Abstract
Brams mentions John A. Ferejohn's resolution of paradox by reformulating situation in such a way that Being's choices money in or to put are changed to two of namely, the guesses and the guesses incorrectly. Formulated in this way, situation becomes a decision problem under risk without a dominating strategy for chooser. It appears, consequently, that maximization of utility dictates choice of only B2 over choice of both boxes. (For simplicity, we regard utility of money to be a linear function of amount of money. If not, amounts of money can be calibrated to make payoffs reflect actual utilities.) Note, however, that states of world, Being guesses and Being guesses incorrectly, are not independent of what chooser does. Therefore in computing expected utilities, not probabilities of these two states as such must be used, but rather conditional probabilities with respect to chooser's choices. Let E be event The chooser takes only B2; E complementary event, He takes both boxes; F event the predicts E; F complementary event, the predicts R. Finally, let C be event, the guesses correctly. Then Pr(C I E) = Pr(F I E); for to predict correctly when E occurs means to predict E when E occurs. This is relevant probability associated with upper-left cell in matrix shown in Brams's Figure 2.
Published Version
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