Applying the Jeffrey decision model to rational betting and information acquisition

✍ Scribed by Ernest W. Adams; Roger D. Rosenkrantz

• Book ID: 104645928
• Publisher: Springer US
• Year: 1980
• Tongue: English
• Weight: 927 KB
• Volume: 12
• Category: Article
• ISSN: 0040-5833
• DOI: 10.1007/bf00154655

✦ Synopsis

Assuming that utilities are increasing in preference, Jeffrey formulated certain axioms which preferences must satisfy in order that there should exist probabilities and utilities 'measuring the preferences' and satisfying the Jeffrey Mixture Law. Bolker (1965) has proved the relevant Representation Theorem, and recently, Domotor (1978) has axiomatized the theory under much weaker 'structural conditions' than those assumed by Bolker. Our present concern is not with axiomatization, however, and we shall for the most part ignore the connection between utilities and preferences, as well as that between quantitative and qualitative probability relations.

An equivalent formulation of the Jeffrey Mixing Law a relating acts, states and consequences, which helps bring out the connection with standard Bayesian decision theory based on act-independent states, is:

where the cj are possible consequences, and where conditional probabilities that are undefined are set equal to zero. This law reduces to the familiar act-independent expression for expected utility when the following three assumptions are met:

Act lndependence: P(s~la) = P(si).