Related papers: On Penrose's square-root law and beyond
The wisdom of crowds is an umbrella term for phenomena suggesting that the collective judgment or decision of a large group can be more accurate than the individual judgments or decisions of the group members. A well-known example…
The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common - but very different - ways to measure the…
The division of mandates to the European Parliament posed difficulties since the beginning of its operation. Introduction of the degressive proportionality principle to legal acts intensified further discussion on this subject. The…
The goal of this paper is to disentangle the roles of volume and of participation rate in the price response of the market to a sequence of transactions. To do so, we are inspired the methodology introduced in arXiv:1402.1288,…
In linear models of consensus dynamics, the state of the various agents converges to a value which is a convex combination of the agents' initial states. We call it democratic if in the large scale limit (number of agents going to infinity)…
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…
This paper examines an area of Game Theory called Voting Power Theory. With the adoption of a measure theoretic framework it argues that the many different indices and tools currently used for measuring voting power can be replaced by just…
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:…
Majority voting is one of the few black-box interventions that can improve a fixed stochastic predictor: repeated access can be cheaper than changing a high-capability model. Classical fixed-competence theory makes this intervention look…
Universal power laws have been scrutinised in physics and beyond, and a long-standing debate exists in econophysics regarding the strict universality of the nonlinear price impact, commonly referred to as the square-root law (SRL). The SRL…
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 many proportional parliamentary elections, electoral thresholds (typically 3-5%) are used to promote stability and governability by preventing the election of parties with very small representation. However, these thresholds often result…
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…
We study an extension of the voter model in which each agent is endowed with an innate preference for one of two states that we term as "truth" or "falsehood". Due to interactions with neighbors, an agent that innately prefers truth can be…
Debates on an EU-leaving referendum arose in several member states after Brexit. We want to highlight how the exit of an additional country affects the power distribution in the Council of the European Union. We inspect the power indices of…
Arrow's Impossibility Theorem states that any constitution which satisfies Independence of Irrelevant Alternatives (IIA) and Unanimity and is not a Dictator has to be non-transitive. In this paper we study quantitative versions of Arrow…
We study in details the turnout rate statistics for 77 elections in 11 different countries. We show that the empirical results established in a previous paper for French elections appear to hold much more generally. We find in particular…
We revisit the recent breakthrough result of Gkatzelis et al. on (single-winner) metric voting, which showed that the optimal distortion of 3 can be achieved by a mechanism called Plurality Matching. The rule picks an arbitrary candidate…
This paper presents a novel mechanism to endogenously determine the fair division of a state into electoral districts in a two-party setting. No geometric constraints are imposed on voter distributions or district shapes; instead, it is…
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…