One person, one weight: when is weighted voting democratic?

In a classical “jury theorem” setting, the collective performance of a group of independent decision-makers is maximized by a voting rule that assigns weight to individuals compatibly with skills. The primary concern is that such weighted voting interferes with majoritarianism, since excessive power may be granted to a competent minority. In this paper, we address a surprisingly undertheorized issue of much significance to collective decision-making: the overlap of optimal weighted voting and the democratic, ubiquitous simple majority rule which is typically adopted in public decision-making. Running Monte Carlo simulations on the distribution of skills in large groups, our main findings are rather counterintuitive. In terms of procedure, the optimal allocation of weights is almost always democratic or “semi-democratic”, in that it satisfies or draws close to “one person, one weight”. In terms of outcome, the chosen alternative under optimal weighted voting is almost always the one that would have been selected by the simple majority rule, which satisfies “one person, one vote”. We thereby submit that the decision rules supported by the proceduralist and epistemic approaches to collective decision-making, effectively coincide more often than one would expect.