Truth-tracking judgment aggregation over interconnected issues

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.