stage games repeatedly. In the second stage of the game, a group of four subjects bargains over how to divide fixed amount of resources among themselves through the WMV determined in the first stage. In the first stage, two out of four subjects in the group, independently and simultaneously, choose from two options that jointly determine the distribution of a given number of votes among four members. These two subjects face a 2 ~ 2 matrix that shows the distribution of votes, but not associated voting powers, among four members for each outcome. Therefore, to obtain higher rewards, subjects need to learn about the latter by actually playing the second stage. The matrix subjects face in the first stage changes during the experiment to test subjects' understanding of relationships between distribution of votes and voting power. The results of our experiments suggest that although (a) many subjects learn to choose, in the votes apportionment stage, the option associated with a higher voting power, (b) it is not easy for them to learn the underlying relationships between the two and correctly anticipate their voting powers when they face a new distribution of votes.

Stylized facts in Brazilian vote distributions

Elections, specially in countries such as Brazil with an electorate of the order of 100 million people, yield large-scale data-sets embodying valuable information on the dynamics through which individuals influence each other and make choices. In this work we perform an extensive analysis of data sets available for Brazilian proportional elections of legislators and city councillors throughout the period 1970-2012, which embraces two distinct political regimes: a military dictatorship and a democratic phase. Through the distribution $P(v)$ of the number of candidates receiving $v$ votes, we perform a comparative analysis of different elections in the same calendar and as a function of time. The distributions $P(v)$ present a scale-free regime with a power-law exponent $\alpha$ which is not universal and appears to be characteristic of the electorate. Moreover, we observe that $\alpha$ typically increases with time. We propose a multi-species model consisting in a system of nonlinear differential equations with stochastic parameters that allows to understand the empirical observations. We conclude that the power-law exponent $\alpha$ constitutes a measure of the degree of feedback of the electorate interactions. To know the interactivity of the population is relevant beyond the context of elections, since a similar feedback may occur in other social contagion processes.Comment: 8 pages, 8 figures, a version with some modifications was published in PLoS ON

Fast plurality consensus in regular expanders

Pull voting is a classic method to reach consensus among $n$ vertices with differing opinions in a distributed network: each vertex at each step takes on the opinion of a random neighbour. This method, however, suffers from two drawbacks. Even if there are only two opposing opinions, the time taken for a single opinion to emerge can be slow and the final opinion is not necessarily the initially held majority. We refer to a protocol where 2 neighbours are contacted at each step as a 2-sample voting protocol. In the two-sample protocol a vertex updates its opinion only if both sampled opinions are the same. Not much was known about the performance of two-sample voting on general expanders in the case of three or more opinions. In this paper we show that the following performance can be achieved on a $d$-regular expander using two-sample voting. We suppose there are $k \ge 3$ opinions, and that the initial size of the largest and second largest opinions is $A_1, A_2$ respectively. We prove that, if $A_1 - A_2 \ge C n \max\{\sqrt{(\log n)/A_1}, \lambda\}$, where $\lambda$ is the absolute second eigenvalue of matrix $P=Adj(G)/d$ and $C$ is a suitable constant, then the largest opinion wins in $O((n \log n)/A_1)$ steps with high probability. For almost all $d$-regular graphs, we have $\lambda=c/\sqrt{d}$ for some constant $c>0$. This means that as $d$ increases we can separate an opinion whose majority is $o(n)$, whereas $\Theta(n)$ majority is required for $d$ constant. This work generalizes the results of Becchetti et. al (SPAA 2014) for the complete graph $K_n$

Blame and punishment? The electoral politics of extreme austerity in Greece

Can governments that introduce extreme austerity measures survive elections? Contrary to economic voting expectations, the PASOK government in Greece initially appeared to cope quite well, claiming victory in regional elections in 2010 despite widespread anti-austerity protest. In this paper, we interpret this result with the help of a post-election survey, which also covered future voting intention. The explanatory power of models based on theories of economic voting and blame attribution as well as the electoral impact of the government’s representation of the crisis as an existential threat are assessed. Our analysis challenges the interpretation of the 2010 election as an indication of support for PASOK’s austerity policies and reveals weaknesses in its support base, which help contextualise its downfall in the 2012 Parliamentary elections. The paper also underlines the importance of studying the impact of crises discourses on voting choice, particularly since blame attribution receives little support in this case