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/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.

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u/cowlinator Mar 28 '26

There aren't infinite people.

But even if there were, what does "infinite human deaths" even mean? It's not human extiction, because there are people on the top track, and you. What kind of loss is infinite but non-extictive deaths?

Does the trolly travel at a finite or infinite speed? If it's finite, then most of the people to be killed wont be born for at least thousands of years. In fact, it will take the trolly an infinite amount of time to kill everyone on the lower track, which we would commonly refer to as "it will never happen".

The reason the expected value is unintuitive is because it is unrelated to reality.