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Elections for public offices in democratic nations are large-scale examples of collective decision-making. As a complex system with a multitude of interactions among agents, we can anticipate that universal macroscopic patterns could emerge…
The following paper is part of the authors' response to an invitation from the Constitutional Affairs Committee (AFCO) of the European Parliament to advise on mathematical methods for the allocation of Parliamentary seats between the 27…
Citizen-focused democratic processes where participants deliberate on alternatives and then vote to make the final decision are increasingly popular today. While the computational social choice literature has extensively investigated voting…
In the traditional voting manipulation literature, it is assumed that a group of manipulators jointly misrepresent their preferences to get a certain candidate elected, while the remaining voters are truthful. In this paper, we depart from…
Are there voting methods which (i) give everyone, including minorities, an equal share of effective power even if voters act strategically, (ii) promote consensus rather than polarization and inequality, and (iii) do not favour the status…
Determining the power distribution of the members of a shareholder meeting or a legislative committee is a well-known problem for many applications. In some cases it turns out that power is nearly proportional to relative voting weights,…
{\em Distortion} is a well-established notion for quantifying the loss of social welfare that may occur in voting. As voting rules take as input only ordinal information, they are essentially forced to neglect the exact values the agents…
We consider an agent community wishing to decide on several binary issues by means of issue-by-issue majority voting. For each issue and each agent, one of the two options is better than the other. However, some of the agents may be…
In a strategy-proof mechanism, the influence of an agent may be measured as the set of outcomes an agent can bring about by varying her (reported) type. More specifically, we refer to an agent's influence on her own relevant outcomes as her…
We study systems with two symmetric absorbing states, such as the voter model and variations of it, which have been broadly used as minimal neutral models in genetics, population ecology, sociology, etc. We analyze the effects of a key…
We consider voting on multiple independent binary issues. In addition, a weighting vector for each voter defines how important they consider each issue. The most natural way to aggregate the votes into a single unified proposal is…
Some argue that political stability is best served through a two-party system. This study refutes this. The author mathematically defines the stability and rigidity of electoral systems comprised of any quantity of electors and parties. In…
Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Here we propose a generative model based on a stochastic differential equation that allows us to analyse…
This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is…
We design a recursive measure of voting power based on partial as well as full voting efficacy. Classical measures, by contrast, incorporate solely full efficacy. We motivate our design by representing voting games using a division lattice…
In many applications of cooperative game theory -- from corporate governance and cartel formation to parliamentary voting -- not all winning coalitions are feasible. Ideological distances, institutional constraints, or pre-electoral…
Election results are determined by numerous social factors that affect the formation of opinion of the voters, including the network of interactions between them and the dynamics of opinion influence. In this work we study the result of…
The paper develops a theory of power for delegable proxy voting systems. We define a power index able to measure the influence of both voters and delegators. Using this index, which we characterize axiomatically, we extend an earlier…
The voting systems known as Alternative Vote (AV) and Single Transferable Vote (STV) are extensively used for elections in Australia, possibly more than in any other jurisdiction. Often proposed as superior alternatives to Plurality and…
Voters making a binary decision purchase votes from a centralized clearing house, paying the square of the number of votes purchased. The net payoff to an agent with utility $u$ who purchases $v$ votes is $\Psi (S_{n+1})u-v^{2}$, where…