Nov 15 10 tweets 3 min read
yesterday i ran a poll with a coin flip trolley problem.

unfortunately, the clear majority answer leads to EVERYONE dying with 100% probability!!

what happened??

1/
2/

here's the poll. i took @ole_b_peters' excellent coin flip betting scenario and recast it as a trolley problem

it's an example of a problem where the expected value and the long-run average are NOT the same! this blew my mind when i first heard it

3/

the expected value calculation is simple

50% chance of gaining 50% (×150%)
50% chance of losing 40% (×60%)
→ 0.5×1.5 + 0.5×0.6 = 1.05

so on average, the expected GAIN is 5% per coin flip

so how can that possibly lead to LOSING 100% with 100% probability??
4/

to factor out the risk aversion, this follow-up poll flips the coin infinitely many times. that way, you DEFINITELY get the long run average, instead of having to worry about getting an unlucky run.

unfortunately, in the long run it always goes to 0

5/

consider what happens when you flip 1 heads and 1 tails.

you go up 50% but down 40%.
150% × 60% = 90%

so with an even number of heads and tails, you LOSE 10% every two rounds

ALL of the positive expected value comes from EXTREMELY rare streaks of many extra heads flips
6/

how rare?

well, exceptionally rare. exponentially rare. in the limit of infinite flips, so rare that the probability actually goes to zero.
7/

if you're uncomfortable with the infinity, then flip for "only" some reasonable finite time – say one flip per second for a week

you could reset and try that over & over for the life of the universe and never find a single positive week-long run
8/

if you have 20 minutes, you can watch this video where ole peters walks you through the problem step by step.

(it's intended for a general audience, so you don't need any crazy math prerequisites to watch it!)

9/9

hopefully this is a useful example for the discussion on "risk-neutral utilitarianism"

we often motivate bayes with "dutch book" arguments

this is kinda a dutch book for risk-neutral utilitarianism. you'd keep flipping the +EV coin forever, until everyone's dead :(
10/

wait i forgot the punchline!!!!

this is an example of a "non-ergodic" system: even as N→∞, individual runs DON'T converge to the expected value.

that is,,,,,

THE N'S DO NOT JUSTIFY THE MEANS

the end.

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# More from @prerationalist

Nov 15
REQUEST FOR EVERYONE

pls put a good URL or other backup contact in your bio today!!

then tomorrow we can all use @mechanical_monk's listfollowers.com to download a CSV of all our mutuals WITH good backup contact link!
previously we've done like "hey DM me if you wanna stay in touch if twitter crashes" but the problem is that requires everyone to message everyone which is a ton of work & i didn't do it

vs this strategy just requires everyone to do 1 thing once (update their bio)

O(N) vs O(N²)
i don't think twitter is in huge danger of crashing tbh

but this would be a nice CSV for us all to have years in the future, & now is a good schelling moment to put it together
Mar 24
*gestures surreptitiously*

hey

hey u

wanna see some rare impossible qualia
STYGIAN BLUE

it's blue, but it's as dark as black

"impossible" because how could a fully dark color have any saturation/color??
similarly, here you can see a red that's as bright as pure white

(again, look at the left for 20-60s, then switch over to the right)
Dec 30, 2021
How A Log Market Scoring Rule Works thread

i was gonna do this at some point, now seems like a good time

0/
if you're not familiar with prediction markets in general, see this quick reply thread i just did with an overview

a log market scoring rule implements the market part of a prediction market. it's great because it's automated & always liquid

1/
to quickly recap, the first piece of a prediction market is a "conditional ATM"

you put in regular money, and it prints out "conditional money"

e.g. for a single yes/no event, you can put in \$1 of regular money and get out both Y\$1 (worth \$1 if "yes") and N\$1 (worth \$1 if "no")
Dec 30, 2021
my favorite thing is when poasters end their feuds and become bros
inspired by @taalumot & @deepfates
Sep 21, 2021
intro to "bouncy numbers"! 🧵

(I have been wanting to explain this for a while, and I don't think my current explaining approach is perfect, but it's good to start with something!)

there's a punchline, but I'm gonna start by introducing "bouncy numbers" as their own thing

1/
a regular number sits on the number line and it sits still.

for example, here is the number 1.

(see, no bouncing!)
a "bouncy" number moves as if it were attached to an (ideal) spring.

here's a "bouncy" 1.

notice how it starts on the number line at 1, then swing over through 0 and eventually to -1, then swings back and starts over.
Sep 20, 2021
it's not about the note taking app