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ARNOTT: I absolutely agree that the fair P/E ratio today is higher than the fair ratio of 40 or 80 years ago.
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The FsPF scheduler operates by applying the proportional fair principle to each RB at a time, and allocating each RB to the user who maximizes the fairness ratio.
Another assumption is that the agent's (fair) betting ratio for a proposition is independent of the truth value of this proposition.
On a slightly different account Sophia's subjective probability for A is measured by her fair betting ratio for A, i.e., that number r = b/(a + b) such that she considers the following bet to be fair: $a if A, and $-b otherwise (a, b ≥ 0 with inequality for at least one).
Note that it does not help to say that Sophia's fair betting ratio for A is that number r = b/(a + b) such that she considers the following bet to be fair: $1 − r = a/(a + b) if A, and $-r = -b/(a + b) otherwise (a, b ≥ 0 with inequality for at least one).
Its twofold thesis is that (fair) betting ratios should indeed obey the probability calculus, but that degrees of belief, being different from (fair) betting ratios, need not.
Fair pay ratios, investment in research and development and productive infrastructure is the future.
Sophia's subjective probabilities are measured by, but not identical to her (fair) betting ratios.
This uncovers one assumption of the measurement in terms of (fair) betting ratios: the ideal doxastic agent is assumed to be neither risk averse nor risk prone.
The version of the Dutch Book Theorem that licenses this inference says that an agent's fair betting ratios obey the probability calculus if and only if the agent never considers a Dutch Book as fair.
The idea is that whenever one is forced to bet on the pignistic level, the degrees of belief from the credal level are used to calculate (fair) betting ratios that satisfy the probability axioms.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com