Paradox

PASCAL’S IMPROBABLE CALCULATIONS 233in contemporary economics as the law of the diminishingmarginal utility of money. The rate of diminution resistsprecise calculation, but Daniel Bernoulli inferred that it is alogarithmic function. This would preclude infinite sums.In economics, the most popular solution to both thewager and the St. Petersburg paradox is evaluative finitism.Following Daniel Bernoulli, economists formulate the axiomsof decision theory in a way that ensures value is necessarilyfinite. This limit on desire grates against severaleconomic themes. Economists tell us that desire is insatiable,that ends cannot be irrational, and that what counts arepeople’s beliefs about what they can acquire rather than whatactually exists. Right or wrong, Pascal seeks the infinitereward of heaven and flees from the infinite punishment ofhell. Indeed, most people have religious hopes and fears ofinfinite proportion. Whether or not infinite value can beactually secured, the economist seems obliged to model thechoices of those who believe in infinite value.Economists try to enforce their finitism by pepperingdoubters with the puzzles that accrue from allowing nearlyany infinite aspect into decision theory. Take the possibilityof infinite time. In Foundations of Statistics, Leonard Savagenotes that the longer you save, the more you have. So it seemsan immortal should save forever! Savage sidelines the enigmaby stipulating that his theory only applies to finite quantities.But the puzzle does not require infinite value. Suppose a bottleof Everbetter wine improves endlessly but only to the limitset by the quality of a moderately nice wine. (Pollock 1983)This finitely good wine gets better only in the way 1/n getscloser to 0. When should an immortal connoisseur drink thewine? Not now because it will be better later. Not at anyparticular time later because the wine would be even better