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private_messaging comments on Pascal's Muggle: Infinitesimal Priors and Strong Evidence - Less Wrong
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What you have is a divergent sum whose sign will depend to the order of summation, so maybe some sort of re-normalization can be applied to make it balance itself out in absence of evidence.
Actually, there is no order of summation in which the sum will converge, since the terms get arbitrary large. The theorem you are thinking of applies to conditionally convergent series, not all divergent series.
Strictly speaking, you don't always need the sums to converge. To choose between two actions you merely need the sign of difference between utilities of two actions, which you can represent with divergent sum. The issue is that it is not clear how to order such sum or if it's sign is even meaningful in any way.
Without discussing the merits of your proposal, this is something that clearly falls under "mathematical/epistemic/decision-theoretic reason to reject Pascal's Wager and Mugger", so I don't understand why you left that comment here.