 Condorcet assumed that each individual is better than random at making a correct judgment (the competence assumption) and that different individuals’ judgments are stochastically independent, given the state of the world (the independence assumption). Formally, let \(V_1, V_2 , \ldots ,V_n\) (capital letters) denote the random variables generating the specific individual votes \(v_1, v_2 , \ldots ,v_n\) (small letters), and let \(V = f(V_1, V_2 , \ldots ,V_n)\) denote the resulting random variable representing the social decision \(v = f(v_1, v_2 , \ldots ,v_n)\) under a given aggregation rule \(f\), such as majority rule. Condorcet’s assumptions can be stated as follows: