scholarly journals Preferences Single-Peaked on a Circle

2020 ◽  
Vol 68 ◽  
pp. 463-502 ◽  
Author(s):  
Dominik Peters ◽  
Martin Lackner
Keyword(s):  
Polynomial Time ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Recognition Algorithm ◽  
Approval Voting ◽  
Voting Rules ◽  
One Dimensional ◽  
Facility Location Problems ◽  
Impossibility Results ◽  
Fast Recognition

We introduce the domain of preferences that are single-peaked on a circle, which is a generalization of the well-studied single-peaked domain. This preference restriction is useful, e.g., for scheduling decisions, certain facility location problems, and for one-dimensional decisions in the presence of extremist preferences. We give a fast recognition algorithm of this domain, provide a characterisation by finitely many forbidden subprofiles, and show that many popular single- and multi-winner voting rules are polynomial-time computable on this domain. In particular, we prove that Proportional Approval Voting can be computed in polynomial time for profiles that are single-peaked on a circle. In contrast, Kemeny's rule remains hard to evaluate, and several impossibility results from social choice theory can be proved using only profiles in this domain.

POPULAR SPANNING TREES

2013 ◽  
Vol 24 (05) ◽  
pp. 655-677 ◽  
Author(s):  
ANDREAS DARMANN
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Scoring Functions ◽  
Approval Voting ◽  
Voting Rules ◽  
Sharp Separation ◽  
Polynomially Solvable

Combinatorial Optimization is combined with Social Choice Theory when the goal is to decide on the quality of a spanning tree of an undirected graph. Given individual preferences over the edges of the graph, spanning trees are compared by means of a Condorcet criterion. The comparisons are based on scoring functions used in classic voting rules such as approval voting and Borda voting. In this work, we investigate the computational complexity involved in deciding on the quality of a spanning tree with respect to the different voting rules adapted. In particular, we draw the sharp separation line between polynomially solvable and computationally intractable instances.

scholarly journals Optimal Voting Rules

1995 ◽  
Vol 9 (1) ◽  
pp. 51-64 ◽  
Author(s):  
Peyton Young
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Likelihood Estimation ◽  
Voting Rules ◽  
Voting Rule ◽  
Marquis De Condorcet ◽  
Kenneth Arrow

Modern social choice theory, following Kenneth Arrow, treats voting as a method for aggregating diverse preferences and values. An earlier view, initiated by Marquis de Condorcet, is that voting is a method for aggregating information. Voters’ opinions differ because they make errors of judgment; absent these errors they would all agree on the best choice. The goal is to design a voting rule that identifies the best choice with highest probability. This paper examines maximum likelihood estimation. Surprisingly, the optimal rule can also be axiomatized by variations of Arrow's axioms.

The General Will and Social Choice Theory

1992 ◽  
Vol 54 (1) ◽  
pp. 34-49 ◽  
Author(s):  
Benjamin Radcliff
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Collective Choice ◽  
General Will ◽  
Arrow’S Theorem ◽  
Impossibility Results ◽  
Arrow's Theorem ◽  
Choice Literature

The concept of the General Will has been criticized as being either tyrannical or empirically unattainable. From a social choice perspective, Riker (1982) and others have merged the substance of both perspectives. The new argument maintains that Arrow's Theorem and similar impossibility results imply that the General Will is both dangerous and “intellectually absurd.” While not denying the relevance of the collective choice literature, it is argued that such apocalyptic conclusions are premature.

scholarly journals Goal-Based Collective Decisions: Axiomatics and Computational Complexity

2018 ◽  
Author(s):  
Arianna Novaro ◽  
Umberto Grandi ◽  
Dominique Longin ◽  
Emiliano Lorini
Keyword(s):  
Computational Complexity ◽  
Social Choice ◽  
Polynomial Time ◽  
Majority Rule ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Collective Decision ◽  
Winner Determination ◽  
Collective Decisions ◽  
Probabilistic Polynomial Time

We study agents expressing propositional goals over a set of binary issues to reach a collective decision. We adapt properties and rules from the literature on Social Choice Theory to our setting, providing an axiomatic characterisation of a majority rule for goal-based voting. We study the computational complexity of finding the outcome of our rules (i.e., winner determination), showing that it ranges from Nondeterministic Polynomial Time (NP) to Probabilistic Polynomial Time (PP).

SOCIAL CHOICE FOR DATA FUSION

2004 ◽  
Vol 03 (04) ◽  
pp. 619-631
Author(s):  
SHANFENG ZHU ◽  
QIZHI FANG ◽  
WEIMIN ZHENG
Keyword(s):  
Decision Theory ◽  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Information Age ◽  
Theoretic Approach ◽  
Voting Rules ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
New Algorithms

Social choice theory is the study of decision theory on how to aggregate separate preferences into group's rational preference. It has wide applications, especially on the design of voting rules, and brings far-reaching influence on the development of modern political science and welfare economics. With the advent of the information age, social choice theory finds its up-to-date application on designing effective Metasearch engines. Metasearch engines provide effective searching by combining the results of multiple source search engines that make use of diverse models and techniques. In this work, we analyze social choice algorithms in a graph-theoretic approach. In addition to classical social choice algorithms, such as Borda and Condorcet, we study one special type of social choice algorithms, elimination voting, to tackle Metasearch problem. Some new algorithms are proposed and examined in the fusion experiment on TREC data. It shows that these elimination voting algorithms achieve satisfied performance when compared with Borda algorithm.

scholarly journals A welfarist critique of social choice theory: interpersonal comparisons in the theory of voting

2015 ◽  
Vol 8 (2) ◽  
pp. 34
Author(s):  
Aki Lehtinen
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Strategic Voting ◽  
Voting Theory ◽  
Voting Rules ◽  
Philosophical Critique ◽  
Strategic Behaviour ◽  
Interpersonal Comparisons ◽  
Normative Evaluation

This paper provides a philosophical critique of social choice theory insofar as it deals with the normative evaluation of voting and voting rules. I will argue that the very method of evaluating voting rules in terms of whether they satisfy various conditions is deeply problematic because introducing strategic behaviour leads to a violation of any condition that makes a difference between voting rules. I also argue that it is legitimate to make interpersonal comparisons of utilities in voting theory. Combining a realistic account of voters’ behaviour with a utilitarian evaluation of the outcomes then leads to the judgment that strategic voting is beneficial. If it is, then Arrow's theorem does not have far-reaching consequences for democracy because one of its conditions is not normatively acceptable.

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