Lotteries and Probability Theory

Abstract

A variety of decisions seem to require resort to a coin toss, die roll, or the drawing of straws?in other words, a fair lottery. This raises the question of what features distinguish fair lotteries from alternative procedures. The intuitive answer is that a fair lottery generates each of its possible outcomes with equal probability. But probability is a contentious term. There are a variety of conceptions of probability, and it may be the case that equiprobable lotteries are useful for decision-making under some conceptions but not others. This paper considers four of the leading conceptions of probability?the frequentist, objective, subjective, and logical conceptions. It argues that unless the logical conception is adopted, it is impossible to make sense of the contribution that lotteries can make to decision-making.