Aggregation of Correlated Judgments on Multiple Interconnected Issues

This paper theoretically studies the outcome of the dependency among votes. In particular, we pay attention to the event that aggregation of logically consistent judgments by a large number of voters leads to a logically inconsistent collective judgment, i.e., discursive dilemma. In contrast to results found in the literature, which assumes independent voting, we find that if the dependence among votes exists, enhancing voters’ competences does not always entail a decrease in the probability of collective inconsistency. More precisely, a non-monotonic relation can arise between individual competences and the likelihood of collective inconsistency. Moreover, even a paradoxical monotonic relation can arise, in which the likelihood of the collective inconsistency increases as voters’ competences increase. We also examine the probability of collective inconsistency when a voter’s competence is variable. The result is qualitatively similar to that obtained from the model assuming constant competences. We conclude that allowing for dependencies between votes can give rise to a new problem about the difficulty of achieving collective consistency in collective decision-making on logically interconnected issues.