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Lottery Purchases Aren’t Explained by Expected Value Maximization


For decades, state governments have promoted lotteries as a way to raise money without especially onerous taxes. The public, it has been argued, is willing to spend a few dollars on a chance of winning some big bucks, and politicians can use these proceeds as a substitute for more onerous taxes on the middle class and working class.

But the evidence suggests that lottery purchases can’t be explained by decision models based on expected value maximization. Rather, the tickets allow buyers to experience a sense of thrill and indulge in a fantasy that they might become rich. More general utility functions based on things other than the lottery prizes can also account for lottery purchases.

The first recorded lotteries to offer tickets for sale with prizes in the form of cash were held in the Low Countries in the 15th century to raise money for town fortifications and to help the poor. These early lotteries were organized by a hierarchy of agents, each passing the money paid for tickets up through the organization until it was banked.

Most modern lotteries are operated by private or state-owned companies, and the prizes are often paid out in the form of a lump sum (cash). Winners can choose to receive this in a single payment or annuity payments. In the latter case, a portion of each payment is withheld as income tax and thus reduces the net amount received. This is contrary to the expectations of many lottery participants, who believe that they will pocket a larger amount in a lump sum.