23 - Why conditionalize?

Summary

INTRODUCTION (1997)

This paper presents what is nowadays called the ‘diachronic Dutch book argument’. I wrote it in 1972 as a handout for a course, with no thought of publication. I thought then that the argument was wellknown. Yet I could not find it presented in print, so I had to reconstruct it for myself. I showed my handout to Paul Teller; he presented the argument, with my permission and with full acknowledgement, in his article ‘Conditionalization and Observation’. Teller's article has become the standard source for the argument. But it seems to leave a question in some readers' minds: why does the argument call for conditionalizing on the subject's total increment of experiential evidence, no more and no less? Since my handout had addressed just that question, I decided there was some reason to publish it after all. Apart from a little editing to simplify notation, it appears here in its original form.

The diachronic Dutch book argument can be broken into two halves. Consider a conditional bet: that is, a bet that will be null and void unless its condition is met. We note, first, that the conditional bet is equivalent in its outcome, come what may, to a certain pair of unconditional bets. We note, second, that the conditional bet is also equivalent in its outcome, come what may, to a certain contingency plan whereby one's future betting transactions are made to depend on the arrival of new evidence. The first equivalence yields a well-known synchronic argument relating the prices of conditional and unconditional bets.