Related papers: Standardizing Representation for Equality with a P…
Apportionment is the task of assigning resources to entities with different entitlements in a fair manner, and specifically a manner that is as proportional as possible. The best-known application is the assignment of parliamentary seats to…
The goal of multi-winner elections is to choose a fixed-size committee based on voters' preferences. An important concern in this setting is representation: large groups of voters with cohesive preferences should be adequately represented…
Sortition is based on the idea of choosing randomly selected representatives for decision making. The main properties that make sortition particularly appealing are fairness -- all the citizens can be selected with the same probability --…
In multiwinner approval voting, forming a committee that proportionally represents voters' approval ballots is an essential task. The notion of justified representation (JR) demands that any large "cohesive" group of voters should be…
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…
State delegations are often chosen through single-member district elections, creating a tension between respecting district majorities and reflecting the statewide electorate. First-past-the-post (FPTP) follows each district's majority but…
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…
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…
The apportionment problem constitutes a fundamental problem in democratic societies: How to distribute a fixed number of seats among a set of states in proportion to the states' populations? This--seemingly simple--task has led to a rich…
In the classic apportionment problem the goal is to decide how many seats of a parliament should be allocated to each party as a result of an election. The divisor methods provide a way of solving this problem by defining a notion of…
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…
The problem of how to allocate to states the seats in the US House of Representatives is the most studied instance of what is termed the `apportionment problem'. We propose a new method of apportionment which is stochastic, which meets the…
Distribution of seats in The European Parliament postulated by Treaty of Lisbon should be degressively proportional. The meaning of degressively proportional concept can be found in two principles annexed to the draft of European Parliament…
The Population Stability Index (PSI) is a widely used measure in credit risk modeling and monitoring within the banking industry. Its purpose is to monitor for changes in the population underlying a model, such as a scorecard, to ensure…
When delegations to an assembly or council represent differently sized constituencies, they are often allocated voting weights which increase in population numbers (EU Council, US Electoral College, etc.). The Penrose square root rule…
The Constitutionally mandated task of assigning Congressional seats to the various U.S. States proportional to their represented populations ("according to their numbers") has engendered much contention, but rather less consensus. Using the…
In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that…
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…
Participatory budgeting (PB) is a democratic paradigm whereby voters decide on a set of projects to fund with a limited budget. We consider PB in a setting where voters report ordinal preferences over projects and have (possibly) asymmetric…
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…