There is a small remark in Rational Choice in an Uncertain World: The Psychology of Judgment and Decision Making about insurance saying that all insurance has negative expected utility, we pay too high a price for too little a risk, otherwise insurance companies would go bankrupt.
No—Insurance has negative expected monetary return, which is not the same as expected utility. If your utility function obeys the law of diminishing marginal utility, then it also obeys the law of increasing marginal disutility. So, for example, losing 10x will be more than ten times as bad as losing x. (Just as gaining 10x is less than ten times as good as gaining x.)
Therefore, on your utility curve, a guaranteed loss of x can be better than a 1/1000 chance of losing 1000x.
ETA: If it helps, look at a logarithmic curve and treat it as your utility as a function of some quantity. Such a curve obeys diminishing marginal utility. At any given point, your utility increases less than proportionally going up, but more than proportionally going down.
(Incidentally, I acutally wrote an embarrasing article arguing in favor of the thesis roland presents, and you can still probably find on it the internet. That exchange is also an example of someone being bad at explaining. If my opponent had simply stated the equivalence between DMU and IMD, I would have understood why that argument about insurance is wrong. Instead, he just resorted to lots of examples of when people buy insurance that are totally unconvincing if you accept the quoted argument.)
I voted this up, but I want to comment to point out that this is a really important point. Don’t be tricked into not getting insurance just because it has a negative expected monetary value.
I voted Silas up as well because it’s an important point but it shouldn’t be taken as a general reason to buy as much insurance as possible (I doubt Silas intended it that way either). Jonathan_Graehl’s point that you should self-insure if you can afford to and only take insurance for risks you cannot afford to self-insure is probably the right balance.
Personally I don’t directly pay for any insurance. I live in Canada (universal health coverage) and have extended health insurance through work (much to my dismay I cannot decline it in favor of cash) which means I have far more health insurance than I would purchase with my own money. Given my aversion to paperwork I don’t even fully use what I have. I do not own a house or a car which are the other two areas arguably worth insuring. I don’t have dependents so have no need for life or disability coverage. All other forms of insurance fall into the ‘self-insure’ category for me given my relatively low risk aversion.
No—Insurance has negative expected monetary return, which is not the same as expected utility. If your utility function obeys the law of diminishing marginal utility, then it also obeys the law of increasing marginal disutility. So, for example, losing 10x will be more than ten times as bad as losing x. (Just as gaining 10x is less than ten times as good as gaining x.)
Therefore, on your utility curve, a guaranteed loss of x can be better than a 1/1000 chance of losing 1000x.
ETA: If it helps, look at a logarithmic curve and treat it as your utility as a function of some quantity. Such a curve obeys diminishing marginal utility. At any given point, your utility increases less than proportionally going up, but more than proportionally going down.
(Incidentally, I acutally wrote an embarrasing article arguing in favor of the thesis roland presents, and you can still probably find on it the internet. That exchange is also an example of someone being bad at explaining. If my opponent had simply stated the equivalence between DMU and IMD, I would have understood why that argument about insurance is wrong. Instead, he just resorted to lots of examples of when people buy insurance that are totally unconvincing if you accept the quoted argument.)
I voted this up, but I want to comment to point out that this is a really important point. Don’t be tricked into not getting insurance just because it has a negative expected monetary value.
I voted Silas up as well because it’s an important point but it shouldn’t be taken as a general reason to buy as much insurance as possible (I doubt Silas intended it that way either). Jonathan_Graehl’s point that you should self-insure if you can afford to and only take insurance for risks you cannot afford to self-insure is probably the right balance.
Personally I don’t directly pay for any insurance. I live in Canada (universal health coverage) and have extended health insurance through work (much to my dismay I cannot decline it in favor of cash) which means I have far more health insurance than I would purchase with my own money. Given my aversion to paperwork I don’t even fully use what I have. I do not own a house or a car which are the other two areas arguably worth insuring. I don’t have dependents so have no need for life or disability coverage. All other forms of insurance fall into the ‘self-insure’ category for me given my relatively low risk aversion.