Evaluating approval-based multiwinner voting in terms of robustness to noise (original) (raw)

Modeling Voters in Multi-Winner Approval Voting

2021

In many real world situations, collective decisions are made using voting and, in scenarios such as committee or board elections, employing voting rules that return multiple winners. In multi-winner approval voting (AV), an agent submits a ballot consisting of approvals for as many candidates as they wish, and winners are chosen by tallying up the votes and choosing the top-$k$ candidates receiving the most approvals. In many scenarios, an agent may manipulate the ballot they submit in order to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex and uncertain situations, agents may use heuristics instead of incurring the additional effort required to compute the manipulation which most favors them. In this paper, we examine voting behavior in single-winner and multi-winner approval voting scenarios with varying degrees of uncertainty using behavioral data obtained from Mechanical Turk. We find that people generally manipulate their vo...

Heuristics in Multi-Winner Approval Voting

arXiv (Cornell University), 2019

In many real world situations, collective decisions are made using voting. Moreover, scenarios such as committee or board elections require voting rules that return multiple winners. In multi-winner approval voting (AV), an agent may vote for as many candidates as they wish. Winners are chosen by tallying up the votes and choosing the top-k candidates receiving the most votes. An agent may manipulate the vote to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex and uncertain situations, agents may use heuristics to strategize, instead of incurring the additional effort required to compute the manipulation which most favors them. In this paper, we examine voting behavior in multi-winner approval voting scenarios with complete information. We show that people generally manipulate their vote to obtain a better outcome, but often do not identify the optimal manipulation. Instead, voters tend to prioritize the candidates with the highest utilities. Using simulations, we demonstrate the effectiveness of these heuristics in situations where agents only have access to partial information.

Multiwinner Approval Voting: An Apportionment Approach

SSRN Electronic Journal, 2000

We extend approval voting so as to elect multiple candidates, who may be either individuals or members of a political party, in rough proportion to their approval in the electorate. We analyze two divisor methods of apportionment, first proposed by Jefferson and Webster, that iteratively depreciate the approval votes of voters who have one or more of their approved candidates already elected. We compare the usual sequential version of these methods with a nonsequential version, which is computationally complex but feasible for many elections. Whereas Webster apportionments tend to be more representative of the electorate than those of Jefferson, the latter, whose equally spaced vote thresholds for winning seats duplicate those of cumulative voting in 2-party elections, is even-handed or balanced.

COMPUTATIONAL ASPECTS OF APPROVAL VOTING AND DECLARED-STRATEGY VOTING

2000

Acknowledgements I will always be grateful to my research advisor, Ron K. Cytron, for his guidance, perspective, encouragement and patience. He has been a pleasure to work with and a great help in exploring and evaluating research ideas and directions. I am passionate about this research and feel very lucky to have had the opportunity to work with him on it.

Voting rules as statistical estimators

We adopt an 'epistemic' interpretation of social decisions: there is an objectively correct choice, each voter receives a 'noisy signal' of the correct choice, and the social objective is to aggregate these signals to make the best possible guess about the correct choice. One epistemic method is to fix a probability model and compute the maximum likelihood estimator (MLE), maximum a posteriori estimator (MAP) or expected utility maximizer (EUM), given the data provided by the voters. We first show that an abstract voting rule can be interpreted as MLE or MAP if and only if it is a scoring rule. We then specialize to the case of distance-based voting rules, in particular, the use of the median rule in judgement aggregation. Finally, we show how several common 'quasiutilitarian' voting rules can be interpreted as EUM.

On the robustness of preference aggregation in noisy environments

Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems - AAMAS '07, 2007

In an election held in a noisy environment, agents may unintentionally perturb the outcome by communicating faulty preferences. We investigate this setting by introducing a theoretical model of noisy preference aggregation and formally defining the (worst-case) robustness of a voting rule. We use our model to analytically bound the robustness of various prominent rules. Our results essentially specify the voting rules that allow for reasonable preference aggregation in the face of noise.

Heuristic Strategies in Uncertain Approval Voting Environments

2020

In many collective decision making situations, agents vote to choose an alternative that best represents the preferences of the group. Agents may manipulate the vote to achieve a better outcome by voting in a way that does not reflect their true preferences. In real world voting scenarios, people often do not have complete information about other voter preferences and it can be computationally complex to identify a strategy that will maximize their expected utility. In such situations, it is often assumed that voters will vote truthfully rather than expending the effort to strategize. However, being truthful is just one possible heuristic that may be used. In this paper, we examine the effectiveness of heuristics in single winner and multi-winner approval voting scenarios with missing votes. In particular, we look at heuristics where a voter ignores information about other voting profiles and makes their decisions based solely on how much they like each candidate. In a behavioral ex...

Simulating the effects of misperception on the manipulability of voting rules

The fact that rank aggregation rules are susceptible to manipulation by varying degrees has long been known. In this work we study the effect of noise on manipulation i.e. we assume that individuals are not able to perceive the preferences of others without distortion. To study the frequency of various outcomes we simulate a large number of rank aggre-gations and manipulations on random profiles with the help of a software package developed by the authors in the Python language and discuss some preliminary results.

On the Gap between Outcomes of Voting Rules

adaptive agents and multi agents systems, 2017

Various voting rules (or social choice procedures) have been proposed to select a winner from the preferences of an entire population: Plurality, veto, Borda, Minimax, Copeland, etc. Although in theory, these rules may yield drastically different outcomes, for real-world datasets, behavioral social choice analyses have found that the rules are often in perfect agreement with each other! This work attempts to give a mathematical explanation of this phenomenon. We quantify the gap between the outcomes of two voting rules by the pairwise margin between their winners. We show that for many common voting rules, the gap between them can be almost as large as 1 when the votes are unrestricted. As a counter, we study the behavior of voting rules when the vote distribution is a uniform mixture of a small number of multinomial logit distributions. This scenario corresponds to a population consisting of a small number of groups, each voting according to a latent preference ranking. We show that for any such voting profile on g groups, at least 1/2g fraction of the population prefers the winner of a Borda election to any other candidate.

On the manipulability of approval voting and related scoring rules

Social Choice and Welfare, 2012

We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of alternatives: by comparison of worst alternatives, best alternatives, or by comparison based on stochastic dominance. We perform a similar exercise for k-approval rules, where voters approve of a fixed number k of alternatives. These results can be used to compare (k-)approval rules with respect to their manipulability. Analytical results are obtained for the case of two voters, specifically, the values of k for which the k-approval rule is minimally manipulable -has the smallest number of manipulable preference profiles -under the various preference extensions are determined. For the number of voters going to infinity, an asymptotic result is that the kapproval rule with k around half the number of alternatives is minimally manipulable among all scoring rules. Further results are obtained by simulation and indicate that k-approval rules may improve on the approval rule as far as manipulability is concerned. JEL-Classification: D71, D72