scholarly journals Convergence of Iterative Scoring Rules

2016 ◽  
Vol 57 ◽  
pp. 573-591 ◽  
Author(s):  
Omer Lev ◽  
Jeffrey S. Rosenschein
Keyword(s):  
Linear Order ◽  
Scoring Rules ◽  
Voting Systems ◽  
Choice Functions ◽  
Stable States ◽  
Voting Rules ◽  
Voting Rule ◽  
Social Choice Functions ◽  
Breaking Mechanism ◽  
Iterative Voting

In multiagent systems, social choice functions can help aggregate the distinct preferences that agents have over alternatives, enabling them to settle on a single choice. Despite the basic manipulability of all reasonable voting systems, it would still be desirable to find ways to reach plausible outcomes, which are stable states, i.e., a situation where no agent would wish to change its vote. One possibility is an iterative process in which, after everyone initially votes, participants may change their votes, one voter at a time. This technique, explored in previous work, converges to a Nash equilibrium when Plurality voting is used, along with a tie-breaking rule that chooses a winner according to a linear order of preferences over candidates. In this paper, we both consider limitations of the iterative voting method, as well as expanding upon it. We demonstrate the significance of tie-breaking rules, showing that no iterative scoring rule converges for all tie-breaking. However, using a restricted tie-breaking rule (such as the linear order rule used in previous work) does not by itself ensure convergence. We prove that in addition to plurality, the veto voting rule converges as well using a linear order tie-breaking rule. However, we show that these two voting rules are the only scoring rules that converge, regardless of tie-breaking mechanism.

scholarly journals Determining Possible and Necessary Winners Given Partial Orders

2011 ◽  
Vol 41 ◽  
pp. 25-67 ◽  
Author(s):  
L. Xia ◽  
V. Conitzer
Keyword(s):  
Linear Order ◽  
Partial Orders ◽  
Scoring Rules ◽  
Linear Orders ◽  
Voting Rules ◽  
Voting Rule

Usually a voting rule requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a voting rule, a profile of partial orders, and an alternative (candidate) c, two important questions arise: first, is it still possible for c to win, and second, is c guaranteed to win? These are the possible winner and necessary winner problems, respectively. Each of these two problems is further divided into two sub-problems: determining whether c is a unique winner (that is, c is the only winner), or determining whether c is a co-winner (that is, c is in the set of winners). We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We completely characterize the complexity of possible/necessary winner problems for the following common voting rules: a class of positional scoring rules (including Borda), Copeland, maximin, Bucklin, ranked pairs, voting trees, and plurality with runoff.

Computer simulations of voting systems

2000 ◽  
Vol 03 (01n04) ◽  
pp. 181-194 ◽  
Author(s):  
Dominique Lepelley ◽  
Ahmed Louichi ◽  
Fabrice Valognes
Keyword(s):  
Monte Carlo ◽  
Computer Simulations ◽  
Monte Carlo Methods ◽  
Scoring Rules ◽  
Voting Systems ◽  
Voting Rules ◽  
Asymptotic Case ◽  
Majority Principle ◽  
Voting Procedures ◽  
Democratic Principles

All voting procedures are susceptible to give rise, if not to paradoxes, at least to violations of some democratic principles. In this paper, we evaluate and compare the propensity of various voting rules -belonging to the class of scoring rules- to satisfy two versions of the majority principle. We consider the asymptotic case where the numbers of voters tends to infinity and, for each rule, we study with the help of Monte Carlo methods how this propensity varies as a function of the number of candidates.

scholarly journals Even More Effort Towards Improved Bounds and Fixed-Parameter Tractability for Multiwinner Rules

2021 ◽  
Author(s):  
Sushmita Gupta ◽  
Pallavi Jain ◽  
Saket Saurabh ◽  
Nimrod Talmon
Keyword(s):  
Weighted Average ◽  
Scoring Rules ◽  
Voting Rules ◽  
Voter Preferences ◽  
Voting Rule ◽  
The Family ◽  
Fixed Parameter ◽  
Real World Applications ◽  
Ordered Weighted Average ◽  
Fruitful Research

