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De Finetti's theorem without symmetries?

Bruno de Finetti (de Finetti (1970)) suggested that chance is objectified credence. The suggestion is explained and defended in Jeffrey (1983, ch.12), Skyrms (1980 ch.I), Skyrms (1984, ch.3), and Diaconis and Skyrms (2017, ch.7), but I still find it hard to understand. It seems to assume that rational credence functions are symmetrical in a way in which I think they shouldn't be.

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