One 50% bet is worse than fifty 1% bets?

[D H]

I disagree again: we can replace the human state of mind with a utility function that provides numbers to distinguish between these four scenarios.

And how do you obtain that utility function? The answer is of course by interviewing people to ascertain their state of mind. And making overly simplified assumptions. Expected utility theory is, at least per Rabin and Thaler (http://www.researchgate.net/profile/Richard_Thaler/publication/4902162_Anomalies_Risk_Aversion/links/09e4151030d3ce0fdf000000.pdf ), an ex-hypothesis. It is a Norwegian blue (they used exactly those words).

No, the expected value of the gamble is considerably more than the rock solid guarantee.

I agree, I used the wrong word. I should have said expected outcome rather than expected utility. A good portion of people will choose the rock solid guarantee even though the expected outcome of that option is considerably less than the expected outcome of the gamble. That's why I asked IDimension which option he/she would choose.

When it comes to gambling, there is nothing predictable about it.

Sure there is. I worked lots of jobs to get myself through college 35-40 years ago: Factory worker, farm hand, cook, pot washer, waiter, college tutor. None of those paid well (most paid minimum wage). My most lucrative job of all was tutoring the naive rich kids at the hoity-toity school I attended about how to play poker. Never big (those online poker games are downright scary); the winnings formed the bulk of my eating, drinking, and womanizing budget. Every once in a while this forced me for a week or two to be a teetotalling monk who sustained himself with cereal, ramen & noodles, and mac&cheese. But most of the time, college was quite nice. If you know the odds, if you know how to read people, and if you know how to hide from your opponents that you have a full boat (or alternatively, jack high), poker is anything but uncertain.

That was small potatoes compared to the legalized gambling I've been doing for the last 35 years. I have a nice little nest egg thanks to being a bit of a cheapskate and also thanks to being a bit risk taking and not having stuffed my hard-earned, cheapskate dollars into my mattress. It's very hard to save up enough for a decent retirement by stuffing your hard-earned savings in your mattress (or even into a bank account). One has to take some risks in life in the face of uncertain and imperfect information.

On an even grander scale, decision making under uncertainty is what makes modern society tick. Modern society would not be what it is were it not for the legalized gambling that goes on in Wall Street, in venture capital firms, in companies big and small that decide whether to bid on some contract, and in the huge number of mom-and-pop companies where the founder said "Forget this working for someone else. I'm going to start the business I've always wanted to run."

 

[pbuk]

And how do you obtain that utility function? The answer is of course by interviewing people to ascertain their state of mind. And making overly simplified assumptions.

That's not how I obtain my utility function for any given scenario, although there are necessarily some simplifications.

Expected utility theory is, at least per Rabin and Thaler (http://www.researchgate.net/profile/Richard_Thaler/publication/4902162_Anomalies_Risk_Aversion/links/09e4151030d3ce0fdf000000.pdf ), an ex-hypothesis.

I skimmed that paper. It seems to argue that because a particular naively constructed utility function leads to anomalies when applied over a large, possibly infinite, domain then there is no utility function that does not lead to anomalies over any domain. I reject this.