Related papers: Fair Representation and a Linear Shapley Rule
In the standard arrovian framework and under the assumption that individual preferences and social outcomes are linear orders on the set of alternatives, we study the rules which satisfy suitable symmetries and obey the majority principle.…
We introduce Flexible Representative Democracy (FRD), a novel hybrid of Representative Democracy (RD) and Direct Democracy (DD) in which voters can alter the issue-dependent weights of a set of elected representatives. In line with the…
When selecting a subset of candidates (a so-called committee) based on the preferences of voters, proportional representation is often a major desideratum. When going beyond simplistic models such as party-list or district-based elections,…
Oftentimes, the Shapley value becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of homogeneous group games by using an…
This paper is to obtain a simple dividing-diagram of the congressional districts, where the only limit is that each district should contain the same population if possibly. In order to solve this problem, we introduce three different…
Elections are the central institution of democratic processes, and often the elected body -- in either public or private governance -- is a committee of individuals. To ensure the legitimacy of elected bodies, the electoral processes should…
Probabilistic values, including Shapley values and semivalues, provide a model-agnostic framework to attribute the behavior of a black-box model to data points or features, with a wide range of applications including explainable artificial…
In this paper, we address the problem of fair sharing of the total value of a crowd-sourced network system between major participants (founders) and minor participants (crowd) using cooperative game theory. Shapley allocation is regarded as…
In a previous article Don Bennett and I looked for, found and proposed a game in which the Standard Model Gauge Group $S(U(2) \times U(3))$ gets singled out as the "winner". This "game" means that the by Nature chosen gauge group should be…
We study two influential voting rules proposed in the 1890s by Phragm\'en and Thiele, which elect a committee or parliament of k candidates which proportionally represents the voters. Voters provide their preferences by approving an…
How to elect the representatives in legislative bodies is a question that every modern democracy has to answer. This design task has to consider various elements so as to fulfill the citizens' expectations and contribute to the maintenance…
Shapley value is originally a concept in econometrics to fairly distribute both gains and costs to players in a coalition game. In the recent decades, its application has been extended to other areas such as marketing, engineering and…
This paper considers the ranking problem of candidates for a certain position based on ballot papers filled by voters. We suggest a ranking procedure of alternatives using cooperative game theory methods. For this, it is necessary to…
Primary law of the European Union demands that the allocation of the seats of the European Parliament between the Member States must obey the principle of degressive proportionality. The principle embodies the political aim that the more…
The dynamics of random transitive delegations on a graph are of particular interest when viewed through the lens of an emerging voting paradigm, liquid democracy. This paradigm allows voters to choose between directly voting and…
Cohort Shapley value is a model-free method of variable importance grounded in game theory that does not use any unobserved and potentially impossible feature combinations. We use it to evaluate algorithmic fairness, using the well known…
Liquid democracy is a novel paradigm for collective decision-making that gives agents the choice between casting a direct vote or delegating their vote to another agent. We consider a generalization of the standard liquid democracy setting…
We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…
Participatory budgeting is one of the exciting developments in deliberative grassroots democracy. We concentrate on approval elections and propose proportional representation axioms in participatory budgeting, by generalizing relevant…
The article develops a parametric model of fairness called "$\varepsilon$-fairness" that can be represented using a single second-order cone constraint and incorporated into existing decision-making problem formulations without impacting…