You are offered either one thousand euros outright or a two-in-ten chance of winning ten thousand euros. You probably prefer one of these options. But what is that preference based on?
The first option offers a guaranteed payoff, while the second offers an uncertain one. How should we compare the two? It is a long-standing problem. In the 18th century, Daniel Bernoulli, who was also pondering the tricky St Petersburg game (see our feature " Mathematics of gambling"), proposed reasoning in terms of "moral expectation".
Maximizing your "moral expectation"
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The idea is relatively simple: first, you assume that a possession or sum of money gives you a certain utility—a certain numerical measure of satisfaction. You might decide, for example, that one thousand euros would allow you to buy the latest fashionable electronic gadget. With ten thousand euros, however, you could replace your car—and not before time!
The details do not matter. You may have good reasons for deciding, say, that one thousand euros gives you a utility of 70 units (or U(1,000) = 70), while ten thousand euros gives you a utility of 300 (or U(10,000) = 300—and you are perfectly entitled to do so: it is your utility, after all!).
Next, when faced with a set of uncertain payoffs, you weight the utility U of each payoff by its probability and add the results. In our example, reasonably assuming that U(0) = 0 (having no money has zero utility), the first option has a "moral expectation" E1 equal to U(1,000) × 1 = 70, while the second has a "moral expectation" E2 equal to U(10,000) × 0.2 + U(0) × 0.8 = 60.
