The Necessary Uniformity of Physical Probability

ABSTRACT According to contemporary consensus, physical probabilities may be “non‐uniform”: they need not correspond to a uniform measure over the space of physically possible worlds. Against consensus, I argue that only uniform probabilities connect robustly to long‐run frequencies. Suppose, for example, that a uniform measure assigns a probability of x to a coin landing Heads on any given toss (independently of the outcomes on other tosses). Then, in almost all physically possible worlds containing many tosses, the frequency of Heads outcomes approximates x. Thus, if the physical probability of Heads is not x, the frequency deviates from this probability in almost all physically possible worlds. But this would undermine the robust connection between long‐run frequencies and physical probabilities. Conclusion: the uniform measure assigns the correct physical probability to Heads outcomes! This paper makes the argument rigorous and general, and evaluates its significance.