Coherence (philosophical gambling strategy)

In a thought experiment proposed by the Italian probabilist Bruno de Finetti in order to justify Bayesian probability, an array of wagers is coherent precisely if it does not expose the wagerer to certain loss if his opponent is prudent.

Operational subjective probabilities as wagering odds

You must set the price of a promise to pay $1 if John Smith wins tomorrow's election, and $0 otherwise. You know that your opponent will be able to choose either to buy such a promise from you at the price you have set, or require you to buy such a promise from your opponent, still at the same price. In other words: you set the odds, but your opponent decides which side of the bet will be yours. The price you set is the "operational subjective probability" that you assign to the proposition on which you are betting. The set of prices is therefore coherent when they satisfy the probability axioms and related results such as the inclusion-exclusion principle.

Related Topics:
Probability axioms - Inclusion-exclusion principle

~ ~ ~ ~ ~ ~ ~ ~ ~ ~