If an agent’s belief in a proposition is represented by imprecise probabilities, i.e. intervals of probability values, a phenomenon called dilation can occur, where updating the agent’s belief with a new observation can only widen the probability interval, thus making the agent more uncertain, regardless of the observation made. Similar to standard updating, dilation can also occur in the context of imprecise opinion pooling, where the imprecise beliefs of multiple agents are aggregated. In this work, we provide the first formal investigation of dilation and its counterpart, contraction, in the context of imprecise opinion pooling. To this end, we use a recently defined voting rule, Voting for Bins (VfB), as a means to handle dilation and contraction, consistent with intuitions about the quality of additional opinions. VfB, inspired by the Condorcet Jury Theorem (CJT), is extended to account for correlation by an opinion leader. This model is further generalized to account for average correlation.

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Taming Dilation in Imprecise Pooling

  • Jonas Karge

摘要

If an agent’s belief in a proposition is represented by imprecise probabilities, i.e. intervals of probability values, a phenomenon called dilation can occur, where updating the agent’s belief with a new observation can only widen the probability interval, thus making the agent more uncertain, regardless of the observation made. Similar to standard updating, dilation can also occur in the context of imprecise opinion pooling, where the imprecise beliefs of multiple agents are aggregated. In this work, we provide the first formal investigation of dilation and its counterpart, contraction, in the context of imprecise opinion pooling. To this end, we use a recently defined voting rule, Voting for Bins (VfB), as a means to handle dilation and contraction, consistent with intuitions about the quality of additional opinions. VfB, inspired by the Condorcet Jury Theorem (CJT), is extended to account for correlation by an opinion leader. This model is further generalized to account for average correlation.