Related papers: Stochastic apportionment
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…
Several measures of partisan bias are reviewed for single member districts with two dominant parties. These include variants of the simple bias that considers only deviation of seats from 50% at statewide 50% vote. Also included are…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
We analyze properties of apportionment functions in context of the problem of allocating seats in the European Parliament. Necessary and sufficient conditions for apportionment functions are investigated. Some exemplary families of…
While proportionality is frequently named as a desirable property of voting rules, its interpretation in multiwinner voting differs significantly from that in apportionment. We aim to bridge these two distinct notions of proportionality by…
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 --…
We study multiwinner elections with approval-based preferences. An instance of a multiwinner election consists of a set of alternatives, a population of voters---each voter approves a subset of alternatives, and the desired committee size…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
We consider the problem of state selection for a stochastic system, initially in an unstable stationary state, when multiple metastable states compete for occupation. Using path-integral techniques we derive remarkably simple and accurate…
Consider an election where N seats are distributed among parties with proportions p_1,...,p_m of the votes. We study, for the common divisor and quota methods, the asymptotic distribution, and in particular the mean, of the seat excess of a…
We consider the following problem in which a given number of items has to be chosen from a predefined set. Each item is described by a vector of attributes and for each attribute there is a desired distribution that the selected set should…
Assuming that partisan fairness and responsiveness are important aspects of redistricting, it is important to measure them. Many measures of partisan bias are satisfactory for states that are balanced with roughly equal proportions of…
Proportional representation (PR) has long been believed the ideal system for the equality of individuals in apportioning the seats of a legislature body to subgroups. We observe that PR implicitly assumes the (standard) number of…
The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case…
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…
Fair division is a significant, long-standing problem and is closely related to social and economic justice. The conventional division methods such as cut-and-choose are hardly applicable to realworld problems because of their complexity…
We study an elementary two-player card game where in each round players compare cards and the holder of the smallest card wins. Using the rate equations approach, we treat the stochastic version of the game in which cards are drawn…
This paper considers the arbitrary-proportional finite-set-partitioning problem which involves partitioning a finite set into multiple subsets with respect to arbitrary nonnegative proportions. This is the core art of many fundamental…
The fair allocation of scarce resources is a central problem in mathematics, computer science, operations research, and economics. While much of the fair-division literature assumes that individuals have underlying cardinal preferences,…
We derive the most probable distribution of resources for a simple society. We find that a probabilistic analysis forbids both too much and too less equity, and selects instead a minimally ordered state. We give the detailed calculations…