Calibration of Subjective Probability Judgments in a Naturalistic Setting

Results of previous calibration studies are used to identify features of the decision maker and the decision environment which might be expected to result in good calibration. Racetrack bettors and, in particular, the UK parimutuel betting market are identified as possessing such characteristics. In order to explore calibration in this setting, an analysis is undertaken of bets placed on 19,396 horses. A close correlation is observed between the subjective probability judgments of horses' success, implicit in the bettors' wagering activities, and the objective probability of success of the horses concerned. Explanations for the results are offered in terms of characteristics of racetrack bettors and the naturalistic setting, with particular reference to the operation of the betting market. The results contribute to an emergent school of thought which advocates naturalistic enquiry as a complement to laboratory-based experiments in further developing the understanding of decision making.     

Bets and Boundaries: Assigning Probabilities to Imprecisely Specified Events

Uncertainty and vagueness/imprecision are not the same: one can be certain about events described using vague predicates and about imprecisely specified events, just as one can be uncertain about precisely specified events. Exactly because of this, a question arises about how one ought to assign probabilities to imprecisely specified events in the case when no possible available evidence will eradicate the imprecision (because, say, of the limits of accuracy of a measuring device). Modelling imprecision by rough sets over an approximation space presents an especially tractable case to help get one’s bearings. Two solutions present themselves: the first takes as upper and lower probabilities of the event X the (exact) probabilities assigned X’s upper and lower rough-set approximations; the second, motivated both by formal considerations and by a simple betting argument, is to treat X’s rough-set approximation as a conditional event and assign to it a point-valued (conditional) probability. With rough sets over an approximation space we get a lot of good behaviour. For example, in the first construction mentioned the lower probabilities are n-monotone, for every . When we examine other models of approximation/imprecision/vagueness, and in particular, proximity spaces, we lose a lot of that good behaviour. In the literature there is not (even) agreement on the definition of upper and lower approximations for events (subsets) in the underlying domain. Betting considerations suggest one choice and, again, ways to assign upper and lower and point-valued probabilities, but nothing works well. Special Issue on Vagueness Edited by Rosanna Keefe and Libor Bêhounek     

Do Bettors Correctly Perceive Odds? Three Studies of How Bettors Interpret Betting Odds as Probabilistic Information

This paper reports on three studies investigating how accurately bettors (=people who regularly bet on sports events) interpret the probabilistic information implied by betting odds. All studies were based on data collected by web surveys prompting a total of 186 experienced bettors to convert sets of representative odds into frequency judgments. Bayesian statistical methods were used to analyze the data. From the results, the following conclusions were made: (i) On the whole, the bettors produced well‐calibrated judgments, indicating that they have realistic perceptions of odds. (ii) Bettors were unable to consciously adjust judgments for different margins. (iii) Although their interval judgments often covered the estimates implied by the odds, the bettors tended to overestimate the variation of expected profitable bets between months. The results are consistent with prior research showing that people tend to make accurate probability judgments when faced with tasks characterized by constant and clear feedback. Copyright © 2015 John Wiley & Sons, Ltd.     

The Value of Knowledge/Rationality or the Knowledge/Rationality of Value?: Implications for Education

This paper reviews and augments important work in philosophy of education on intrinsic aims for education, of knowledge, of knowledge of values, and of rationality. A contemporary conception of knowledge as ``rationality's `data-base' is proposed and an in-depth section on the intrinsic value of rationality is incorporated.     

What Are Degrees of Belief?

Probabilism is committed to two theses:

Free Will, Moral Responsibility, and the Problem of “OOMPH”

Thomas Reid developed an important theory of freedom and moral responsibility resting on the concept of agent-causation, by which he meant the power of a rational agent to cause or not cause a volition resulting in an action. He held that this power is limited in that occasions occur when one's emotions or other forces may preclude its exercise. John Martin Fischer has raised an objection – the not enough ‘Oomph’ objection – against any incompatibilist account of freedom and moral responsibility. In this essay I argue that Fischer's not enough ‘Oomph’ objection fails to provide any reasons for rejecting Reid's incompatibilist, agent-causation account of freedom and moral responsibility.     

Politics for Learning or Learning for Politics?

It is argued that political democracyand citizenship should not be taken as primarygoals within university education. Instead theauthor argues for a notion of ``academicdemocracy' with the overall goal or ethos oflearning together. Moreover it is argued that``learning' then should be understood accordingto ``practical traditions of knowledge', whichmeans that truth is not the ultimate goal. Theultimate goal is practices that lead to thegood of men and women.