*Lara Buchak*

- Published in print:
- 2013
- Published Online:
- April 2014
- ISBN:
- 9780199672165
- eISBN:
- 9780191759048
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199672165.003.0004
- Subject:
- Philosophy, Philosophy of Mind

This chapter provides a representation theorem for risk-weighted expected utility theory (proved in the Appendices). The theorem outlines a set of constraints on individuals’ preferences that are ...
More

This chapter provides a representation theorem for risk-weighted expected utility theory (proved in the Appendices). The theorem outlines a set of constraints on individuals’ preferences that are strictly weaker than the constraints of expected utility theory. It is shown that if an individual’s preferences meet these constraints, then we can represent her beliefs, her desires, and her attitude towards risk by precise numerical values. The dispute between expected utility theory and risk-weighted expected utility theory is characterized in terms of whether to accept an axiom known as Tradeoff Consistency or instead a combination of two weaker axioms: Comonotonic Tradeoff Consistency and Strong Comparative Probability. It is shown that this dispute corresponds to forbidding or allowing individuals to care about global properties of gambles.Less

This chapter provides a representation theorem for risk-weighted expected utility theory (proved in the Appendices). The theorem outlines a set of constraints on individuals’ preferences that are strictly weaker than the constraints of expected utility theory. It is shown that if an individual’s preferences meet these constraints, then we can represent her beliefs, her desires, and her attitude towards risk by precise numerical values. The dispute between expected utility theory and risk-weighted expected utility theory is characterized in terms of whether to accept an axiom known as Tradeoff Consistency or instead a combination of two weaker axioms: Comonotonic Tradeoff Consistency and Strong Comparative Probability. It is shown that this dispute corresponds to forbidding or allowing individuals to care about global properties of gambles.

*Andrew Bacon*

- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198712060
- eISBN:
- 9780191780264
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198712060.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

Hartry Field has recently suggested that a non-standard probability calculus better represents our beliefs about vague matters. His theory has two notable features: (i) that your attitude to P when ...
More

Hartry Field has recently suggested that a non-standard probability calculus better represents our beliefs about vague matters. His theory has two notable features: (i) that your attitude to P when you are certain that P is higher-order borderline ought to be the same as your attitude when you are certain that P is simply borderline, and (ii) that when you are certain that P is borderline you should have no credence in P and no credence in ~. This chapter rejects both elements of this view and advocates instead for the view that when you are in possession of all the possible evidence, and it is borderline whether P is borderline, it is borderline whether you should believe P. Secondly, it argues for probabilism: the view that your credences ought to conform to the probability calculus. To get a handle on these issues, the chapter looks at Dutch book arguments and comparative axiomatizations of probability theory.Less

Hartry Field has recently suggested that a non-standard probability calculus better represents our beliefs about vague matters. His theory has two notable features: (i) that your attitude to P when you are certain that P is higher-order borderline ought to be the same as your attitude when you are certain that P is simply borderline, and (ii) that when you are certain that P is borderline you should have no credence in P and no credence in ~. This chapter rejects both elements of this view and advocates instead for the view that when you are in possession of all the possible evidence, and it is borderline whether P is borderline, it is borderline whether you should believe P. Secondly, it argues for probabilism: the view that your credences ought to conform to the probability calculus. To get a handle on these issues, the chapter looks at Dutch book arguments and comparative axiomatizations of probability theory.