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In the theory of voting, the Plurality rule for preferences that come in the form of linear orders selects the alternatives most frequently appearing in the first position of those orders, while the Anti-Plurality rule selects the…

Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to jump to single transferable vote (STV) as the…

Proportional representation (PR) is one of the central principles in voting. Elegant rules with compelling PR axiomatic properties have the potential to be adopted for several important collective decision making settings. I survey some…

We propose a criterion of equidistribution by the differentiability of certain arithmetic invariants. Combined with the slope method and the asymptotic measures, this criterion gives a new "conceptual" proof to equidistribution results…

In this paper, we study the problem of Participatory Budgeting (PB) with approval ballots, inspired by Multi-Winner Voting schemes. We present generalized preference aggregation methods for participatory budgeting, especially for finding…

Given a set of agents with approval preferences over each other, we study the task of finding $k$ matchings fairly representing everyone's preferences. We model the problem as an approval-based multiwinner election where the set of…

This paper proposes a voting process in which voters allocate fractional votes to their expected utility in different domains: over proposals, other participants, and sets containing proposals and participants. This approach allows for a…

The proportional veto principle, which captures the idea that a candidate vetoed by a large group of voters should not be chosen, has been studied for ranked ballots in single-winner voting. We introduce a version of this principle for…

We present an alternative voting system that aims at bridging the gap between proportional representative systems and majoritarian, single winner election systems. The system lets people vote for multiple parties, but then assigns each…

A new unequal probability sampling method is proposed. This method is sequential. The decision to select or not each unit is made based on the order in which the units appear. A variant of this method allows selecting a sample from a…

A method is given for determining a mixed social choice out of a paired-comparison matrix. The method combines a projection procedure introduced in previous papers of the same authors and a classical method due to Zermelo. The resulting…

The first observation of the paper is that methods for determining proportional representation in electoral systems may be suitable as alternatives to the pro-rata order matching algorithm used in stock exchanges. The main part of our work…

We consider three algorithms for allocating parliamentary seats by proportional representation. The usual approach to describing such algorithms is to compute a quota of votes that each party uses to "acquire'' representatives. This kind of…

In this paper, we experimentally compare major approval-based multiwinner voting rules. To this end, we define a measure of similarity between two equal-sized committees subject to a given election. Using synthetic elections coming from…

Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…

Voting methods are instrumental design elements of democracies. Citizens use them to express and aggregate their preferences to reach a collective decision. However, voting outcomes can be as sensitive to voting rules as they are to…

Consider $\mathbb{G}$ the progressive enlargement of a filtration $\mathbb{F}$ with a random time $\tau$. Assuming that, in $\mathbb{F}$, the martingale representation property holds, we examine conditions under which the martingale…

Social choice is replete with various settings including single-winner voting, multi-winner voting, probabilistic voting, multiple referenda, and public decision making. We study a general model of social choice called Sub-Committee Voting…

We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional…

Voting is a very general method of preference aggregation. A voting rule takes as input every voter's vote (typically, a ranking of the alternatives), and produces as output either just the winning alternative or a ranking of the…