Related papers: Redistricting for Proportionality
One way of evaluating social choice (voting) rules is through a utilitarian distortion framework. In this model, we assume that agents submit full rankings over the alternatives, and these rankings are generated from underlying, but…
It is well known that no reasonable voting rule is strategyproof. Moreover, the common Plurality rule is particularly prone to strategic behavior of the voters and empirical studies show that people often vote strategically in practice.…
In the metric distortion problem, a set of voters and candidates lie in a common metric space, and a committee of $k$ candidates must be elected. The objective is to minimize a social cost, defined as a function of the distances between…
We study the design of voting rules in the metric distortion framework. It is known that any deterministic rule suffers distortion of at least $3$, and that randomized rules can achieve distortion strictly less than $3$, often at the cost…
A key promise of democratic voting is that, by accounting for all constituents' preferences, it produces decisions that benefit the constituency overall. It is alarming, then, that all deterministic voting rules have unbounded distortion:…
In rank aggregation, the task is to aggregate multiple weighted input rankings into a single output ranking. While numerous methods, so-called social welfare functions (SWFs), have been suggested for this problem, all of the classical SWFs…
In district-based multi-party elections, electors cast votes in their respective districts. In each district, the party with maximum votes wins the corresponding seat in the governing body. Election Surveys try to predict the election…
Fairness in multiwinner elections, a growing line of research in computational social choice, primarily concerns the use of constraints to ensure fairness. Recent work proposed a model to find a diverse \emph{and} representative committee…
We consider a two-round election model involving $m$ voters and $n$ candidates. Each voter is endowed with a strict preference list ranking the candidates. In the first round, the candidates are partitioned into two subsets, $A$ and $B$,…
We study two concepts of proportionality in the model of approval-based committee elections. In degressive proportionality small minorities of voters are favored in comparison with the standard linear proportionality. Regressive…
In representative democracies, the election of new representatives in regular election cycles is meant to prevent corruption and other misbehavior by elected officials and to keep them accountable in service of the ``will of the people."…
Apportionment is the problem of distributing $h$ indivisible seats across states in proportion to the states' populations. In the context of the US House of Representatives, this problem has a rich history and is a prime example of…
We propose a method for redistricting, decomposing a geographical area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are compact and contiguous. Each district is the…
In multiwinner approval voting, the goal is to select $k$-member committees based on voters' approval ballots. A well-studied concept of proportionality in this context is the justified representation (JR) axiom, which demands that no large…
In redistricting litigation, effective enforcement of the Voting Rights Act has often involved providing the court with districting plans that display a larger number of majority-minority districts than the current proposal (as was true,…
The U.S. Supreme Court is currently deliberating over whether a proposed mathematical formula should be used to detect unconstitutional partisan gerrymandering. We show that in some cases, this formula will only flag bizarrely shaped…
Geographical considerations such as contiguity and compactness are necessary elements of political districting in practice. Yet an analysis of the problem without such constraints yields mathematical insights that can inform real-world…
This past decade has seen a noticeable uptick in asymmetric election results along with the inevitable claims of gerrymandering and litigation. Research, too, has followed, giving rise to intense scrutiny of elections, where the goal is to…
We study situations where a group of voters need to take a collective decision over a number of public issues, with the goal of getting a result that reflects the voters' opinions in a proportional manner. Our focus is on interconnected…
How to fairly apportion congressional seats to states has been debated for centuries. We present an alternative perspective on apportionment, centered not on states but "families" of state, sets of states with "divisor-method" quotas with…