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Theories of value can be bounded or unbounded. Bounded theories say that the total amount of expected value tends towards an upper limit. For example, if future people matter less than present people, then a discount rate could be applied to the happiness of future people, so that the total value of all future happiness is large but finite. Unbounded theories say that the amount of expected value has no upper limit. So if the universe might go on forever, then there might be no end to the amount of value that could be realized.

Unbounded theories create problems for us if our goal is to maximize expected value. If we have a non-zero credence that we can create an infinite amount of value, then it seems that this should dominate our decision-making. This is because an infinite amount of value multiplied by any finite credence will, in expectation, be infinite in value, making it better than any finitely-valued prospect.

Even bounded theories can have problems with large, finite sums of value that we have a low chance of bringing about. Cases could occur where we have a tiny chance of creating a huge but finite amount of value. If the finite amount of value is high enough, pursuing this action can have greater expected value than actions with a very high probability of producing a moderately large amount of value.

Further reading

Baumann, Peter. 2009. Counting on numbers. Analysis 69(3): 446–448.

Bostrom, Nick. 2009. Pascal's mugging. Analysis 69(3): 443-445.

Martin, Robert. 2013. The St. Petersburg paradox. In Edward Zalta (ed.), Stanford Encyclopedia of Philosophy.