Heuristic Voting as Ordinal Dominance Strategies

Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected utility, which requires a cardinal utility function as well as detailed probabilistic information. However, often such probabilities are not easy to estimate or apply. To this end, we present a framework that allows "shades of gray" of likelihood without probabilities. Specifically, we create a hierarchy of sets of world states based on a prospective poll, with inner sets contain more likely outcomes. This hierarchy of likelihoods allows us to define what we term ordinally-dominated strategies. We use this approach to justify various known voting heuristics as bounded-rational strategies.Comment: This is the full version of paper #6080 accepted to AAAI'1

On the convergence of iterative voting: how restrictive should restricted dynamics be?

We study convergence properties of iterative voting procedures. Such procedures are defined by a voting rule and a (restricted) iterative process, where at each step one agent can modify his vote towards a better outcome for himself. It is already known that if the iteration dynamics (the manner in which voters are allowed to modify their votes) are unrestricted, then the voting process may not converge. For most common voting rules this may be observed even under the best response dynamics limitation. It is therefore important to investigate whether and which natural restrictions on the dynamics of iterative voting procedures can guarantee convergence. To this end, we provide two general conditions on the dynamics based on iterative myopic improvements, each of which is sufficient for convergence. We then identify several classes of voting rules (including Positional Scoring Rules, Maximin, Copeland and Bucklin), along with their corresponding iterative processes, for which at least one of these conditions hold

Strategic voting with incomplete information

Classical results in social choice theory on the susceptibility of voting rules to strategic manipulation make the assumption that the manipulator has complete information regarding the preferences of the other voters. In reality, however, voters only have incomplete information, which limits their ability to manipulate. We explore how these limitations affect both the manipulability of voting rules and the dynamics of systems in which voters may repeatedly update their own vote in reaction to the moves made by others. We focus on the Plurality, Veto, κ-approval, Borda, Copeland, and Maximin voting rules, and consider several types of information that are natural in the context of these rules, namely information on the current front-runner, on the scores obtained by each alternative, and on the majority graph induced by the individual preferences

Protecting elections by recounting ballots

Complexity of voting manipulation is a prominent topic in computational social choice. In this work, we consider a two-stage voting manipulation scenario. First, a malicious party (an attacker) attempts to manipulate the election outcome in favor of a preferred candidate by changing the vote counts in some of the voting districts. Afterwards, another party (a defender), which cares about the voters' wishes, demands a recount in a subset of the manipulated districts, restoring their vote counts to their original values. We investigate the resulting Stackelberg game for the case where votes are aggregated using two variants of the Plurality rule, and obtain an almost complete picture of the complexity landscape, both from the attacker's and from the defender's perspective

Stategic Candidacy with Keen Candidates

Presented at the Games, Agents and Incentives WorkshopIn strategic candidacy games, both voters and candidates have preferences over the set of candidates, and candidates make strategic decisions about whether to run an electoral campaign or withdraw from the election, in order to manipulate the outcome according to their preferences. In this work, we extend the standard model of strategic candidacy games to scenarios where candidates may find it harmful for their reputation to withdraw from the election and would only do so if their withdrawal changes the election outcome for the better; otherwise, they would be keen to run the campaign. We study the existence and the quality of Nash equilibria in the resulting class of games, both analytically and empirically, and compare them with the Nash equilibria of the standard model. Our results demonstrate that while in the worst case there may be none or multiple, bad quality equilibria, on average, these games have a unique, optimal equilibrium state

Trembling hand equilibria of plurality voting

Trembling hand (TH) equilibria were introduced by Selten in 1975. Intuitively, these are Nash equilibria that remain stable when players assume that there is a small probability that other players will choose off-equilibrium strategies. This concept is useful for equilibrium refinement, i.e., selecting the most plausible Nash equilibria when the set of all Nash equilibria can be very large, as is the case, for instance, for Plurality voting with strategic voters. In this paper, we analyze TH equilibria of Plurality voting. We provide an efficient algorithm for computing a TH best response and establish many useful properties of TH equilibria in Plurality voting games. On the negative side, we provide an example of a Plurality voting game with no TH equilibria, and show that it is NP-hard to check whether a given Plurality voting game admits a TH equilibrium where a specific candidate is among the election winners