A social choice procedure is developed for selecting an alternative from a finite set on the basis of paired-comparison voting. Ballot data are used to construct a lottery on the alternatives that is socially as preferred as every other lottery. The constructed lottery is then used to select a winner. An axiomatization of social preferences among lotteries that justifies the procedure is included. The procedure will always select a consensus majority alternative when one exists, and it will never select an alternative that is Pareto dominated by another alternative.