 Correctness, state, and votes. Each alternative possesses a “true” or “objective” value, quality, or correctness level. If alternatives are beliefs or belief sets, value usually depends on truth; if alternatives are evaluations of objects, value might depend on distance to correct evaluations; etc. Value is determined by an unknown “state”. Let \(\mathcal{S}\) be the non-empty set of possible states. The votes of individuals \(1, 2, \ldots\) and the state are interpreted as the outcomes of random variables \(\mathbf{v}_{1},\) \(\mathbf{v}_{2}, \ldots\) with range \(\mathcal{A}\) and \(\mathbf{s}\) with range \(\mathcal{S}\), respectively. One can be more or less sophisticated: