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roystgnr comments on Risk aversion does not explain people's betting behaviours - Less Wrong
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What always gets me in experiments offering gambles is the implictly unquestioned assumption that it's rational for a subject to assume that the claimed odds of a bet are in fact the actual odds of the bet. That would certainly make the analysis much simpler, but a tempting simplification isn't necessarily an accurate one.
Just because we focus on the likely irrationality of Neville refusing to bet $50 at purportedly even odds against $55, and ignore the similar irrationality of an experimenter offering to bet $55 at even odds against $50, that doesn't mean Neville isn't updating his beliefs based on the experimenter's behavior. If Neville then stubbornly assigns expected probabilities other than .5 and .5 to the bet outcomes, must he be an irrational person who is doomed to forgo a bounty of cash from generous economics researchers, or might he be a rational person who is merely inducting properly from his prior observations of three-card monty tables and extended warranty offers?
When I read "Neville [...] will reject a single 50-50 deal where he gains $55 or loses $50" the first thing I do is ask myself: "Can I imagine myself rejecting a similar 50-50 deal?" Because if I can't imagine that, then the thought experiment can't possibly apply to the way I think about money.
In this case, though, I have no trouble imagining this. I have some reservations about $20000 being the cutoff, but I'm willing to accept that for now to see the math; also, I believe in geometric progressions, so I suspect the cutoff doesn't matter too much.
If hypothetical Neville refused the bet because he suspects it's rigged, that doesn't affect me. When I checked Neville's refusal against my own intuitions, I accepted the 50/50 odds as given. I suppose it's possible that I'm subconsciously being suspicious of the odds, and that is leading me to be risk averse. Is that what you're suggesting?
Subconscious suspicion is one possibility; evolution only cares about your behavior, not so much about how much introspection you did to get there.
It's certainly not the only possibility, though. Another example: Reduce the bet to 55 cents vs 50 cents and I'd imagine refusing it myself, for the obvious reason that the expected gain is grossly less than the transaction costs of stopping to think about the bet, look for possible "catches", flip the coin, and collect any winnings. There's probably other rational reasons to be "bet averse" that I haven't thought of, too.
If you remove the cutoff, then Neville will not accept 50-50 odds of losing $1500 or winning any amount of money.
What I meant is, I believe that there's a cutoff, but I'm not sure $20000 is the right value, for me. As I said, I don't think the value of the cutoff is terribly important.
Yes. I think I already mentioned that the real reason why I wouldn't take a 50% chance of winning $110 and 50% chance of losing $100 is that if someone is willing to offer such a bet to me, then they most likely know something about the coin to be flipped that I don't. If I was offered such a bet in a way extremely hard to cheat at (say, using random.org), I would happily take it -- but I don't expect anyone doing that, anyway.