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James_Miller comments on What makes buying insurance rational? - Less Wrong Discussion
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It can be rational because of diminishing marginal utility (happiness) of money. Imagine if I'm poor I get 100 units of pleasure from having an extra $10,000 whereas if I'm rich I get only 50 units of pleasure from having an extra $10,000. If I face some risk of becoming poor I would be willing to buy insurance that takes money from me in the state in which I'm rich and gives it to me in the state in which I'm poor even if on average I end up losing money, because on average I will end up gaining utility.