Search

Fair Betting Quotient (FBQ)

Last updated Oct 21, 2022 Edit Source

Your fair betting quotient (FBQ) for A is p if you think that the following is a fair bet (you are willing to take either side):

• If A is true, you win $(1 - p)S$
• If A is not true, you lose $pS$

Betting table is different from decision tables. Columns are different bets.

A Bet for A Bet against A
T $(1-p)S$ $-(1-p)S$
F $-pS$ $pS$

Suppose a set of credences (or FBQ’s) is incoherent. We can always construct a Dutch Book. Have the agent bet for propositions with credences (or FBQs) that are too high, and against propositions with credences (or FBQs) that are too low.