(Warning: completely obvious reasoning that I'm only posting because I haven't seen it spelled out anywhere.)
Some people say, expanding on an idea of de Finetti, that Bayesian rational agents should offer two-sided bets based on their beliefs. For example, if you think a coin is fair, you should be willing to offer anyone a 50/50 bet on heads (or tails) for a penny. Jack called it the "will-to-wager assumption" here and I don't know a better name.
In its simplest form the assumption is false, even for perfectly rational agents in a perfectly simple world. For example, I can give you my favorite fair coin so you can flip it and take a peek at the result. Then, even though I still believe the coin is fair, I'd be a fool to offer both sides of the wager to you, because you'd just take whichever side benefits you (since you've seen the result and I haven't). That objection is not just academic: using your sincere beliefs to bet money against better informed people is a bad idea in real world markets as well.
Then the question arises, how can we fix the assumption so it still says something sensible about rationality? I think the right fix should go something like this. If you flip a coin and peek at the result, then offer me a bet at 90:10 odds that the coin came up heads, I must either accept the bet or update toward believing that the coin indeed came up heads, with at least these odds. I don't get to keep my 50:50 beliefs about the coin and refuse the bet at the same time. More generally, a Bayesian rational agent offered a bet (by another agent who might have more information) must either accept the bet or update their beliefs so the bet becomes unprofitable. The old obligation about offering two-sided bets on all your beliefs is obsolete, use this one from now on. It should also come in handy in living room Bayesian scuffles, throwing some money on the table and saying "bet or update!" has a nice ring to it.
What do you think?
At the scale of living room bets, risk aversion is not a factor, because even a small amount of risk aversion around $100 stakes would imply crazy high risk aversion at larger stakes. It grows exponentially, see this post by Stuart. Most people use risk aversion (diminishing marginal utility of money) as an excuse for loss aversion which is straight up irrational.
As to your second objection, Bayesians don't believe in meta-uncertainty, their willingness to bet is represented by one number which is their uncertainty (a.k.a. their probability).
You're right about this strictly speaking, but liquidity constraints can result in the same practical outcome as risk aversion, and these are definitely relevant "on the margin". I could be willing to take a $10 - $500 bet in the abstract, but if that requires me to borrow the $500 should I lose (for an extra $300 cost, say), it's no longer rational for me to take that side of the bet! It would have to be a $10 - $200 bet or something, but obviously that creates a bid-ask spread w... (read more)