If you use Bayesianism + CDT, and the coin has already landed: Yes, you never take the d20 bet.
Why CDT is well-motivated for Bayesianism by default: Because CDT motivates taking bets according to one’s subjective probabilities. Without CDT (or something close), non-Bayesian agents can choose to decline bets that would naively be good according to their subjective probabilities. This makes it harder to apply Dutch book arguments to them (to argue they should be Bayesian). See my recent post, “Simple Dutch books versus Sleeping Beauty halfers”.
As my post suggests, it is worth considering EDT+FNC as a quasi-Bayesian anthropic decision theory, as the main alternative to CDT+SIA. Here’s how EDT+FNC reasons on the d20:
“I have no information other than the problem setup; there is no FNC update to make so far. Evidentially on my choosing Heads, Omega has made it Tails, meaning I lose. Similarly, I lose evidentially on choosing Tails. Evidentially on the d20 bet, I’m not guaranteed to lose. Therefore I should pick the d20 bet.”
So they pick the d20 bet despite assigning at least 50% subjective probability to at least one of Heads and Tails.
I think one route towards finding alternatives to Bayesianism is to consider decision theories with Dutch book resistance and/or ex ante optimality, and think of what probabilities/beliefs go well with them.
I really appreciate this comment, because I must admit I was not even previously aware of FNC, and I think FNC+EDT solves my problem of completing the corresponding decision theory for my notion of beliefs.
I already was favorable to Halpern’s MWER as a decision rule, but MWER leaves the question, as well as (implicitly) the anthropic update question, open as free parameters. I think filling these in with FNC’s “simply add ” and EDT’s “simply add ” completes the picture in a way that might very well be satisfying to me.
Re: d20
If you use Bayesianism + CDT, and the coin has already landed: Yes, you never take the d20 bet.
Why CDT is well-motivated for Bayesianism by default: Because CDT motivates taking bets according to one’s subjective probabilities. Without CDT (or something close), non-Bayesian agents can choose to decline bets that would naively be good according to their subjective probabilities. This makes it harder to apply Dutch book arguments to them (to argue they should be Bayesian). See my recent post, “Simple Dutch books versus Sleeping Beauty halfers”.
As my post suggests, it is worth considering EDT+FNC as a quasi-Bayesian anthropic decision theory, as the main alternative to CDT+SIA. Here’s how EDT+FNC reasons on the d20:
“I have no information other than the problem setup; there is no FNC update to make so far. Evidentially on my choosing Heads, Omega has made it Tails, meaning I lose. Similarly, I lose evidentially on choosing Tails. Evidentially on the d20 bet, I’m not guaranteed to lose. Therefore I should pick the d20 bet.”
So they pick the d20 bet despite assigning at least 50% subjective probability to at least one of Heads and Tails.
Since FNC is not even Bayesian (dynamic inconsistency as pointed out by Stuart Armstrong), Bayesianism does not combine well with EDT. See Stuart Armstrong’s Anthropics: Full Non-indexical Conditioning (FNC) is inconsistent.
I think one route towards finding alternatives to Bayesianism is to consider decision theories with Dutch book resistance and/or ex ante optimality, and think of what probabilities/beliefs go well with them.
I really appreciate this comment, because I must admit I was not even previously aware of FNC, and I think FNC+EDT solves my problem of completing the corresponding decision theory for my notion of beliefs.
I already was favorable to Halpern’s MWER as a decision rule, but MWER leaves the