As Wilkinson 1 points out, the objective probabilities
do not apply to the research hypotheses because these have no associated population to which an objective probability can be applied.
Kerr's most egregious error, however, is a different one: his assumption that the probable cause inquiry inherently involves an assessment of objective probabilities
Savage (1954)--building on that of von Neumann and Morgenstern (1944)--presented, to me among many others, a convincing axiomatic argument that, in acting under uncertainty, one should maximize expected utility using probability beliefs where objective probabilities
are not know.
It is a piece of well-received philosophical common sense that there is no room in a deterministic theory for objective probabilities
To the extent that the betting public acquire race-specific information to inform their assessment of the true chances of individual runners, the actual degree of bias will depart from this limiting case, and the proportions bet will approach more closely the distribution of objective probabilities
Most of the "critics" classical approach to probability of generating risk-generating events have turned against "objectivity": In tests conducted studies and also appeared many argue that is not a random phenomenon a phenomenon that can be measured using objective probabilities
The divergence between subjective and objective probabilities
can cause trouble.
These hypothesized qualities range from sensation-seeking personalities (Caldwell, 1974; Dickerson, Fabre, & Bayliss, 1986) to the possession of biases and heuristics leading to poor estimations of objective probabilities
(Kahneman & Tversky, 1972).
We can alter Equation (7) so that it is consistent with the contingent-claims approach by replacing objective probabilities
with risk-neutral probabilities, and by discounting the expected benefits on the left-hand side of the equation at the riskless rate.