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We propose a probabilistic model to aggregate the answers of respondentsanswering multiple-choice questions. The model does not assume that everyonehas access to the same information, and so does not assume that the consensusanswer is correct. Instead, it infers the most probable world state, even ifonly a minority vote for it. Each respondent is modeled as receiving a signalcontingent on the actual world state, and as using this signal to bothdetermine their own answer and predict the answers given by others. Byincorporating respondent's predictions of others' answers, the model inferslatent parameters corresponding to the prior over world states and theprobability of different signals being received in all possible world states,including counterfactual ones. Unlike other probabilistic models foraggregation, our model applies to both single and multiple questions, in whichcase it estimates each respondent's expertise. The model shows goodperformance, compared to a number of other probabilistic models, on data fromseven studies covering different types of expertise.

A statistical model for aggregating judgments by incorporating peer predictions