In continuing the discussion of the concept of fairness, lets now look at lotteries. Lotteries are different; we don’t seem to demand fairness to participate. In a series of fair lotteries below the gross proceeds are evenly distributed among the participants. (For a review of my definition of fairness see my previous post).

Mean is the average payout: (total payout/ number of players). For all the three lotteries above the mean is 1, or your money back. Though this doesn’t describe what we see in the chart very well. For all lotteries above, mean returns look okay, no matter the payoff distribution or skew.
Median is the middle value of a series; the median is useful when distributions have extreme values which skew the mean value. In this example the median return for series 2 and 3 is zero. Median is a better approximate of the probable payout for those games.
Lottery payoffs are best represented by series 3 – one winner of all the money. It is unlikely that anyone would be motivated to play game 1, since simply getting you money back plus a little is not a very exciting proposition.
If we had our lottery promoter hat on, it is likely that we would prefer to sell tickets for lottery two or three rather than one. My take is that random large rewards are viewed as exciting.
In 2006, average proceeds for all US state lotteries were distributed as follows:
- approximately 65% in winnings payout
- 4% Sales General and Administrative expenses
- 31% retained by the state treasury.
Perhaps the old line “you can’t win if you don’t play” should be modified to “they can’t win if you don’t play.”
This is why economists refer to lotteries as a form of voluntary tax. In the case of all US State lotteries, initial government take of 35% compares favourably to regular income tax rates since most lottery participants pay less than 35% in average tax rates. In many instances, the proceeds are also taxed for an additional win for the sponsor state, when they receive essentially a double taxation dip of more than 50% of the bets.
So why do we suspend our sense of fairness to play these games? In the case of charity lotteries it is perhaps the excuse we need to give to a good cause. For regular lotteries, it appears that lottery operators are successful at building excitement by focusing on the mean and highlighting skewed results. This is how lottery tickets are sold. In our example more tickets will be sold for the next draw if a picture of player 10 appears in a newspaper advertisement with the proceeds check, smiling for the camera. The advertising campaigns are celebrations of non-probable random events. We don’t expect fairness in this type of game; we are satisfied with buying the excitement.
Unfortunately, we can draw many parallels to financial services from lottery marketing schemes. Instead of focusing on the plentiful returns available to market indexes, and building portfolios to capture those profits, financial service companies focus on the excitement of beating the averages. The incentives appear unbalanced. High fees paid to capture random large rewards don’t work in your investment accounts, though it may be more exciting.













