Optimal voting rules under uncertainty

The theory of ‘constitutional’ choice of voting rules developed by Buchanan and Tullock is an extended to an explicit decision-theoretic form. Voters in the ‘constitutional’ position choose what they believe will be their optimal share or majority rule for making social decisions, by maximizing their individual expected utility from the anticipated social decisions, under conditions of uncertainty. The rule that maximizes expected social benefits depends upon (1) the expected distribution and intensity of preferences on future issues, and (2) the decisionmaking procedures and costs. ‘Decisionmaking’ and ‘external’ costs are shown to be interrelated. Following this analysis, failure to pass laws imposes ‘external’ costs in the same way that passing them does, so that the optimal majority may be lower when desirable laws are viewed as changing over time. Decisionmaking costs depend upon the way in which voters are persuaded to support or oppose bills, upon the distribution of preferences on bills, and on vote-trading possibilities. If vote-trading is almost costless, a wide range of decision rules has nearly equal social benefits. Finally, the model is used to discuss optimal voting rules for several decisionmaking bodies.