How ought you to evaluate your options if you're uncertain about what's fundamentally valuable? A prominent response is Expected Value Maximisation (EVM)—the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected value across axiologies. But the expected value of an option depends on quantitative probability and value facts, and in particular on value comparisons across axiologies. We need to explain what it is for such facts to hold. Also, EVM (...) is by no means self-evident. We need an argument to defend that it’s true. This book introduces an axiomatic approach to answer these worries. It provides an explication of what EVM means by use of representation theorems: intertheoretic comparisons can be understood in terms of facts about which options are better than which, and mutatis mutandis for intratheoretic comparisons and axiological probabilities. And it provides a systematic argument to the effect that EVM is true: the theory can be vindicated through simple axioms. The result is a formally cogent and philosophically compelling extension of standard decision theory, and original take on the problem of axiological or normative uncertainty. (shrink)

De Finetti's treatise on the theory of probability begins with the provocative statement PROBABILITY DOES NOT EXIST, meaning that probability does not exist in an objective sense. Rather, probability exists only subjectively within the minds of individuals. De Finetti defined subjective probabilities in terms of the rates at which individuals are willing to bet money on events, even though, in principle, such betting rates could depend on state-dependent marginal utility for money as well as on beliefs. Most later authors, from (...) Savage onward, have attempted to disentangle beliefs from values by introducing hypothetical bets whose payoffs are abstract consequences that are assumed to have state-independent utility. In this paper, I argue that de Finetti was right all along: PROBABILITY, considered as a numerical measure of pure belief uncontaminated by attitudes toward money, does not exist. Rather, what exist are de Finetti's `previsions', or betting rates for money, otherwise known in the literature as `risk neutral probabilities'. But the fact that previsions are not measures of pure belief turns out not to be problematic for statistical inference, decision analysis, or economic modeling. (shrink)

Following a long-standing philosophical tradition, impartiality is a distinctive and determining feature of moral judgments, especially in matters of distributive justice. This broad ethical tradition was revived in welfare economics by Vickrey, and above all, Harsanyi, under the form of the so-called Impartial Observer Theorem. The paper offers an analytical reconstruction of this argument and a step-wise philosophical critique of its premisses. It eventually provides a new formal version of the theorem based on subjective probability.

This note is a generalization and improved interpretation of the main result of Karni and Schmeidler. A decision-maker is supposed to possess a preference relation on acts and another preference relation on state-prize lotteries, both of which are assumed to satisfy the von Neumann–Morgenstern axioms. In addition, the two preference relations restricted to a state of nature are assumed to agree. We show that these axioms are necessary and sufficient for the existence of subjective expected utility over acts with state-dependent (...) utility functions and a subjective probability measure. This subjective probability measure is unique when conditioned on the set of states of nature in which not all the prizes are equally desirable. (shrink)

Decision theorists have attempted to accommodate several violations of decision theory’s axiomatic requirements by modifying how agents’ choice options are individuated and formally represented. In recent years, prominent authors have worried that these modifications threaten to trivialize decision theory, make the theory unfalsifiable, impose overdemanding requirements on decision theorists, and hamper decision theory’s internal coherence. In this paper, I draw on leading descriptive and normative works in contemporary decision theory to address these prominent concerns. In doing so, I articulate and (...) assess several different criteria for individuating and formally representing agents’ choice options. (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)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the evidence (...) calls for. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)