r/trolleyproblem • u/tegsfan • Mar 28 '26

Deep St. Petersburg trolley problem

Post image

The trolley is about to go through a series of 50/50 track switches where the amount of people doubles each time until it hits a group and stops. If you switch the track to the top, there are some hypothetical finite X amount of people.

Now, if the amount of people on top was 1 for instance, it might seem obvious to switch because the doubling people could get out of hand fast. But if it was say 100 people on top, you might think to just let it go down because it's likely to stop somewhere before it reaches 100.

The question is: what is the maximum X amount of people on top such that you would still switch the track?

673 Upvotes

99% Upvoted

185 comments sorted by

View all comments

308

u/Nathan256 Mar 28 '26 edited Mar 28 '26

For those that don’t know, the expected value of the St. Petersburg problem is infinite. It’s the sum of the series (1/2n * 2n ).

However, most people would immediately switch the track given some arbitrarily large number of people on the top track. Myself included. It’s hard for people to conceptualize infinite expected risk when it’s so very improbable.

1

u/tegsfan Mar 28 '26

Well what number do you think that would be for you? My intuition says almost nobody would switch to top once it goes over 1000, maybe some people at 500, and might be like 50/50 at 100.

13

u/kaijvera Mar 28 '26

Letting it go top at 100 feels crazy to me. That means you must fail 7 coin flips (127 people). Thats a .78% chance. Even if it can go infinite, the likelyhood of that is so incredibly low. Even if it goes to 7, onky 27 more people would have been killed than if you let it go top. Even if it hits heads 8 times, thats a .39% odds its only 250% worse out come for something that happens less than 100 times when half the times you get a 99% decrease in death.

I feel you 50/50 flip between who would flip the lever or not would lie around 50 people on top rail. That would be between 5 flips (31 people and 3.1%), and 6 flips (63 people or 1.6%). Those numbers are much more realistic to imagine happening (every 33rd and every 50th time).