Facts, Values and Quanta

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.Comment: 30 pages, AMS Late

The Third Way on Objective Probability: A Skeptic's Guide to Objective Chance

The goal of this paper is to sketch and defend a new interpretation or theory of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The subtitle obviously emulates the title of Lewis seminal 1980 paper A Subjectivist s Guide to Objective Chance while indicating an important difference in perspective. The view developed below shares two major tenets with Lewis last (1994) account of objective chance: (1) The Principal Principle tells us most of what we know about objective chance; (2) Objective chances are not primitive modal facts, propensities, or powers, but rather facts entailed by the overall pattern of events and processes in the actual world. But it differs from Lewis’ account in most other respects. Another subtitle I considered was A Humean Guide ... But while the account of chance below is compatible with any stripe of Humeanism (Lewis , Hume s, and others ), it presupposes no general Humean philosophy. Only a skeptical attitude about probability itself is presupposed (as in point (2) above); what we should say about causality, laws, modality and so on is left a separate question. Still, I will label the account to be developed “Humean objective chance”

Humean Effective Strategies

In a now-classic paper, Nancy Cartwright argued that the Humean conception of causation as mere regular co-occurrence is too weak to make sense of our everyday and scientific practices. Specifically she claimed that in order to understand our reasoning about, and uses of, effective strategies, we need a metaphysically stronger notion of causation and causal laws than Humeanism allows. Cartwright’s arguments were formulated in the framework of probabilistic causation, and it is precisely in the domain of (objective) probabilities that I am interested in defending a form of Humeanism. In this paper I will unpack some examples of effective strategies and discuss how well they fit the framework of causal laws and criteria such as CC from Cartwright’s and others’ works on probabilistic causality. As part of this discussion, I will also consider the concept or concepts of objective probability presupposed in these works. I will argue that Cartwright’s notion of a nomological machine, or a mechanism as defined by Stuart Glennan, is better suited for making sense of effective strategies, and therefore that a metaphysically primitive notion of causal law (or singular causation, or capacity, as Cartwright argues in (1989)) is not – here, at least – needed. These conclusions, as well as the concept of objective probabilities I defend, are largely in harmony with claims Cartwright defends in The Dappled World. My discussion aims, thus, to bring out into the open how far Cartwright’s current views are from a radically anti-Humean, causal-fundamentalist picture

A Universal Scheme for Transforming Binary Algorithms to Generate Random Bits from Loaded Dice

In this paper, we present a universal scheme for transforming an arbitrary algorithm for biased 2-face coins to generate random bits from the general source of an m-sided die, hence enabling the application of existing algorithms to general sources. In addition, we study approaches of efficiently generating a prescribed number of random bits from an arbitrary biased coin. This contrasts with most existing works, which typically assume that the number of coin tosses is fixed, and they generate a variable number of random bits.Comment: 2 columns, 10 page

In Honor of Matthew Rabin: Winner of the John Bates Clark Medal

Although there is some evidence that Matthew Rabin existed before 1990, we had the pleasure of discovering him for ourselves when, in the early 1990s, he sent each of us a copy of his manuscript "Incorporating Fairness into Game Theory and Economics" [2]. Matthew was, at this time, an assistant professor in Berkeley's economics department, having recently finished his graduate training at MIT. The paper was remarkable in many ways, and it induced us both to call around and ask: "Who is this guy Rabin?" Now, just a decade later, we find ourselves writing an article in honor of his winning the John Bates Clark award. So, who is this guy

Teaching a University Course on the Mathematics of Gambling

Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article we objectively compare these books for their probability content, their gambling content, and their mathematical level, to see which ones might be most suitable, depending on student interests and abilities. This is not a book review (e.g., none of the books is recommended over others) but rather an essay offering advice about which topics to include in a course on the mathematics of gambling