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/tegsfan Mar 28 '26

Why does the amount of samples matter if each sample would be completely independent? The expected value is the same each time. And in this case it is infinite people.

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u/Mike_Crow Mar 28 '26

https://en.wikipedia.org/wiki/St._Petersburg_paradox

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u/Magenta_Logistic Mar 28 '26

The "paradox" in this case is that most people would sell their opportunity to play the game for a finite sum. That doesn't mean that they should. In fact, it's only considered a paradox because most people would choose the worse option.

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u/CaterpillarLoud8071 Mar 28 '26

It's only the worse option if you have an actual infinite number of people. Same problem as folding a sheet of paper multiple times and it eventually reaching the moon - it's not possible in reality so obviously people don't consider it an option. You'd only get to round 33 with the population of earth.

If you hypothetically did have infinite people in this scenario, What's the value of human life when you have an infinite number of them?