Papers on Games, Decisions, and Probability

Why Ain’t Evidentialists Rich?

A common argument for favouring Evidential Decision Theory (EDT) over Causal Decision Theory (CDT) is that EDT has predictably higher expected returns in Newcomb Problems. But this doesn’t show much. For almost any pair of theories you can come up with cases where one does, on average, better than the other. Here I describe a case involving dynamic choice where EDT predictably does worse than CDT. (This paper is forthcoming in Analysis.)

Brian Weatherson

The Sporting Attitude

Contribution to a symposium on Steffen Borge’s “The Philosophy of Football”.

Brian Weatherson

Accuracy and the Imps

Recently several authors have argued that accuracy-first epistemology ends up licensing problematic epistemic bribes. They charge that it is better, given the accuracy-first approach, to deliberately form one false belief if this will lead to forming many other true beliefs. We argue that this is not a consequence of the accuracy-first view. If one forms one false belief and a number of other true beliefs, then one is committed to many other false propositions, e.g., the conjunction of that false belief with any of the true beliefs. Once we properly account for all the falsehoods that are adopted by the person who takes the bribe, it turns out that the bribe does not increase accuracy.

James M. Joyce, Brian Weatherson

Interests, Evidence and Games

Pragmatic encroachment theories have a problem with evidence. On the one hand, the arguments that knowledge is interest-relative look like they will generalise to show that evidence too is interest-relative. On the other hand, our best story of how interests affect knowledge presupposes an interest-invariant notion of evidence. The aim of this paper is to sketch a theory of evidence that is interest-relative, but which allows that ‘best story’ to go through with minimal changes. The core idea is that the evidence someone has is just what evidence a radical interpreter says they have. And a radical interpreter is playing a kind of game with the person they are interpreting. The cases that pose problems for pragmatic encroachment theorists generate fascinating games between the interpreter and the interpretee. They are games with multiple equilibria. To resolve them we need to detour into the theory of equilibrium selection. I’ll argue that the theory we need is the theory of risk-dominant equilibria. That theory will tell us how the interpreter will play the game, which in turn will tell us what evidence the person has. The evidence will be interest-relative, because what the equilibrium of the game is will be interest-relative. But it will not undermine the story we tell about how interests usually affect knowledge.

Brian Weatherson

For Bayesians, Rational Modesty Requires Imprecision

Gordon Belot has recently developed a novel argument against Bayesianism. He shows that there is an interesting class of problems that, intuitively, no rational belief forming method is likely to get right. But a Bayesian agent’s credence, before the problem starts, that she will get the problem right has to be 1. This is an implausible kind of immodesty on the part of Bayesians. My aim is to show that while this is a good argument against traditional, precise Bayesians, the argument doesn’t neatly extend to imprecise Bayesians. As such, Belot’s argument is a reason to prefer imprecise Bayesianism to precise Bayesianism.

Brian Weatherson

Games, Beliefs and Credences

In previous work I’ve defended an interest-relative theory of belief. This paper continues the defence. I have four aims. First, to offer a new kind of reason for being unsatisfied with the simple Lockean reduction of belief to credence. Second, to defend the legitimacy of appealing to credences in a theory of belief. Third, to illustrate the importance of theoretical, as well as practical, interests in an interest-relative account of belief. And finally, to have another try at extending my basic account of belief to cover propositions that are practically and theoretically irrelevant to the agent.

Brian Weatherson

Memory, Belief and Time

I argue that what evidence an agent has does not supervene on how she currently is. Agents do not always have to infer what the past was like from how things currently seem; sometimes the facts about the past are retained pieces of evidence that can be the start of reasoning. The main argument is a variant on Frank Arntzenius’s Shangri La example, an example that is often used to motivate the thought that evidence does supervene on current features.

Brian Weatherson

Running Risks Morally

I defend normative externalism from the objection that it cannot account for the wrongfulness of moral recklessness. The defence is fairly simple—there is no wrong of moral recklessness. There is an intuitive argument by analogy that there should be a wrong of moral recklessness, and the bulk of the paper consists of a response to this analogy. A central part of my response is that if people were motivated to avoid moral recklessness, they would have to have an unpleasant sort of motivation, what Michael Smith calls “moral fetishism”.

Brian Weatherson

Ross on Sleeping Beauty

In two excellent recent papers, Jacob Ross has argued that the standard arguments for the ‘thirder’ answer to the Sleeping Beauty puzzle lead to violations of countable additivity. The problem is that most arguments for that answer generalise in awkward ways when he looks at the whole class of what he calls Sleeping Beauty problems. In this note I develop a new argument for the thirder answer that doesn’t generalise in this way.

Brian Weatherson

Knowledge, Bets and Interests

This paper argues that the interest-relativity of knowledge cannot be explained by the interest-relativity of belief. The discussion starts with an argument that knowledge plays a key pair of roles in decision theory. It is then argued that knowledge cannot play that role unless knowledge is interest-relative. The theory of the interest-relativity of belief is reviewed and revised. That theory can explain some of the cases that are used to suggest knowledge is interest-relative. But it can’t explain some cases involving ignorance, or mistake, about the odds at which a bet is offered. The paper ends with an argument that these cases require positing interest-relative defeaters, which affect whether an agent knows something without affecting whether she believes it, or is justified in believing it.

Brian Weatherson

Stalnaker on Sleeping Beauty

A contribution to a book symposium on Stalnaker’s Our Knowledge of the Internal World, focussing on the way his framework helps cast new light on the Sleeping Beauty problem.

Brian Weatherson

What Good are Counterexamples?

Intuitively, Gettier cases are instances of justified true beliefs that are not cases of knowledge. Should we therefore conclude that knowledge is not justified true belief? Only if we have reason to trust intuition here. But intuitions are unreliable in a wide range of cases. And it can be argued that the Gettier intuitions have a greater resemblance to unreliable intuitions than to reliable intuitions. What’s distinctive about the faulty intuitions, I argue, is that respecting them would mean abandoning a simple, systematic and largely successful theory in favour of a complicated, disjunctive and idiosyncratic theory. So maybe respecting the Gettier intuitions was the wrong reaction, we should instead have been explaining why we are all so easily misled by these kinds of cases.

Brian Weatherson

From Classical to Intuitionistic Probability

We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of “essentially Kolmogorovian” probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism – in which the probability functions are taken relative to intuitionistic logic – rather than by adopting a radically non-Kolmogorovian, e.g. non-additive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response amongst those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability…

Brian Weatherson

Begging the Question and Bayesians

In a recent article Patrick Maher shows that the ‘depragmatised’ form of Dutch Book arguments for Bayesianism tend to beg the question against their most interesting anti-Bayesian opponents. I argue that the same criticism can be levelled at Maher’s own argument for Bayesianism.

Brian Weatherson

Keynes, Uncertainty and Interest Rates

Uncertainty plays an important role in The General Theory, particularly in the theory of interest rates. Keynes did not provide a theory of uncertainty, but he did make some enlightening remarks about the direction he thought such a theory should take. I argue that some modern innovations in the theory of probability allow us to build a theory which captures these Keynesian insights. If this is the right theory, however, uncertainty cannot carry its weight in Keynes’s arguments. This does not mean that the conclusions of these arguments are necessarily mistaken; in their best formulation they may succeed with merely an appeal to risk.

Brian Weatherson