Eliciting Objective Probabilities via Lottery Insurance Games

Since utilities and probabilities jointly determine choices, event-dependent utilities complicate the elicitation of subjective event probabilities. However, for the usual purpose of obtaining the information embodied in agent beliefs, it is sufficient to elicit objective probabilities, i.e., probabilities obtained by updating a known common prior with that agent’s further information. Bayesians who play a Nash equilibrium of a certain insurance game before they obtain relevant information will afterward act regarding lottery ticket payments as if they had event-independent risk-neutral utility and a known common prior. Proper scoring rules paid in lottery tickets can then elicit objective probabilities.