Related papers: Single-crossing Implementation
We introduce two-crossing elections as a generalization of single-crossing elections, showing a number of new results. First, we show that two-crossing elections can be recognized in polynomial time, by reduction to the well-studied…
In elections, a set of candidates ranked consecutively (though possibly in different order) by all voters is called a clone set, and its members are called clones. A clone structure is a family of all clone sets of a given election. In this…
Roughly speaking, gerrymandering is the systematic manipulation of the boundaries of electoral districts to make a specific (political) party win as many districts as possible. While typically studied from a geographical point of view,…
An electorate with fully-ranked innate preferences casts approval votes over a finite set of alternatives. As a result, only partial information about the true preferences is revealed to the voting authorities. In an effort to understand…
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…
In an election in which each voter ranks all of the candidates, we consider the head-to-head results between each pair of candidates and form a labeled directed graph, called the margin graph, which contains the margin of victory of each…
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,…
In an election, we are given a set of voters, each having a preference list over a set of candidates, that are distributed on a social network. We consider a scenario where voters may change their preference lists as a consequence of the…
We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for these rules is known to be…
Eliciting the preferences of a set of agents over a set of alternatives is a problem of fundamental importance in social choice theory. Prior work on this problem has studied the query complexity of preference elicitation for the…
In this paper, we introduce the following new concept in graph drawing. Our task is to find a small collection of drawings such that they all together satisfy some property that is useful for graph visualization. We propose investigating a…
Candidate control of elections is the study of how adding or removing candidates can affect the outcome. However, the traditional study of the complexity of candidate control is in the model in which all candidates and votes are known up…
The traditional election control problem focuses on the use of control to promote a single candidate. In parliamentary elections, however, the focus shifts: voters care no less about the overall governing coalition than the individual…
We study the complexity of determining a winning committee under the Chamberlin--Courant voting rule when voters' preferences are single-crossing on a line, or, more generally, on a median graph (this class of graphs includes, e.g., trees…
We investigate preference profiles for a set $\mathcal{V}$ of voters, where each voter $i$ has a preference order $\succ_i$ on a finite set $A$ of alternatives (that is, a linear order on $A$) such that for each two alternatives $a,b\in A$,…
We study the computational complexity of controlling the result of an election by breaking ties strategically. This problem is equivalent to the problem of deciding the winner of an election under parallel universes tie-breaking. When the…
The crossing number of a graph $G$ is the least number of crossings over all possible drawings of $G$. We present a structural characterization of graphs with crossing number one.
We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given…
Integrity of elections is vital to democratic systems, but it is frequently threatened by malicious actors. The study of algorithmic complexity of the problem of manipulating election outcomes by changing its structural features is known as…
Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We…