– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Ramsey (1926) sketches a proposal for measuring the subjective probabilities of an agent by their observable preferences, assuming that the agent is an expected utility maximizer. I show how to extend the spirit of Ramsey's method to a strictly wider class of agents: risk-weighted expected utility maximizers (Buchak 2013). In particular, I show how we can measure the risk attitudes of an agent by their observable preferences, assuming that the agent is a risk-weighted expected utility maximizer. Further, we can leverage (...) this method to measure the subjective probabilities of a risk-weighted expected utility maximizer. (shrink)

State-dependent utility is a problem for the behavioural branch of decision theory under uncertainty. It questions the very possibility that beliefs be revealed by choice data. According to the current literature, all models of beliefs are equally exposed to the problem. Moreover, the problem is solvable only when the decision-maker can influence the resolution of uncertainty. This article gives grounds to reject these two views. The various models of beliefs can be shown to be unequally exposed to the problem of (...) state-dependent utility. The problem can be argued to be solved even when the decision-maker has no influence over the resolution of uncertainty. The implications of such reappraisal for a philosophical appreciation of the revealed preference methodology are discussed. (shrink)

We reexamine some of the classic problems connected with the use of cardinal utility functions in decision theory, and discuss Patrick Suppes's contributions to this field in light of a reinterpretation we propose for these problems. We analytically decompose the doctrine of ordinalism, which only accepts ordinal utility functions, and distinguish between several doctrines of cardinalism, depending on what components of ordinalism they specifically reject. We identify Suppes's doctrine with the major deviation from ordinalism that conceives of utility functions as (...) representing preference differences, while being non- etheless empirically related to choices. We highlight the originality, promises and limits of this choice-based cardinalism. (shrink)

This paper examines the preference-based approach to the identification of beliefs. It focuses on the main problem to which this approach is exposed, namely that of state-dependent utility. First, the problem is illustrated in full detail. Four types of state-dependent utility issues are distinguished. Second, a comprehensive strategy for identifying beliefs under state-dependent utility is presented and discussed. For the problem to be solved following this strategy, however, preferences need to extend beyond choices. We claim that this a necessary feature (...) of any complete solution to the problem of state-dependent utility. We also argue that this is the main conceptual lesson to draw from it. We show that this lesson is of interest to both economists and philosophers. (shrink)

Contemporary decision theory places crucial emphasis on a family of mathematical results called representation theorems, which relate criteria for evaluating the available options to axioms pertaining to the decision-maker’s preferences. Various claims have been made concerning the reasons for the importance of these results. The goal of this article is to assess their semantic role: representation theorems are purported to provide definitions of the decision-theoretic concepts involved in the evaluation criteria. In particular, this claim shall be examined from the perspective (...) of philosophical theories of the meaning of theoretical terms. (shrink)

Abstract:This paper explores the contrast between mentalistic and behaviouristic interpretations of decision theory. The former regards credences and utilities as psychologically real, while the latter regards them as mere representations of an agent's preferences. Philosophers typically adopt the former interpretation, economists the latter. It is argued that the mentalistic interpretation is preferable if our aim is to use decision theory for descriptive purposes, but if our aim is normative then the behaviouristic interpretation cannot be dispensed with.