Multiwinner elections have proven to be a fruitful research topic with many real world applications. We contribute to this line of research by improving the state of the art regarding the computational complexity of computing good committees. More formally, given a set of candidates C, a set of voters V, each ranking the candidates according to their preferences, and an integer k; a multiwinner voting rule identifies a committee of size k, based on these given voter preferences. In this paper we consider several utilitarian and egailitarian OWA (ordered weighted average) scoring rules, which are an extensively researched family of rules (and a subfamily of the family of committee scoring rules). First, we improve the result of Betzler et al. [JAIR, 2013], which gave a O(n^n) algorithm for computing winner under the Chamberlin Courant rule (CC), where n is the number of voters; to a running time of O(2^n), which is optimal. Furthermore, we study the parameterized complexity of the Pessimist voting rule and describe a few tractable and intractable cases. Apart from such utilitarian voting rules, we extend our study and consider egalitarian median and egalitarian mean (both committee scoring rules), showing some tractable and intractable results, based on nontrivial structural observations.

scholarly journals Convergence and Quality of Iterative Voting Under Non-Scoring Rules

2017 ◽  
Author(s):  
Aaron Koolyk ◽  
Tyrone Strangway ◽  
Omer Lev ◽  
Jeffrey S. Rosenschein
Keyword(s):  
Social Choice ◽  
Empirical Analysis ◽  
Stated Preferences ◽  
Scoring Rules ◽  
Response Strategy ◽  
Voting Rules ◽  
Best Response ◽  
Voting Methods ◽  
Iterative Voting

Iterative voting is a social choice mechanism that assumes all voters are strategic, and allows voters to change their stated preferences as the vote progresses until an equilibrium is reached (at which point no player wishes to change their vote). Previous research established that this process converges to an equilibrium for the plurality and veto voting methods and for no other scoring rule. We consider iterative voting for non-scoring rules, examining the major ones, and show that none of them converge when assuming (as most research has so far) that voters pursue a best response strategy. We investigate other potential voter strategies, with a more heuristic flavor (since for most of these voting rules, calculating the best response is NP-hard); we show that they also do not converge. We then conduct an empirical analysis of the iterative voting winners for these non-scoring rules, and compare the winner quality of various strategies.

scholarly journals Decision Making in Committees: Transparency, Reputation, and Voting Rules

2007 ◽  
Vol 97 (1) ◽  
pp. 150-168 ◽  
Author(s):  
Gilat Levy
Keyword(s):  
Decision Making ◽  
Career Concerns ◽  
Decision Making Process ◽  
Voting Rules ◽  
The Public ◽  
Voting Rule ◽  
The Right

In this paper I analyze the effect of transparency on decision making in committees. I focus on committees whose members are motivated by career concerns. The main result is that when the decision-making process is secretive (when individual votes are not revealed to the public), committee members comply with preexisting biases. For example, if the voting rule demands a supermajority to accept a reform, individuals vote more often against reforms. Transparent committees are therefore more likely to accept reforms. I also find that coupled with the right voting rule, a secretive procedure may induce better decisions than a transparent one. (JEL D71, D72)

Full Implementation under Ambiguity

2021 ◽  
Vol 13 (1) ◽  
pp. 148-178
Author(s):  
Huiyi Guo ◽  
Nicholas C. Yannelis
Keyword(s):  
Social Choice ◽  
Expected Utility ◽  
Sufficient Conditions ◽  
Choice Functions ◽  
Maxmin Expected Utility ◽  
Special Cases ◽  
Social Choice Functions ◽  
Bayesian Implementation ◽  
Pareto Efficient ◽  
Choice Set

This paper introduces the maxmin expected utility framework into the problem of fully implementing a social choice set as ambiguous equilibria. Our model incorporates the Bayesian framework and the Wald-type maxmin preferences as special cases and provides insights beyond the Bayesian implementation literature. We establish necessary and almost sufficient conditions for a social choice set to be fully implementable. Under the Wald-type maxmin preferences, we provide easy-to-check sufficient conditions for implementation. As applications, we implement the set of ambiguous Pareto-efficient and individually rational social choice functions, the maxmin core, the maxmin weak core, and the maxmin value. (JEL D71, D81, D82)

scholarly journals Self-selective social choice functions

2007 ◽  
Vol 31 (1) ◽  
pp. 129-149 ◽  
Author(s):  
Semih Koray ◽  
Arkadii Slinko
Keyword(s):  
Social Choice ◽  
Choice Functions ◽  
Social Choice Functions
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