Voting on Actions with Uncertain Outcomes

We introduce a model for voting under uncertainty where a group of voters have to decide on a joint action to take, but the individual voters are uncertain about the current state of the world and thus about the effect that the chosen action would have. Each voter has preferences about what state they would like to see reached once the action has been executed. That is, we need to integrate two kinds of aggregation: beliefs regarding the current state and preferences regarding the next state. The Paradox of Individual Uncertainty Resolution Belief Preference Action Agent 1 A A B stay Agent 2 A B A change Agent 3 B B A stay Collective stay A B change change stay stay Belief Preference Action Agent 1 A A B Agent 2 A B A Agent 3 B B A Collective A B A change [using majority for aggregation of any kind of information] The Paradox of Late Collective Uncertainty Resolution Belief Preference Action Agents 1–2 A or C A C B Agents 3–5 B or C B A C Collective C A B C left A C B left,right left right left,right Belief Preference Action Agents 1–2 A or C A @@@ C B Agents 3–5 B or C B A @@@ C Collective C B A right [using approval voting for beliefs and Borda for preferences] The Paradox of Early Collective Uncertainty Resolution Belief Preference Action Agents 1–9 A or C A C B Agent 10 A or B B C A Collective A A C B down [approval for beliefs, Condorcet for preferences, and lexicographic tie-breaking for actions] A C