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by Eyal Roth Mar 26 2019

The Rule of Succession follows from assuming approximate ignorance about prior frequencies\. It does not, of itself, justify this assumption\. Variations of the rule of succession are obtainable by taking different priors, corresponding to different views of what should count as uninformative\. See discussion on the Wikipedia page on non\-informative priors\. For example if starting with the Jeffreys' prior, then after observing $~$M$~$ heads and $~$N$~$ tails, the expected probability of heads on the next coinflip is:

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