A Condorcet jury theorem for couples

The agents of a jury have to decide between a good and a bad option through simple majority voting. In this paper the jury consists of N independent couples. Each couple consists of two correlated agents of the same competence level. Different couples may have different competence levels. In addition, each agent is assumed to be better than completely random guessing. We prove tight lower and upper bounds for the quality of the majority decision. The lower bound is the same as the competence of majority voting of N independent agents. The upper bound cases for negatively correlated couples can be much better than the value for $2N$ independent agents.