We introduce coherence conditions having a betting scheme interpretation both for a numerical and a comparative conditional possibility assessment. The conditional bets are considered under partially resolving uncertainty and assuming consonance. This means that we allow situations in which the agent may only acquire the information that a non-impossible event occurs, without knowing which is the true state of the world. Further, he/she can only consider families of nested non-impossible events in computing the gain and has a systematically optimistic behavior. Both conditions are proved to be equivalent to the existence of a conditional possibility agreeing with an axiomatic definition based on the algebraic product t-norm, that extends, either numerically or comparatively (through the induced comparative conditional possibility relation), the given assessment.
Betting Schemes for Assessing Coherent Numerical and Comparative Conditional Possibilities
Davide Petturiti;Barbara Vantaggi
2021
Abstract
We introduce coherence conditions having a betting scheme interpretation both for a numerical and a comparative conditional possibility assessment. The conditional bets are considered under partially resolving uncertainty and assuming consonance. This means that we allow situations in which the agent may only acquire the information that a non-impossible event occurs, without knowing which is the true state of the world. Further, he/she can only consider families of nested non-impossible events in computing the gain and has a systematically optimistic behavior. Both conditions are proved to be equivalent to the existence of a conditional possibility agreeing with an axiomatic definition based on the algebraic product t-norm, that extends, either numerically or comparatively (through the induced comparative conditional possibility relation), the given assessment.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
