I'm content to admit I honestly don't know what I would do if a ridiculously contrived situation like this ever came up, and leave it at that until one actually does.
Vsauce: "Hold my lever*
Where does Monty Hall fit into all of this?
After making your choice, if Monty offers to throw away whichever of the remaining two he knows isn't the winner and trade you the other one, always do it.
On second thought I would say do nothing, because you didn't create this situation and don't even know if it's sincere. The trolley might be set to break down no matter what you do. Or possibly everybody tied to the track is an actor. Or the whole thing is wired to explode and kill everyone. Taking any action at all is cooperating with whoever set the whole thing up, thereby making you their accomplice.
He's the middle guy on the 5 person track.
See if I can't get dad's Parkinsons to pay off
Got it. You shout to the five people and ask them if you should pull it. It's likely at least one of the five will want you to take the chance, which means he accepted the risk, which means you no longer have to count his death as an adverse outcome. Now the odds are even and you can safely pull the lever.
And if more than one of them says to pull it, then the odds are clearly in favor of pulling the lever.
wat? The guy's death is an adverse outcome no matter what risk he accepts.
Gambling addict: how many times can I pull it before the trolly gets to the split?
As many have mentioned, the expected number of deaths is 1 for no action and 1.25 if you pull the lever. Many still choose to pull the lever despite the expected number being higher. As I understand it, the reasoning is that the value of reach outcome doesn't scale linearly with the number of people alive/dead. Going from 0 deaths to 1 death is a much larger drop in value than going from 1 death to 2.
Something something one death is a tragedy, a million deaths is a statistic.
1.00 • 1 death = 1 death Vs. 0.25 • 5 deaths = 1.25 deaths
On average you're better off not pulling the lever.
Look at it selfishly:
Pulling the level is the only way to have a shot at not being saddled with the guilt of killing someone. Sure, killing 5 people is worse than killing 1, but avoiding that personal impact entirely is a desirable goal in and of itself.
This was my thought too, initially, but then I remembered that the first possibility happens through inaction. So I guess it depends on whether or not the person sees that as them killing someone
I can't say what is objectively true, but I can say that if I were in that situation, I absolutely would feel responsible for the outcome if I could have reasonably affected it.
Implying you'll be running this multiple times?
The number of attempts is not mathematically affecting the outcome of a single attempts - statistics don't "owe you" any specific outcomes, just based on previous outcomes. It will be the same formula for each
Statistics also won't help you with the guilt when the tram runs over 5 people and now it's just you and the one guy you saved now trauma bonded.
I'm not the idiot who tues people to train tracks. I won't be feeling much guilt
What if, by taking some seemingly benign action, followed by a series of unforeseeable events, you have caused the people to be on the train tracks?
Actually, in this case, unless they are... refilling... the hostages each run, the results of previous runs do affect each additional run. Unless you feel that running someone over the second time kills them a second time.
A true degenerate would pull the lever, hit no one, and immediately pull the lever again yelling ‘double or nothing!’
The initial track has an expected death rate of 1, but that changes to 0 if we flip. So wouldn't we calculate out of 5 tracks for the denominator, meaning the expected death toll is 1 either way?
I understand the math of an expected death of 1.25 (1/4 x 5) and the concept of independent probabilities, but I am not sure we can disregard the knowledge that we are on a track that will have zero probability if we switch..
This reminds me of The Monty Hall problem. (https://en.wikipedia.org/wiki/Monty_Hall_problem) but that may not apply at all. Does someone with a stat background know which is the correct conceptualization?
When you flip it the original track is no longer possible, so it would not be considered. If it was considered, you would also have to consider the one person on that track. If all 5 tracks were equally likely the expected value would be 1.2 deaths.
This doesn't seem like it is similar to Monty Hall. In Monty Hall you win by switching every time unless you picked the winning door first. That's why you have a 2/3 chance to win by switching. This is just a random chance.
We are told the probabilities directly. Expected deaths as number of trials approaches infinity when switching the lever is 0*¾+5*¼ which equals 1.25. Better odds than gamblers face by a long shot but not good.
