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Decision theory can be extended to include counterfactuals, resolving paradoxes like the Allais paradox. This approach allows for desirability maximization even with preferences sensitive to what could have been.

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Area of Science:

  • Decision Theory
  • Philosophy of Probability
  • Rational Choice Theory

Background:

  • Standard decision theory struggles with preferences influenced by counterfactual outcomes.
  • Paradoxes like the Allais paradox highlight limitations in orthodox decision theory when considering alternative possibilities.

Purpose of the Study:

  • To extend Richard Jeffrey's decision theory to incorporate counterfactual prospects.
  • To demonstrate that preferences sensitive to counterfactual considerations can still be desirability-maximizing.
  • To investigate conditions for desirability functions to align with standard expected-utility functions.

Main Methods:

  • Utilizing a multidimensional possible-world semantics for conditionals.
  • Extending decision theory to include counterfactual scenarios.
  • Analyzing preference actualism and desirability maximization.

Main Results:

  • Preferences sensitive to counterfactual considerations can be desirability-maximizing within the extended framework.
  • The study models preferences in paradoxes such as the Allais and Diamond paradoxes.
  • Conditions for expected-utility alignment imply potentially implausible epistemic principles.

Conclusions:

  • The extended decision theory provides a framework for understanding counterfactual-dependent preferences.
  • The research offers a resolution to paradoxes arising from value dependencies between actual and counterfactual outcomes.
  • The findings suggest a tension between standard expected-utility theory and certain epistemic assumptions.