Bad cycles in iterative Approval Voting

This article is about synchronized iterative voting in the context of Approval Voting. Assuming that, before an election, successive polls occur to which voters react strategically, we shall exhibit examples showing the possibility of cycles with strong negative properties (in particular, non election of an existing Condorcet winner, or possible election of a candidate strongly rejected by a majority of the electorate). We also show that such cycles persist if only a proportion of the voters adjust their ballot at each iteration and if their strategy changes when close ties occur

Bad cycles and chaos in iterative Approval Voting

We consider synchronized iterative voting in the Approval Voting system. We give examples with a Condorcet winner where voters apply simple, sincere, consistent strategies but where cycles appear that can prevent the election of the Condorcet winner, or that can even lead to the election of a ''consensual loser'', rejected in all circumstances by a majority of voters. We conduct numerical experiments to determine how rare such cycles are. It turns out that when voters apply Laslier's Leader Rule they are quite uncommon, and we prove that they cannot happen when voters' preferences are modeled by a one-dimensional culture. However a slight variation of the Leader Rule accounting for possible draws in voter's preferences witnesses much more bad cycle, especially in a one-dimensional culture.Then we introduce a continuous-space model in which we show that these cycles are stable under perturbation. Last, we consider models of voters behavior featuring a competition between strategic behavior and reluctance to vote for candidates that are ranked low in their preferences. We show that in some cases, this leads to chaotic behavior, with fractal attractors and positive entropy.Comment: v2: added a numerical study of rarity of bad cycles and equilibriums, and a case of chaotic Continuous Polling Dynamics. Many other improvements throughout the tex

Acyclic Games and Iterative Voting

We consider iterative voting models and position them within the general framework of acyclic games and game forms. More specifically, we classify convergence results based on the underlying assumptions on the agent scheduler (the order of players) and the action scheduler (which better-reply is played). Our main technical result is providing a complete picture of conditions for acyclicity in several variations of Plurality voting. In particular, we show that (a) under the traditional lexicographic tie-breaking, the game converges for any order of players under a weak restriction on voters' actions; and (b) Plurality with randomized tie-breaking is not guaranteed to converge under arbitrary agent schedulers, but from any initial state there is \emph{some} path of better-replies to a Nash equilibrium. We thus show a first separation between restricted-acyclicity and weak-acyclicity of game forms, thereby settling an open question from [Kukushkin, IJGT 2011]. In addition, we refute another conjecture regarding strongly-acyclic voting rules.Comment: some of the results appeared in preliminary versions of this paper: Convergence to Equilibrium of Plurality Voting, Meir et al., AAAI 2010; Strong and Weak Acyclicity in Iterative Voting, Meir, COMSOC 201

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

A Local-Dominance Theory of Voting Equilibria

It is well known that no reasonable voting rule is strategyproof. Moreover, the common Plurality rule is particularly prone to strategic behavior of the voters and empirical studies show that people often vote strategically in practice. Multiple game-theoretic models have been proposed to better understand and predict such behavior and the outcomes it induces. However, these models often make unrealistic assumptions regarding voters' behavior and the information on which they base their vote. We suggest a new model for strategic voting that takes into account voters' bounded rationality, as well as their limited access to reliable information. We introduce a simple behavioral heuristic based on \emph{local dominance}, where each voter considers a set of possible world states without assigning probabilities to them. This set is constructed based on prospective candidates' scores (e.g., available from an inaccurate poll). In a \emph{voting equilibrium}, all voters vote for candidates not dominated within the set of possible states. We prove that these voting equilibria exist in the Plurality rule for a broad class of local dominance relations (that is, different ways to decide which states are possible). Furthermore, we show that in an iterative setting where voters may repeatedly change their vote, local dominance-based dynamics quickly converge to an equilibrium if voters start from the truthful state. Weaker convergence guarantees in more general settings are also provided. Using extensive simulations of strategic voting on generated and real preference profiles, we show that convergence is fast and robust, that emerging equilibria are consistent across various starting conditions, and that they replicate widely known patterns of human voting behavior such as Duverger's law. Further, strategic voting generally improves the quality of the winner compared to truthful voting

The political conditioning of subjective economic evaluations: the role of party discourse

Classic and revisionist perspectives on economic voting have thoroughly analyzed the role of macroeconomic indicators and individual partisanship as determinants of subjective evaluations of the national economy. Surprisingly, however, top-down analysis of parties’ capacity to cue and persuade voters about national economic conditions is absent in the debate. This study uses a novel dataset containing monthly economic salience in party parliamentary speeches, macroeconomic indicators and individual survey data covering the four last electoral cycles in Spain (1996–2011). The results show that the salience of economic issues in the challenger’s discourse substantially increases negative evaluations of performance when this challenger is the owner of the economic issue. While a challenger’s conditioning of public economic evaluations is independent of the state of the economy (and can affect citizens with different ideological orientations), incumbent parties are more constrained by the true state of the economy in their ability to persuade the electorate on this issue

Convergence of Multi-Issue Iterative Voting under Uncertainty

We study the effect of strategic behavior in iterative voting for multiple issues under uncertainty. We introduce a model synthesizing simultaneous multi-issue voting with Meir, Lev, and Rosenschein (2014)'s local dominance theory and determine its convergence properties. After demonstrating that local dominance improvement dynamics may fail to converge, we present two sufficient model refinements that guarantee convergence from any initial vote profile for binary issues: constraining agents to have O-legal preferences and endowing agents with less uncertainty about issues they are modifying than others. Our empirical studies demonstrate that although cycles are common when agents have no uncertainty, introducing uncertainty makes convergence almost guaranteed in practice.Comment: 19 pages, 4 figure

Open Source and Electronic Voting: A New Strategy Toward Technical Procurement for Voting Systems

Direct Recording Electronic Voting Systems (DRE) are some of the most popular forms of electronic voting and yet they are riddled with problems. Current voting systems are poorly designed and migration to newer software can be costly. Inadequate software solutions in voting systems have led to security flaws, bad tabulation, and partisan software design. As government proceeds into an increasingly sophisticated era of voting technology, it needs to consider a better platform. This thesis explores the government procurement strategy associated with modern Direct Recording Electronic Voting Systems. The thesis argues that governments should adopt an open source solution (OSS) for future IT acquisition of voting systems. Adopting an open source solution not only provides practical advantages such as better software design, cheaper implementation, and avoidance of vendor lock-in, but also proposes that OSS provides a strong foundation for future IT policy. Open source’s strength in transparency provides a key factor in voting system design. The thesis recommends that governments adopt a four part strategy for future OSS adoption with voting system. 1) Approve an independent, pro-OSS certification organization that works closely with the U.S Election Assistance Commission, National Institute of Standards and Technology, and other system organizations to create the optimal voting systems guidelines. 2) Update FAR requirements to greater accommodate open source procurement policy. 3) Assist local and state jurisdictions to acquire OSS for DRE machines. 4) Promote open source business strategy by hiring vendors for system integration and analysis This thesis contends that these four policies will improve the electronic voting experience and allow for better future innovation and adoption IT strategies