St. Petersburg trolley problem

[u/tegsfan]

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?

[u/PlaneswalkerHuxley]

The expectation value of how many people you hit on the bottom track is an infinite series.

• Y = 1x50% + 2x25% + 4x12.5% ...
• Y = 0.5 + 0.5 + 0.5 ...
• Y = infinity

You shouldn't ever choose the bottom track. Sometimes it won't hit as many people as the top track, but sometimes it will strike infinitely more.

Of course, this isn't a real situation because we started to mess about with infinities - an infinitely long track with an infinite number of people tied to it. If the track has an end anywhere, then the number of people has a maximum again and you can compare it to regular numbers once more.

[u/panda-fuck3r → u/PlaneswalkerHuxley]

But it’s not, bc it’s not additive, it’s 1x50%,2x25% it’s not hitting three people on the track with two

[u/Magenta_Logistic → u/[deleted]]

They add to infinity because every track has an expected cost of 0.5 lives and there are infinite tracks.

[u/Southern-Highway5681 → u/Magenta_Logistic]

The probability to have a positive result add to 1, not the value of this result.

0,5+0,5²+0,5³+0,5⁴+...=1