Truth-tracking judgment aggregation over interconnected issues

Abstract

This paper analyzes the problem of aggregating individual judgments over two interconnected issues. Voters share a common preference which is state-dependent, but they hold private information about what the state might be. I assume strategic voting in a Bayesian voting game setting and I want to determine voting rules which induce an efficient Bayesian Nash equilibrium in truthful strategies, hence lead to collective judgments that efficiently incorporate all private information. Interconnectedness may lead to private information that is inconsistent with the state, which leads to the impossibility of efficient information aggregation. Once I introduce the possibility of abstention, the negative conclusion no longer prevails and there is always a voting rule which aggregates information efficiently. I obtain a similar positive result when I rule out the possibility of inconsistent private information. I analyze the situations in which such rules exist whenever necessary, as well as the nature of these rules.

Aggregating Probabilistic Judgments

“…Having a probabilistic framework also opens possibilities to study the truth-tracking properties of judgment aggregators, namely how good is a function in aggregating profiles into the most likely judgments. This area of judgment aggregation is still relatively little explored [3]. We intend to explore truth-tracking in future work.…”

“…A consistent probabilistic judgment set is final if it does not imply stronger judgments than the ones it contains. 3 Probabilistic judgments can be subject to probabilistic constraints Γ, where Γ is a set of likelihood formulas to denote that certain combinations of issues must have a certain likelihood. For example for agenda Φ = {p 1 , p 2 , p 3 }, where p 1 , p 2 , and p 3 represent the three possible states of a random variable, we can have the integrity constraint (p 1 ) + (p 2 ) + (p 3 ) = 1.…”