The principle of `One Person, One Vote' is viewed by many as one of the cornerstones of Democracy. But in environments where agents have heterogenous stakes in the decision, a utilitarian social planner would typically prefer non-anonymous rules, i.e. rules that violate this principle. We consider a simple Bayesian voting environment in which agents have private valuations for the alternatives and a voting mechanism is used to determine the outcome. The \emph{price of `One Person, One Vote'} is defined as the fraction reduction in expected welfare when the optimal anonymous mechanism is used relative to the optimal (not necessarily anonymous) mechanism. We analyze how this price behaves as a function of the environment (distribution of preferences). In particular, it is shown that if the inequality of stakes in the population increases, in a well-defined sense, then the price of `One Person, One Vote' is higher. A similar comparative statics holds if the uncertainty about agents' preferences increases. Our results may be useful for social planners who weigh the moral argument (or other arguments) in favor of `One Person, One Vote' with the loss of efficiency that may result by sticking to this principle.