Related papers: Piercing Numbers in Circular Societies
We survey a host of results from discrete geometry that have bearing on the analysis of geometric models of approval voting. Such models view the political spectrum as a geometric space, with geometric constraints on voter preferences.…
Consider a society of voters, each of whom specify an approval set over a linear political spectrum. We examine double-interval societies, in which each person's approval set is represented by two disjoint closed intervals, and study this…
In multiwinner approval elections with many candidates, voters may struggle to determine their preferences over the entire slate of candidates. It is therefore of interest to explore which (if any) fairness guarantees can be provided under…
In approval voting, individuals vote for all platforms that they find acceptable. In this situation it is natural to ask: When is agreement possible? What conditions guarantee that some fraction of the voters agree on even a single…
This work contributes to a foundational question in economic theory: how do individual-level cognitive biases interact with collective choice mechanisms? We study a setting where voters hold intrinsic preference rankings over a set of…
Many hard computational social choice problems are known to become tractable when voters' preferences belong to a restricted domain, such as those of single-peaked or single-crossing preferences. However, to date, all algorithmic results of…
Multi-winner voting is the process of selecting a fixed-size set of representative candidates based on voters' preferences. It occurs in applications ranging from politics (parliamentary elections) to the design of modern computer…
A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. In contrast to a previous article, here the individual votes are allowed to be incomplete, that is, they…
Consider an undirected graph G, representing a social network, where each node is blue or red, corresponding to positive or negative opinion on a topic. In the voter model, in discrete time rounds, each node picks a neighbour uniformly at…
We extend Approval voting to the settings where voters may have intransitive preferences. The major obstacle to applying Approval voting in these settings is that voters are not able to clearly determine who they should approve or…
Social choice becomes easier on restricted preference domains such as single-peaked, single-crossing, and Euclidean preferences. Many impossibility theorems disappear, the structure makes it easier to reason about preferences, and…
We use the ``map of elections'' approach of Szufa et al. (AAMAS-2020) to analyze several well-known vote distributions. For each of them, we give an explicit formula or an efficient algorithm for computing its frequency matrix, which…
We consider elections where both voters and candidates can be associated with points in a metric space and voters prefer candidates that are closer to those that are farther away. It is often assumed that the optimal candidate is the one…
We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted,…
We study single-candidate voting embedded in a metric space, where both voters and candidates are points in the space, and the distances between voters and candidates specify the voters' preferences over candidates. In the voting, each…
Politics around the world exhibits increasing polarization, demonstrated in part by rigid voting configurations in institutions like legislatures or courts. A crux of polarization is separation along a unidimensional ideological axis, but…
When can a majority of voters find common ground, that is, a position they all agree upon? How does the shape of the political spectrum influence the outcome? When mathematical objects have a social interpretation, the associated theorems…
We introduce a single-winner perspective on voting on matchings, in which voters have preferences over possible matchings in a graph, and the goal is to select a single collectively desirable matching. Unlike in classical matching problems,…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
The outcomes of democratic elections rest on individuals' decision-making that is driven by their varying preferences and beliefs. Individuals may prefer consensus to gridlock, or gridlock to consensus, and information may be fractured via…