Random dictatorship domains

Chatterji, Shurojit; Sen, Arunava; Zeng, Huaxia

doi:10.1016/j.geb.2014.03.017

Cited by 33 publications

(23 citation statements)

References 26 publications

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“…] Refusal to entertain lotteries on alternatives can lead to outcomes that to many appear to be inequitable and perhaps even inefficient" (Zeckhauser (1969)). 4 In contemporary research, probabilistic social choice has gained increasing interest in both social choice (see, e.g., Ehlers, Peters, and Storcken (2002), Bogomolnaia, Moulin, and Stong (2005), Chatterji, Sen, and Zeng (2014)) and political science (see, e.g., Goodwin (2005), Dowlen (2009), Stone (2011).…”

Section: Acceptability Of Social Choice Lotteriesmentioning

confidence: 99%

Consistent Probabilistic Social Choice

2016

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Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non-probabilistic social choice, these axioms are incompatible with each other. We show that in the context of probabilistic social choice, these axioms uniquely characterize a function proposed by Fishburn (Rev. Econ. Stud., 51(4), [683][684][685][686][687][688][689][690][691][692] 1984). Fishburn's function returns so-called maximal lotteries, i.e., lotteries that correspond to optimal mixed strategies in the symmetric zero-sum game induced by the pairwise majority margins. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming.

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Section: Acceptability Of Social Choice Lotteriesmentioning

confidence: 99%

Consistent Probabilistic Social Choice

2016

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“…Recent years have seen a surge of similar work on other preference domains, with both possibility and impossibility results. For example, Chatterji et al () give broad connectedness‐type conditions on a domain that imply every strategy‐proof and unanimous mechanism is a random dictatorship. They also show by example that domain conditions known to imply dictatorship results in the deterministic setting are not sufficient in the randomized setting.…”

Section: Introductionmentioning

confidence: 99%

“…We return to our opening examples. In the object allocation problem of Bogomolnaia and Moulin (), the requirements of ordinal efficiency and equal treatment of equals can be expressed by an SCC that, at each profile of ordinal preferences, deems a lottery over allocations to be acceptable if and only if it is consistent with these requirements.In a voting problem, unanimity can be expressed by the SCC where, at any profile where all voters have the same preferred outcome, only the degenerate lottery on that outcome is acceptable, and at any other preferences, all lotteries are acceptable.Since our framework is specifically focused on possibility/impossibility results, it does not capture characterizations such as the random dictatorship result of Chatterji et al (). However, one could refine the SCC so as to rule out random dictatorship (for example, by imposing a “compromise” requirement as in Chatterji et al (), specifying that at some particular profiles, an outcome that is not anyone's top choice should be chosen with some minimum probability).…”

Section: Introductionmentioning

confidence: 99%

On mechanisms eliciting ordinal preferences

Carroll¹

2018

Theoretical Economics

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When is a mechanism designer justified in only asking for ordinal information about preferences? Simple examples show that even if the planner's goal (expressed by a social choice correspondence (SCC)) depends only on ordinal information, eliciting cardinal information may help with incentives. However, if agents may be uncertain about their own cardinal preferences, then a strong robustness requirement can justify the focus on ordinal mechanisms. Specifically, when agents' preferences over pure outcomes are strict, if a planner is able to implement an SCC (in ex post equilibrium) using a mechanism that is robust to interdependence of arbitrary form in cardinal preferences, then there must exist such a mechanism that elicits only ordinal preferences. The strictness assumption can be dropped if we further allow the possibility of non-expected-utility preferences.

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“…There are also works studying the aggregation of partial [77,78] or non-linear rankings (such as pair-wise comparisons among alternatives) [25], since it could be costly/impossible to request agents for a full linear ranking over all possible actions. Some very recent works in social choice also analyze probabilistic voting rules, where the agents' votes affect a probability distribution over outcomes [11,16].…”

Section: Related Workmentioning

confidence: 99%

Every team deserves a second chance: an extended study on predicting team performance

Marcolino

Lakshminarayanan

Nagarajan

et al. 2016

Auton Agent Multi-Agent Syst

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Voting among different agents is a powerful tool in problem solving, and it has been widely applied to improve the performance in finding the correct answer to complex problems. We present a novel benefit of voting, that has not been observed before: we can use the voting patterns to assess the performance of a team and predict their final outcome. This prediction can be executed at any moment during problem-solving and it is completely domain independent. Hence, it can be used to identify when a team is failing, allowing an operator to take remedial procedures (such as changing team members, the voting rule, or increasing the allocation of resources). We present three main theoretical results: (1) we show a theoretical explanation of why our prediction method works; (2) contrary to what would be expected based on a simpler explanation using classical voting models, we show that we can make accurate predictions irrespective of the strength (i.e., performance) of the teams, and that in fact, the prediction can work better for diverse teams composed of different agents than uniform teams made of copies of the best agent; (3) we show that the quality of our prediction increases with the size of the action space. We perform extensive experimentation in two different domains: Computer Go and Ensemble Learning. In Computer Go, we obtain high Multi-Agent Syst (2017) 31:1003-1054 quality predictions about the final outcome of games. We analyze the prediction accuracy for three different teams with different levels of diversity and strength, and show that the prediction works significantly better for a diverse team. Additionally, we show that our method still works well when trained with games against one adversary, but tested with games against another, showing the generality of the learned functions. Moreover, we evaluate four different board sizes, and experimentally confirm better predictions in larger board sizes. We analyze in detail the learned prediction functions, and how they change according to each team and action space size. In order to show that our method is domain independent, we also present results in Ensemble Learning, where we make online predictions about the performance of a team of classifiers, while they are voting to classify sets of items. We study a set of classical classification algorithms from machine learning, in a data-set of hand-written digits, and we are able to make high-quality predictions about the final performance of two different teams. Since our approach is domain independent, it can be easily applied to a variety of other domains.

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Random dictatorship domains

Cited by 33 publications

References 26 publications

Consistent Probabilistic Social Choice

Consistent Probabilistic Social Choice

On mechanisms eliciting ordinal preferences

Every team deserves a second chance: an extended study on predicting team performance

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