Expected Utilities of Lotteries

[Torie]

It is all about the marginal utility of money. Most people would ascribe a much higher marginal utility to the first one million, then to subsequent millions, but the odds here are so extreme, and the expected cost of risk reduction so high, ie the expected return from taking more risk so high, that even given our marginal utility curve, most would still prefer to take more risk for more money here.

The posited paradox (which is not really a paradox, just that the marginal utility of money is not linear), is about folks willing to take more risk if the chances of landing a substantial amount of money are small anyway, as opposed to being in the bag, so in that sense if you lose, the odds are with the second bet that you would have ended up with nothing anyway whichever bet you picked, while in the first the odds of getting a substantial amount of money taking the safer bet were 100%.  Most of us would fall for the paradox if the numbers were considerably less extreme, because if the sum of money is large enough, it would take a very high rate of return indeed for us being willing to risk losing it all. That is why we buy insurance, which has a negative expected rate of return (administrative costs have to be paid for), but we still consider it worth it.

[Torie]

What do you call the thingy then, when it is far more painful to your when you net worth drops from 1 million to zero, than from 2 million to 1 million, if not something that involves the word "utility."  The balance of your post I did not understand very well, and I think my insurance analogy is apt. One pays something to avoid a catastrophic loss, and giving up a bunch of money if one gets lucky to secure avoiding a  catastrophic loss, is what drives the need for insurance.

Sometimes, intuitive common sense cuts to the chase better than complex formulas, in my experience. I am reasonably confident I have this one right, but perhaps not.

[Torie]

I will ponder that comment. I still think I am right and you are wrong, but I need to put my lawyer hat on to try to tackle it all, and well, I don't "work" on Sundays. And if you are right, I will have learned something, so it is a win win for me either way, since this is an issue that really interests me, the risk and reward thing. It is what drives my important choices in life. Thanks Ag.

[Torie]

I understand the expected return thing, but my point is that risking a sure thing, is different than risking something that is a long shot anyway. That is entirely sensible. That indeed is the way most of us run our lives really, who are rational when it comes to money matters.