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Decision Theory: A Formal Philosophical Introduction

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Introduction to Formal Philosophy

Part of the book series: Springer Undergraduate Texts in Philosophy ((SUTP))

Abstract

Decision theory is the study of how choices are and should be made.in a variety of different contexts. Here we look at the topic from a formal-philosophical point of view with a focus on normative and conceptual issues. After considering the question of how decision problems should be framed, we look at the both the standard theories of chance under conditions of certainty, risk and uncertainty and some of the current debates about how uncertainty should be measured and how agents should respond to it.

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Notes

  1. 1.

    The restriction to a finite number of states of the world is made for simplicity, but the expected value will still be well defined even if we drop it.

  2. 2.

    What level of resources is justified will of course depend on what is at stake.

  3. 3.

    Savage was perfectly aware of this objection and drew an important distinction between small-world and grand-world decision problems. But he never produced a theory which, to his own and others satisfaction, explained how to convert grand-world problems into small-world ones satisfying the two requirements.

  4. 4.

    It should be noted that the assumption of Consequentialism does not rule out a role for non-consequentialist considerations, in particular in determining the composition of the set of options. For instance if some actions are not permissable because they would violate someone’s rights then they would be excluded from the option set. What it does assume is that such non-consequentialist considerations do not enter beyond this point.

  5. 5.

    To be clear, it is the ontological doctrine just described that should be rejected, not the associated epistemological doctrine according to which knowledge of preferences ultimately rests on observations of choice. The latter, in contrast to the former, has much to recommend it.

  6. 6.

    It is important to note that it’s essential to the possibility of an additive representation that no cross-locational comparisons are possible. For such comparisons would constrain the co-scaling of the u j and there would then be no guarantee that the permitted co-scaling allowed for an additive representation.

  7. 7.

    For arguments that it is not a requirement of rationality see [11] and [33].

  8. 8.

    I take this term from Broome [10].

  9. 9.

    Savage in fact introduces one further postulate necessary for the extension of the expected utility representation to infinite consequences sets. This final postulate is very much in the spirit of the Sure-thing principle and as it does not raise any additional conceptual issues, I will not state it here.

  10. 10.

    Printed, along with Savage’s letter in reply, in Drèze [12, pp. 76–81].

  11. 11.

    See, for instance, Drèze [12], Karni et al. [21] and Karni and Mongin [20] for a discussion of this issue.

  12. 12.

    See for instance, Simon [31], Gigerenzer and Selten [15, 37] and Rubinstein [28].

  13. 13.

    See for instance, Halpern [16] and Lipman [26].

  14. 14.

    See for instance [8].

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  1. London School of Economics and Political Science, London, UK

    Richard Bradley

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  1. Division of Philosophy, Royal Institute of Technology (KTH), Stockholm, Sweden

    Sven Ove Hansson

  2. Center for Information and Bubble Studies, University of Copenhagen, Copenhagen, Denmark

    Vincent F. Hendricks

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Bradley, R. (2018). Decision Theory: A Formal Philosophical Introduction. In: Hansson, S., Hendricks, V. (eds) Introduction to Formal Philosophy. Springer Undergraduate Texts in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-77434-3_34

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