The sensitivity of infinite sums to ordering seems to me to be fatal for the idea of attaching values to arbitrary infinite sums. People have tried in the context of attaching infinite utilities to paradoxical games like St. Petersburg, but they have never got very far. There are theorems about the impossibility of defining well-behaved preference relations over the set of all probability distributions over some space; for example.
The sensitivity of infinite sums to ordering seems to me to be fatal for the idea of attaching values to arbitrary infinite sums. People have tried in the context of attaching infinite utilities to paradoxical games like St. Petersburg, but they have never got very far. There are theorems about the impossibility of defining well-behaved preference relations over the set of all probability distributions over some space; for example.
Ord discusses St. Petersburg in the paper!