Distant Truth: Bias Under Vote Distortion Costs Svetlana Obraztsova Nanyang Technological University Singapore lana@ntu.edu.sg Omer Lev University of Toronto Toronto, Canada omerl@cs.toronto.edu Evangelos Markakis Athens University of Economics and Business Athens, Greece markakis@gmail.com Zinovi Rabinovich Nanyang Technological University Singapore zinovi@ntu.edu.sg Jeffrey S. Rosenschein Hebrew University of Jerusalem Jerusalem, Israel jeff@cs.huji.ac.il ABSTRACT In recent years, there has been increasing interest within the computational social choice community regarding mod- els where voters are biased towards specific behaviors or have secondary preferences. An important representative exam- ple of this approach is the model of truth bias, where voters prefer to be honest about their preferences, unless they are pivotal. This model has been demonstrated to be an effec- tive tool in controlling the set of pure Nash equilibria in a voting game, which otherwise lacks predictive power. How- ever, in the models that have been used thus far, the bias is binary, i.e., the final utility of a voter depends on whether he cast a truthful vote or not, independently of the type of lie. In this paper, we introduce a more robust framework, and eliminate this limitation, by investigating truth-biased vot- ers with variable bias strength. Namely, we assume that even when voters face incentives to lie towards a better out- come, the ballot distortion from their truthful preference incurs a cost, measured by a distance function. We study various such distance-based cost functions and explore their effect on the set of Nash equilibria of the underlying game. Intuitively, one might expect that such distance metrics may induce similar behavior. To our surprise, we show that the presented metrics exhibit quite different equilibrium behav- ior. CCS Concepts •Theory of computation → Solution concepts in game theory; Convergence and learning in games; Keywords Voting; Truth-bias; Dynamics Appears in: Proc. of the 16th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2017), S. Das, E. Durfee, K. Larson, M. Winikoff (eds.), May 8–12, 2017, S˜ao Paulo, Brazil. Copyright c  2017, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved. 1. INTRODUCTION My election method is only for honest men. — Jean-Charles de Borda 1 The issue of aggregating different opinions to reach a sin- gle decision has been investigated for centuries, regarding both the process itself (elections ) and the induced outcomes. Various thinkers have tried to design voting mechanisms that will reach an outcome that best reflects the partici- pants’ views. However, looming over these attempts is the very common tendency by voters to hide their real prefer- ences and vote strategically—vote in a way that will make the outcome more preferable to them. As the Gibbard-Satterthwaite theorem [9, 21] showed that such phenomena are unavoidable (except in dictatorships), much research has turned to analyzing the outcomes of elec- tions. A long line of research arose in this context, starting with [1], on the complexity aspects of strategizing agents, who seek to manipulate the election outcome. A more intricate question is understanding the election outcomes that emerge when voters are strategic. Prima fa- cie, a natural tool to analyze voting outcomes under strate- gic behavior is the Nash equilibrium. However, not only is there an enormous number of equilibria (for plurality, ex- ponential in the number of voters [22]), but also many of these equilibria cannot occur in practice as an election re- sult. For example, in plurality, if all voters rank the same candidate first (even if it is their least-preferred one), this is a Nash equilibrium since no one can unilaterally change the outcome. Hence, the set of Nash equilibria has quite poor predictive power. A recent approach to refine the set of equilibria (and cer- tainly not the only one), is derived from the basic under- standing that all things being equal, people prefer to be truthful [3]. In other words, their utility does not only de- pend on the outcome of the election, but is also influenced by whether they voted according to their true preferences or not. Models with such a truth bias, while initiated by economists [10, 7], have been widely studied by computer 1 There are several English versions of Borda’s remark, but the French original apparently appeared in Sylvestre Fran¸ cois Lacroix’s Eloge Historique de Borda in 1800. 885