Abstract: This paper established a general jury theorem on group decision making where the probabilities of the individuals in making correct choice between two alternatives can be different. And we proved that the higher the probability of any decision maker in the group correctly choosing between two alternatives, the higher the probability of the group correctly choosing the same two alternatives. The general jury theorem also indicates that given two groups of individuals with the same average probability of making the correct choice, the one with a more varied or diverse distribution of probabilities will have a higher probability of making the correct choice. In particular, we proved that as the number of decision makers in the group increases to infinity, this probability tends to the limit 1. The general jury theorem presented in this paper substantially generalizes the well-known Condorcet jury theorem in the group decision making theory, which has not been generalized for 200 years until now.

Key words: Group decision making, Preference relation, Condorcet jury theorem, Probability