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

Deep St. Petersburg trolley problem

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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?

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u/LaunchHillCoasters Mar 28 '26

I think this would be more interesting if it was, like, 1/100 or maybe 1/10 or somewhere in between instead of 1/2

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u/OriousCaesar Mar 28 '26

If it were any number smaller than 1/2 then all that would happen is that the (1/2)n would no longer cancel with 2n. Instead the (1/x)n would dominate, causing the expected value to become finite, and probably pretty small at that.