Something other posters have overlooked here is that one life is guaranteed to be saved if you pull the lever. There are 5 tracks in the image, but the ratios use quarters. If you pull the lever, you have saved one life. You have a 75% chance that you have saved one life with no consequences. You have a 25% chance of killing a net of 4 people. By that method, your expected number of kills is 1, no matter your choice.
However, I really think I look at it more on the chance of good outcomes, personally. If I pull the lever I have a 75% chance of saving everyone, and only a 25% chance of bad outcomes. I can live with that choice. I can live with the decision to take action, because to not take action is still choice.
You are counting your saved person twice, once as a 100% save and again when you consider a net count of 4.
You have a 75% chance of saving 1 person, and 25% of killing 4, which means you are still killing 0.25*4 - 0.75*1 = 0.25 people.
Now the logic of "only 25% of bad outcome" is the real gambler's fallacy here. How far would you push it ? Would you pull the lever if it was a 20% chance of killing 10 ? A 10% chance of killing 50 ?
At some number people seem to go "what are the odds it happens to ME" and happily pull a lever even if the consequences outweigh the odds.
Now the logic of "only 25% of bad outcome" is the real gambler's fallacy here. How far would you push it ? Would you pull the lever if it was a 20% chance of killing 10 ? A 10% chance of killing 50 ?
This reminded me of one of the ways of explaining the Monty Hall problem (if there were 100 doors and 98 got revealed as empty would your switch). If there were 100 alternate tracks, 99 of them empty, and the other with 200 people tied to it, I would pull the lever.
I don't know if I would...
For obvious reasons, I could never forgive myself if I promptly got to watch 200 people get butchered by a trolley immune to the laws of physics.
But even if these fairly comfortable 99% odds turned out in my favor... During the years of mental health counselling following my abduction and forced participation in twisted ethics games, I would have to listen to people telling me I saved someone and did the right thing, while knowing that I objectively did not. That I put two times more lives at risk than by not pulling the lever.
If you have 10 000 train tracks, but at the end of one of them is a nuke blowing up a city of 10 million people, do you pull the damned lever ? I sure don't.
That's a fair point, a nuclear bomb is so disastrous it would be better to let one person die than a small chance the nuke will go off. However we have significantly changed the order of magnitude here, 10 million people is 1000x more than the number of tracks.
In regards to the original question: I don't think feeling responsible for 5 deaths would be 5 times worse than feeling responsible for 1 death. The emotional cost of going from 0 deaths to 1 death is much higher than the emotional cost of going from 1 death to 5 deaths. The "greater good" argument says do nothing, my ability to sleep at night says pull the lever.
Yeah same even without all the math I'd sleep much better knowing I did something to potentially help than just lying down and doing nothing.
I would ask them
Oh that's an interesting one. The expected value is higher if you pull the lever, so based on pure logic you shouldn't.
But I think I would, hoping for that 3/4 where I don't live with the guilt. I guess you can't expected value qualitative factors. But I always roll 1s in Blood Bowl so maybe that's dangerous.
Based on the comments I think pulling the lever would look better in front of a jury so I might have to reluctantly do that
25% chance is good enough odds for me to pull! 75% chance of saving everyone sounds good to me!
You’ll kill 1.25 people to save 1?
Is this because you’re bad at math, or enjoy gambling with others’ lives?
I think I liked another commenter's explanation that the value of saving everyone is much higher than the value of merely saving 5.
It ain't my life being risked, so I'll be a high roller in this scenario.
Edit:
My inner Uncle Steven Delanor Rancford Libby III taken over when I see 75% success chance!
can we up to six?
needs someone to reveal one of the tracks and ask if you want to stick or switch
Monty Hall trolley.
Depends on how you calculate expected value if you assume the empty tracts being taken is zero you do nothing to avoid unnecessary los of life, but if you assume those empty tracks being taken is a life saved and the value of saving a life is more than third of a value of losing a a life then you should pull the lever
If a gambler kills 5 ppl they will never stop pulling that lever
So, if I do nothing, I see one death, guaranteed?
I'm going with the sure thing, I'm no gambler.
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