How hard is it to control an election? (original) (raw)

Some notes on voting schemes and the will of the majority

Public Choice, 1969

This paper is a study in the theory of committees and elections. By a committee we will mean any group of people who arrive at a decision by means of voting. By a voting scheme I we will mean any method by which individual voting decisions are aggregated into committee decisions. Given various voting schemes we shall examine three techniques by which members may seek to manipulate committee decisions to their advantage: a) additions or deletions to the alternatives to be considered b) deliberate distortions of one's own voting preferences c) manipulation of the order in .which alternatives are voted upon, and shall prove some theorems about rational voting behavior when preferences are unidimensionally scalable.

A "winner" under any voting rule ? An experiment on the single transferable vote

2009

In this paper, we expose the results of a voting experiment realised in 2007, during the French Presidential election. This experiment aimed at confronting the Single Transferable vote (SVT) procedure to two criteria : simplicity and the selection of a Condorcet-winner. Building on our electoral sample's preferences, we show that this voting procedure can design a different winner, depending on the vote counting process. With the vote counting process advocated by Hare, the winner is Nicolas Sarkozy, while the Coombs vote counting process has François Bayrou as winner. For these two vote counting processes, the details of the experiment are the same and it is shown that the simplicity criterion is respected. However, with regard to the Condorcet-winner criterion, the Coombs methods is the only one to elect the Condorcet-winner, i.e. François Bayrou.

Multi-Winner Elections: Complexity of Manipulation, Control and Winner-Determination

2007

Although recent years have seen a surge of interest in the computational aspects of social choice, no attention has previously been devoted to elections with multiple winners, e.g., elections of an assembly or committee. In this paper, we fully characterize the worst-case complexity of manipulation and control in the context of four prominent multi-winner voting systems. Additionally, we show that several tailor-made multi-winner voting schemes are impractical, as it is N P-hard to select the winners in these schemes.

A simple Condorcet voting method for Final Four elections

2024

An obstacle to the implementation of Condorcet voting methods in political elections is the perceived complexity of these methods. In this note, we propose a simple Condorcet voting method for use in a Final Four election, i.e., after a preliminary process in which up to four candidates qualify for the election. In the Final Four election, voters submit rankings of the candidates. If one candidate beats each of the others in a head-to-head majority comparison using the voters' rankings, that candidate is elected; if not, then among the candidates with at most one head-to-head loss, the candidate with the smallest loss is elected. We analyze this voting method from the perspective of voting theory. It avoids some standard objections to the related Minimax voting method, and it has advantages over the Instant Runoff method that has already been implemented in a number of cities and states.

Multi-winner scoring election methods: Condorcet consistency and paradoxes

Public Choice, 2016

The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality, k-Negative Plurality, k-Borda, and Bloc, which can be considered as generalisations of well-known single-winner scoring rules. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability that a given voting rule picks out the Condorcet committee, given that such a committee exists. The second comparison is based on the likelihood of two paradoxes of committee elections: The Prior Successor Paradox and the Leaving Member Paradox which occur when a member of an elected committee leaves. In doing so, using the well-known Impartial Anonymous Culture condition, we extend the results of Kamwa and Merlin (2015) in two directions. First, our paper is concerned with the probability of the paradoxes no matter the ranking of the leaving candidate. Second, we do not only focus on the occurrence of these paradoxes when one wishes to select a committee of size k = 2 out of m = 4 candidates but we consider more values of k and m.

Manipulative elicitation – A new attack on elections with incomplete preferences

Theoretical Computer Science

Lu and Boutilier [LB11] proposed a novel approach based on "minimax regret" to use classical score based voting rules in the setting where preferences can be any partial (instead of complete) orders over the set of alternatives. We show here that such an approach is vulnerable to a new kind of manipulation which was not present in the classical (where preferences are complete orders) world of voting. We call this attack "manipulative elicitation." More specifically, it may be possible to (partially) elicit the preferences of the agents in a way that makes some distinguished alternative win the election who may not be a winner if we elicit every preference completely. More alarmingly, we show that the related computational task is polynomial time solvable for a large class of voting rules which includes all scoring rules, maximin, Copeland α for every α ∈ [0, 1], simplified Bucklin voting rules, etc. We then show that introducing a parameter per pair of alternatives which specifies the minimum number of partial preferences where this pair of alternatives must be comparable makes the related computational task of manipulative elicitation NP-complete for all common voting rules including a class of scoring rules which includes the plurality, k-approval, k-veto, veto, and Borda voting rules, maximin, Copeland α for every α ∈ [0, 1], and simplified Bucklin voting rules. Hence, in this work, we discover a fundamental vulnerability in using minimax regret based approach in partial preferential setting and propose a novel way to tackle it.

A note on Approval Voting and electing the Condorcet loser

Mathematical Social Sciences, 2016

Analytical representations are developed for the probability that Approval Voting (AV) elects the Condorcet Loser in three-alternative elections with large electorates. A comparison of AV is then made to Plurality Rule (PR) to show that AV is much less susceptible to the risk of electing the Condorcet loser than PR. All calculations in this analysis are based on IAC-like assumptions.

The Condorcet paradox: an experimental approach to a voting process

2003

This paper analyses the effects played by rules within a coordination game. The starting point is constituted by the wide field of Public Choice theories. More precisely the focus of the research is on the stability of the voting process. The experiment is build on a game played through computers and the experimental subjects must perform some choices that can led to different individual and collective solutions. The game that they play is based on a set of rules that must be voted by the players themselves before a new session of the experiment will be run. The idea is to verify the degree of stability of the collective choices (logrolling phenomena).

On the Condorcet Efficiency of Approval Voting and Extended Scoring Rules for Three Alternatives

Studies in Choice and Welfare, 2010

The Condorcet winner in an election is the candidate that would defeat in a series of pairwise elections each of the alternatives. The Condorcet efficiency of a voting rule is thus the conditional probability that this given voting rule picks out the Condorcet winner, given that such a candidate exists. When individual have dichotomous preferences, on the top of existing for each profile, the Condorcet winner is always selected by Approval Voting. The picture is not as favorable when individual preferences are linear orders over m alternatives. Assuming that each strict preference is equally likely to occur and that each voter will approve t alternatives with the same probability q t , Gerhlein and Lepelley showed that Approval Voting is dominated, in terms of Condorcet efficiency, by the rule where each voter casts his vote for exactly m/2 alternatives. Using a probabilistic assumption where voters can be either dichotomous or express strong preferences, we will revisit these results in the threealternative case. In this framework, we will derive the Condorcet efficiency for large populations, and for the large class of extended scoring rules, which encompasses both the classical scoring rules, such as the Plurality rule and the Borda Count, and Approval Voting. † We are indebted to Jean François Laslier and Remzi Sanver for the comments they made on the early versions of this chapter. A usual, all remaining errors are ours.