Lotteries and the Time Horizon

People chose between hypothetical alternatives of (a) a million-dollar lottery prize and (b) a much smaller but certain amount of money When probabilities of winning the lottery were above about 1/100,000, subjects avoided risk, for example, a 1/100,000 probability of the million-dollar prize was chosen about as often as $700 for sure But at probabilities below 1/100,000, subjects sought risk, for example, a 1/1,000,000 probability of the million-dollar prize was chosen about as often as $9 for sure This crossover from risk aversion to risk seeking is predicted by Mazur's (1987) hyperbolic delay discount function with probability expressed as average delay due to strings of losses followed by a win, together with a time horizon limiting subjective delay