Lotteries as Cost-Saving Mechanisms

In decision theory, it's useful to conceptualize all choices as amongst lotteries. Even a choice that has an absolutely certain outcome may be imagined as a sort of trivial lottery, where one outcome had the equivalent of a 100% probability and all other outcomes had the equivalent of a 0% probability. But most of the choices that people typically imagine may be made with certainty cannot, and things that actually can be chosen with certainty are not things to which people give much conscious thought. For example, in a restaurant. one cannot choose tea with certainty; one cannot even choose to order tea with certainty. One can chose to try to order tea; however, whether one's language-processing centers and apparatus of speech will do what one wants is somewhat in doubt. But most people don't recognize the vast majority of their choices as amongst lotteries because it isn't particularly useful for them to make the recognition.

That said, it's still interesting (to me at least!) to note how people respond to the things that nearly everyone does recognize as lotteries. If Group A wants the m members of Group B to do something for them, they can pay D to them each, for a total cost of m · D, or they can offer a prize P; and if m is a moderate-to-large number then almost always the least value of P that will motivate the group is rather less than the the value of m · D, even when there is no sense of supporting a worthy cause. In the clearest illustration, what Group A want of Group B is just money. Most people will give you a five-dollar bill for five one-dollar bills, but few will ordinarily give you that five-dollar bill for four one-dollar bills. However, perhaps a million people will give you five dollars for a one-in-a-million chance at four million dollars.

In the context of various social confusions, there are restrictions on selling chances at money in exchange for money.[1] But chances at money or at other prizes are fairly freely traded for information that is worth money. Think of how many times you are offered a chance at a large sum of money or at a valuable commodity (such as a vehicle) in exchange for taking a consumer survey or for providing contact information. You might refuse — I do — but a lottery is offered because information is provided by more people than could be motivated to do so for the same sum divided into simple payments.

It's often claimed that people are irrational to make bets in which the price of participation exceeds the probability of the payoff times the size of the payoff. I don't want to claim that; the issue is actually very nuanced. (There have been studies that attempt to estimate the extent to which a systemic misappraisal of probabilities affect behavior, but most or all of these studies are hopelessly tainted by the active desire to find irrational behavior and by some questionable presumptions concerning how uncertainty ought to be handled.) But, in any case, it's interesting that a group can conserve its resources by using a lottery to motivate behavior. And, returning to the point that in reality almost everything is a lottery, one has to wonder to what extent the world more generally is getting us to do things on the cheap.


[1] The inescapability of lotteries is fatal to ordinary attempts to condemn gambling as immoral. That something were immoral or unwise would not ipso facto be sufficient to justify outlawing it. And outlawing payment in money while allowing payment in commodities is absurd.

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