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2021-07-16: Vincent Merlin and Nicholas Mattei Session Chair: Ulle Endriss (Amsterdam) --- Vincent Merlin (Caen) The Probability of Disputable Outcomes under Direct and Indirect Elections Defenders of the Electoral College routinely invoke a traditional argument to reject proposals for a national popular vote. Granted, they say, Florida in 2000 was a national nightmare, but the agony would be far greater if such a dispute extended over the entire nation. Proponents of a direct vote reply by conjecturing that the Electoral College increases the frequency of disputable elections. Indeed, the 2020 US presidential election was another instance of disputable election on the legal front. We investigate whether we should expect disputable outcomes to be more frequent under the present US indirect system as compared with a direct vote and, if so, by how much. We use two methods: an historical analysis of actual outcomes in presidential elections, and an a priori formal model borrowed from Social Choice Theory (IAC). Depending on the thresholds one posits for disputability, the historical analysis shows that disputable elections have been about two to six times more frequent under the Electoral College. In a model where all the states have the same population the IAC model produces an impressively compatible intermediate ratio of 4:1. We also explore the impact of differences in the population of the states on the likelihood of legal disputes. Joint work with Jack Nagel and Théo Duchemin. --- Nicholas Mattei (Tulane) Modeling Voters in Multi-Winner Approval Voting In many real world situations, collective decisions are made using voting and, in scenarios such as committee or board elections, employing voting rules that return multiple winners. In multi-winner approval voting (AV), an agent submits a ballot consisting of approvals for as many candidates as they wish, and winners are chosen by tallying up the votes and choosing the top-k candidates receiving the most approvals. In many scenarios, an agent may manipulate the ballot they submit in order to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex and uncertain situations, agents may use heuristics instead of incurring the additional effort required to compute the manipulation which most favors them. In this paper, we examine voting behavior in single-winner and multi-winner approval voting scenarios with varying degrees of uncertainty using behavioral data obtained from Mechanical Turk. We find that people generally manipulate their vote to obtain a better outcome, but often do not identify the optimal manipulation. There are a number of predictive models of agent behavior in the social choice and psychology literature that are based on cognitively plausible heuristic strategies. We show that the existing approaches do not adequately model our real-world data. We propose a novel model that takes into account the size of the winning set and human cognitive constraints; and demonstrate that this model is more effective at capturing real-world behaviors in multi-winner approval voting scenarios. Joint work with Jaelle Scheuerman, Jason Harman, and K. Brent Venable.