It would have served Sam Bankman-Fried to separate utility from dollars.
I was given How Not to Be Wrong for Christmas and am enjoying it so far.
I've watched plenty of Numberphile and Veritasium and have read Stephen Pinker's
similar book, Rationality, yet it introduces many topics I haven't come
across before. One of which is
St. Petersburg paradox:
I put $2 in a pot then flip a coin
If tails, the game ends and you win the money. If heads, I double the
money
I flip the coin again. Repeat step 2
Clearly you should want to play this game, as you win no matter what. The
question is, how much should you be willing to stake for the opportunity to
play? $10? $20? If you do the math you'll find that the expected value (EV) of
this game is infinite — the series diverges. Therefore in theory you should be
willing to stake any finite amount to play the game. This feels wrong. I
wouldn't stake my entire net worth, let alone one paycheck to play. The
mathematics is sound, so the paradox is of human behavior. Perhaps humans
underestimate small probabilities (I've never seen a coin land 10 heads in a
row) or perhaps the question is nonsense (no house could ever fund the other
side of the bet).
The traditional solution is to say the premise of the EV
calculation is wrong: the player should calculate the EV of their utility not of
the raw dollar amount. Further, their utility should be the logarithm of the
dollar amount. I had never heard of doing such a thing: every example in school,
every analysis of a casino/board game, every quant interview question
calculates EV directly with dollars. However, on consideration, it doesn't seem
outlandish. To rappers, money is logarithmic; lines are as often about figures
as they are absolute dollars. Further, for most millionaires it would hurt more
to go broke than it would feel good making another million. With this conception
of utility, the expected value is no longer infinite.
How does this relate to SBF? In Sam's appearance on Conversations with
Tyler, he was posed a similar question: if you could push a button with a
51% chance of doubling the number of sentient beings in the universe (e.g.,
double the number of earths) and a 49% chance of killing all living beings,
would you press it? He answered that he would press it repeatedly. Most
commentators flawed Sam for lacking empathy or being hyper-rational in his
answer. From what I know from Going Infinite the former is fair. But I
don't think the latter is. If Sam calculated his EV using the logarithm of the
number of living beings (which I'm starting to think is correct), he wouldn't
have arrived at the same conclusion and his answer would have been more
wonky/"hyper-rational".
Taking this a step further, could solve some of the problems/paradoxes that
arise with longtermist utilitarian ideas. If you're not familiar, some people
argue that we should not (or should only barely) discount the utility of future
sentient being's lives with time. Therefore since there could be many more
living people in the future we should prioritize protecting the future above all
else. Therefore, even if you choose not to discount with time, you could still
avoid some of the problems with expected values and infinity if you consider
utility to be the logarithm of the number of beings. Surprisingly, in all I've
read about utilitarian philosophy I've never heard this idea, though I'm sure
I'm not the first.
For another time, but you could obviously extend this to SBF's Alameda Research.
I'm curious to what extent, if at all, hedge funds separate EV/utility from
dollars.