Omer Lev

A local-dominance theory of voting equilibria

We suggest a new model for strategic voting based on local dominance, where voters consider a set of possible outcomes without assigning probabilities to them. We prove that voting equilibria under the Plurality rule exist for a broad class of local dominance relations. Furthermore, we show that local dominance-based dynamics quickly converge to an equilibrium if voters start from the truthful state, and we provide weaker convergence guarantees in more general settings. Using extensive simulations of strategic voting on generated and real profiles, we show that emerging equilibria replicate widely known patterns of human voting behavior such as Duvergers law, and that they generally improve the quality of the winner compared to non-strategic voting.

Convergence of Iterative Scoring Rules

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.

Beyond Plurality: Truth-Bias in Binary Scoring Rules

It is well known that standard game-theoretic approaches to voting mechanisms lead to a multitude of Nash Equilibria NE, many of which are counter-intuitive. We focus on truth-biased voters, a model recently proposed to avoid such issues. The model introduces an incentive for voters to be truthful when their vote is not pivotal. This is a powerful refinement, and recent simulations reveal that the surviving equilibria tend to have desirable properties. However, truth-bias has been studied only within the context of plurality, which is an extreme example of k-approval rules with

Convergence and Quality of Iterative Voting Under Non-Scoring Rules.

k=1

Big City vs. the Great Outdoors: Voter Distribution and How It Affects Gerrymandering

. We undertake an equilibrium analysis of the complete range of k-approval. Our analysis begins with the veto rule, the other extreme point of k-approval, where each ballot approves all candidates but one. We identify several crucial properties of pure NE for truth-biased veto. These properties show a clear distinction from the setting of truth-biased plurality. We proceed by establishing that deciding on the existence of NE in truth-biased veto is an NP-hard problem. We also characterise a tight in a certain sense subclass of instances for which the existence of a NE can be decided in poly-time. Finally, we study analogous questions for general k-approval rules.

Convergence of iterative voting

The practical importance of automata on infinite objects has motivated a re-examination of the complexity of automata-theoretic constructions. One such construction is the translation, when possible, of nondeterministic Buchi word automata (NBW) to nondeterministic co-Buchi word automata (NCW). Among other applications, it is used in the translation (when possible) of LTL to the alternation-free μ -calculus. The best known upper bound for the translation of NBW to NCW is exponential (given an NBW with n states, the best translation yields an equivalent NCW with 2 O (n logn ) states). On the other hand, the best known lower bound is trivial (no NBW with n states whose equivalent NCW requires even n + 1 states is known). In fact, only recently was it shown that there is an NBW whose equivalent NCW requires a different structure. In this paper we improve the lower bound by showing that for every integer k ≥ 1 there is a language L k over a two-letter alphabet, such that L k can be recognized by an NBW with 2k + 1 states, whereas the minimal NCW that recognizes L k has 3k states. Even though this gap is not asymptotically very significant, it nonetheless demonstrates for the first time that NBWs are more succinct than NCWs. In addition, our proof points to a conceptual advantage of the Buchi condition: an NBW can abstract precise counting by counting to infinity with two states. To complete the picture, we consider also the reverse NCW to NBW translation, and show that the known upper bound, which duplicates the state space, is tight.

Empirical analysis of plurality election equilibria

Iterative voting is a social choice mechanism whereby voters are allowed to continually make strategic changes to their stated preferences until no further change is desired. We study the iterative voting framework for several common voting rules and show that, for these rules, an equilibrium may never be reached. We also consider several variations of iterative voting and show that with these variations equilibrium likewise may not be reached. Finally, we present an empirical analysis of the quality of candidates elected through iterative voting.

Impartial peer review

We introduce an axiomatic approach to group recommendations, in line of previous work on the axiomatic treatment of trust-based recommendation systems, ranking systems, and other foundational work on the axiomatic approach to internet mechanisms in social choice settings. In group recommendations we wish to recommend to a group of agents, consisting of both opinionated and undecided members, a joint choice that would be acceptable to them. Such a system has many applications, such as choosing a movie or a restaurant to go to with a group of friends, recommending games for online game players, & other communal activities. Our method utilizes a given social graph to extract information on the undecided, relying on the agents influencing them. We first show that a set of fairly natural desired requirements (a.k.a axioms) leads to an impossibility, rendering mutual satisfaction of them unreachable. However, we also show a modified set of axioms that fully axiomatize a group variant of the random-walk recommendation system, expanding a previous result from the individual recommendation case.