I'm not even familiar with Halpern's work. The only serious criticism I have seen regarding the usual consistency rules for subjective probabilities dealt with the "sure thing rule". I didn't find it particularly convincing.

No, I have no trouble justifying a mathematical argument in favor of this kind of consistency. But not everyone else is all that convinced by mathematics. Their attention can be grabbed, however, by the danger of being taken to the cleaners by Dutch book professional bookies.

One of these days, I will get around to producing a posting on probability, developing it from what I call the "surprisal" of a proposition - the amount, on a scale from zero to positive infinity, by which you would be surprised upon learning that a proposition is true.

• Prob(X) = 2^(-Surp(X)).
• Surp(coin flip yields heads)= 1 bit.
• Surp(A) + Surp(B|A) = Surp(A&B)

That last formula strikes me as particularly easy to justify (surprisals are additive). Given that and the first formula, you can easily derive Bayes law. The middle formula simply fixes the scale for surprisals. I suppose we also need a rule that Surp(True)=0