Dilating and contracting arbitrarily

Standard accuracy-based approaches to imprecise credences have the consequence that it is rational to move between precise and imprecise credences arbitrarily, without gaining any new evidence. Building on the Educated Guessing Framework of Horowitz (2019), we develop an alternative accuracy-based approach to imprecise credences that does not have this shortcoming. We argue that it is always irrational to move from a precise state to an imprecise state arbitrarily, however it can be rational to move from an imprecise state to a precise state arbitrarily

The shape of incomplete preferences

Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of state-dependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the state-independence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs.Comment: Published at http://dx.doi.org/10.1214/009053606000000740 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Cluelessness

Decisions, whether moral or prudential, should be guided at least in part by considerations of the consequences that would result from the various available actions. For any given action, however, the majority of its consequences are unpredictable at the time of decision. Many have worried that this leaves us, in some important sense, clueless. In this paper, I distinguish between ‘simple’ and ‘complex’ possible sources of cluelessness. In terms of this taxonomy, the majority of the existing literature on cluelessness focusses on the simple sources. I argue, contra James Lenman in particular, that these would-be sources of cluelessness are unproblematic, on the grounds that indifference-based reasoning is far less problematic than Lenman (along with many others) supposes. However, there does seem to be a genuine phenomenon of cluelessness associated with the ‘complex’ sources; here, indifference-based reasoning is inapplicable by anyone’s lights. This ‘complex problem of cluelessness’ is vivid and pressing, in particular, in the context of Effective Altruism. This motivates a more thorough examination of the precise nature of cluelessness, and the precise source of the associated phenomenology of discomfort in forced-choice situations. The latter parts of the paper make some initial explorations in those directions

Decision-Making with Belief Functions: a Review

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches

Imprecise Bayesianism and Global Belief Inertia

Traditional Bayesianism requires that an agent’s degrees of belief be represented by a real-valued, probabilistic credence function. However, in many cases it seems that our evidence is not rich enough to warrant such precision. In light of this, some have proposed that we instead represent an agent’s degrees of belief as a set of credence functions. This way, we can respect the evidence by requiring that the set, often called the agent’s credal state, includes all credence functions that are in some sense compatible with the evidence. 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 this article I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid it without compromising the initial evidentialist motivation. _1_ Introduction _2_ Precision and Its Problems _3_ Imprecise Bayesianism and Respecting Ambiguous Evidence _4_ Local Belief Inertia _5_ From Local to Global Belief Inertia _6_ Responding to Global Belief Inertia _7_ Conclusio

Are beliefs a matter of taste? A case for Objective Imprecise Information

We argue, in the spirit of some of Jean-Yves Jaffray's work, that explicitly incorporating the information, however imprecise, available to the decision maker is relevant, feasible, and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally that it is crucial when attempting to identify and measure the decision maker's attitude toward imprecise information.Decision under uncertainy;Objective Information;Belief Formation;Methodology of Decision Theory

Transformative experience and the knowledge norms for action: Moss on Paul’s challenge to decision theory

to appear in Lambert, E. and J. Schwenkler (eds.) Transformative Experience (OUP) L. A. Paul (2014, 2015) argues that the possibility of epistemically transformative experiences poses serious and novel problems for the orthodox theory of rational choice, namely, expected utility theory — I call her argument the Utility Ignorance Objection. In a pair of earlier papers, I responded to Paul’s challenge (Pettigrew 2015, 2016), and a number of other philosophers have responded in similar ways (Dougherty, et al. 2015, Harman 2015) — I call our argument the Fine-Graining Response. Paul has her own reply to this response, which we might call the Authenticity Reply. But Sarah Moss has recently offered an alternative reply to the Fine-Graining Response on Paul’s behalf (Moss 2017) — we’ll call it the No Knowledge Reply. This appeals to the knowledge norm of action, together with Moss’ novel and intriguing account of probabilistic knowledge. In this paper, I consider Moss’ reply and argue that it fails. I argue first that it fails as a reply made on Paul’s behalf, since it forces us to abandon many of the features of Paul’s challenge that make it distinctive and with which Paul herself is particularly concerned. Then I argue that it fails as a reply independent of its fidelity to Paul’s intentions

Are Beliefs a Matter of Taste ? A case for Objective Imprecise Information

We argue, in the spirit of some of Jean-Yves Jaffray's work, that explicitly incorporating the information, however imprecise, available to the decision marker is relevant, feasible and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally that it is crucial when attempting to identify and measure the decision maker's attitude toward imprecise information.Beliefs, imprecision, information.