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Say there is this hypothetical lottery. A ticket is USD 1.00; the chance of winning is 1 in 100,000,000,000,000,000; but the prize is more than USD 100,000,000,000,000,000. (For he sake of this argument, please ignore things such as “there is no such amount of money in this world,” etc.) Mathematically, I should buy a ticket; on the other hand, any rational person would know that is an awfully-wasted one dollar. What field of statistics, probability, or science, deals with such things?

(First I thought it could be Subjective Probability, but I think not.)

blackened
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The concept you are looking for is "utility function" which is a common concept in probability theory/mathematical economy/actuarial sciences. The probability is not subjective, but the utility of the outcome is. In probability theory the utility function is tacitly ignored since probability theory is about objective probabilities, not about what decision should one make based on any particular probability (though some texts do mention it). In mathematical economy and actuarial sciences the concept of utility function is fundamental. For instance, the whole basis of insurance is that most people are risk-evasive, which is modeled mathematically by having a concave utility function.

Ittay Weiss
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  • Thanks. Is there a (not too technical) textbook specifically on this topic? – blackened Oct 03 '14 at 10:58
  • There are plenty of books on mathematical economy/actuarial sciences. Actuarial sciences is probably more likely to be less technical than mathematical economy. – Ittay Weiss Oct 03 '14 at 10:59