An Argument for Comparative Probability

We undertake to argue in favor of generalizing the formal concept of probability by replacing the usual quantitative formulation by the hitherto largely ignored comparative formulation. The theory of comparative probability (CP) is a theory of statements of the forms ‘event A is more probable than event B’, ‘events A, B are equally probable’, ‘event A is at least as probable as event B’, having the respective symbolic representations, ‘A > B’, ‘A ~ B’, ‘A ≳ B’. Comparative probability seems to have first been studied by Bernstein (1917), Keynes (1921), de Finetti (1931), and Koopman (1940). The modern era of CP studies perhaps dates from the work of Carnap (1950), Savage (1954), and Kraft et al. (1959). Relatively recent contributors include Scott (1964), Luce (1967, 1968), Fishburn (1970, 1975), Domotor (1969), Fine (1971a, b, 1973), Fine and Gill (1976), Fine and Kaplan (1976), Kaplan (1971, 1974), and Narins (1974).

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