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Knightian Uncertainty: Bayesian Agents and the MMEU rule

My attempted condensation, in case it helps future generations (or in case somebody wants to set me straight): here's my understanding of the "pay $0.50 to win $1.10 if you correctly guess the next flip of a coin that's weighted either 40% or 60% Heads" game:

  • You, a traditional Bayesian, say, "My priors are 50/50 on which bias the coin has. So, I'm playing this single-player 'game':

    "I see that my highest-EV option is to play, betting on either H or T, doesn't matter."

  • Perry says, "I'm playing this zero-sum multi-player game, where my 'Knightian uncertainty' represents a layer in the decision tree where the Devil makes a decision:

    "By minimax, I see that my highest-EV option is to not play."

...and the difference between Perry and Caul seems purely philosophical: I think they always make the same decisions.

Seattle, WA – October 2021 ACX Meetup

I regret to report that I goofed the scheduling, and will be out of town, but @Orborde will be there to run the show! Sorry to miss you. Next time!

Book summary: Selfish Reasons to Have More Kids

you say that IVF costs $12k and surrogacy costs $100k, but also that surrogacy is only $20k more than IVF? That doesn't add up to me.

Ah, yes, this threw me too! I think @weft is right that (a) I wasn't accounting for multiple cycles of IVF being necessary, and (b) medical expenses etc. are part of the $100k surrogacy figure.

sperm/egg donation are usually you getting paid to give those things

Thanks for revealing that I wrote this ambiguously! The figures in the book are for receiving donated eggs/sperm. (Get inseminated for $355, get an egg implanted in you for $10k.)

Book summary: Selfish Reasons to Have More Kids

Ooh, you raise a good point, Caplan gives $12k as the per-cycle cost of IVF, which I failed to factor in. I will edit that in. Thank you for your data!

And you're right that medical expenses are part of the gap: the book says the "$100k" figure for surrogacy includes medical expenses (which you'd have to pay anyway) and "miscellaneous" (which... ???).

So, if we stick with the book's "$12k per cycle" figure, times an average of maybe 2 cycles, that gives $24k, which still leaves a $56k gap to be explained. Conceivably, medical expenses and "miscellaneous" could fill that gap? I'm sure you know better than I!

Everything in the OP matches my memory / my notes, within the level of noise I would expect from my memory / my notes.

Mildly against COVID risk budgets

That's a great point! My rough model is that I'll probably live 60 more years, and the last ~20 years will be ~50% degraded, so by 60 remaining life-years are only 50 QALYs. But... as you point out, on the other hand, my time might be worth more in 10 years, because I'll have more metis, or something. Hmm.

(Another factor: if your model is that awesome life-extension tech / friendly AI will come before the end of your natural life, then dying young is a tragedy, since it means you'll miss the Rapture; in which case, 1 micromort should perhaps be feared many times more than this simple model suggests. I... haven't figured out how to feel about this small-probability-of-astronomical-payoff sort of argument.)

Mildly against COVID risk budgets
  • Hmm! I think the main crux of our disagreement is over "how abstract is '1 hour of life expectancy'?": you view it as pretty abstract, and I view it as pretty concrete.

    The reason I view it as concrete is: I equate "1 hour of life expectancy" to "1 hour spent driving," since I mildly dislike driving. That makes it pretty concrete for me. So, if there's a party that I'm pretty excited about, how far would I be willing to drive in order to attend? 45 minutes each way, maybe? So "a party I'm pretty excited about" is worth about 3 micromorts to me.

    Does this... sound sane?

  • I'm in a house that budgets pretty aggressively, so, in practice, I budget, and maybe I'm wrong about how this would go; but, if I ditched budgeting entirely, and I was consistently bad at assessing tradeoffs, I would expect that I could look back after two weeks and say, "Whoa, I've taken on 50 life-hours of risk over the last two weeks, but I don't think I've gotten 50 hours of life-satisfaction-doubling joy or utility out of seeing people. Evidently, I have a strong bias towards taking more risk than I should. I'd better retrospect on what I've been taking risk doing, and figure out what activities I'm overvaluing."

    Or maybe I'm overestimating my own rationality!

Mildly against COVID risk budgets

Pedantry appreciated; you are quite right!

Mildly against COVID risk budgets

Thanks for the thoughtful counterargument!

Things I think we agree on:

  • you should really be deciding policies rather than initial purchase choices

    Yes, absolutely, strong agreement.

  • "Deciding how to accumulate COVID risk" closely resembles "deciding how to spend a small fraction of your money," but not "deciding how to spend a large fraction of your money": when money is tight, the territory contains a threshold that's costly to go over, so your decision-making process should also contain a threshold that shouldn't be gone over, i.e. a budget; but there is no such nonlinearity when accumulating (normal amounts of) COVID risk, or when spending a small fraction of your money.

  • In principle the right way to make my choice [of what to buy] is to figure out what utility I'll get from each possibility, figure out what utility I'll get from having any given amount more savings, and choose whatever maximizes the total... A common solution is to first pick some amount of money that seems reasonable... And then to go shopping and be guided by that budget.

Actually, I'm not sure I disagree with any of your explicit claims. The only claim I think we might disagree on is something like "budgeting is a good strategy even when costs/benefits add pretty much linearly," as in the 'spend a small fraction of your money' or 'accumulate COVID risk' scenarios: I perceive you as agreeing with that statement, whereas I disagree with it (because it encourages you to think in terms of "whether I'll exceed my budget" instead of the ground truth).

If you do endorse that bolded statement, I'm curious why. I read your comment as explaining why people do budget in low-stakes scenarios, but not why that's optimal. (My best guess at your answer, reading between the lines, is "because it saves a lot of error-prone calculation," which, hmm, doesn't speak to me personally, but people differ, and maybe I overestimate my own ability to do good cost/benefit calculations.)

(Don't get me wrong, I do sometimes do something that looks like budgeting, as you describe, when I'm spending small amounts of money; but I view it as a bad habit that I want to break myself of -- with a proper eye towards TDT, though, of course.)

Mildly against COVID risk budgets

Fantastic. Thanks so much for that link -- I found that whole thread very enlightening.

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