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Collective Decision Making under Incomplete Knowledge: Possible and Necessary Solutions

Most solution concepts in collective decision making are defined assuming complete knowledge of individuals’ preferences and of the mechanism used for aggregating them. This is often unpractical or unrealistic. Under incomplete knowledge, a solution advocated by many consists in quantifying over all completions of the incomplete preference profile (or all instantiations of the incompletely specified mechanism). Voting rules can be ‘modalized’ this way (leading to the notions of possible and necessary winners), and also efficiency and fairness notions in fair division, stability concepts in coalition formation, and more. I give here a survey of works along this line.