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.
With the luck that I have? Hell no!
So, if I do nothing, I see one death, guaranteed?
I’m going with the sure thing, I’m no gambler.
1.00 • 1 death = 1 death Vs. 0.25 • 5 deaths = 1.25 deaths
On average you’re better off not pulling the lever.
Implying you’ll be running this multiple times?
Implying I haven’t already
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.
“aww damn, 5 people are double dead”
I didn’t need math to know that the only way I see a guy beheaded is if I don’t pull the lever, so we got to the same answer.
Found the risk manager.
Look at it selfishly:
- 100% chance of killing someone
- 25% chance of killing someone
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
Should you feel bad for risking it, even if you get lucky? If when you cause something by accident you don’t feel as bad, you’re going partly by intentions, not actual outcomes.
If I could have done something to prevent it, but chose not to, and someone died, I would feel just as bad as if I pulled the lever and killed someone.
These are not independent probabilities and we can’t disregard the initial mathematical data (unless I’m wrong, not a stat major).
A true degenerate would pull the lever, hit no one, and immediately pull the lever again yelling ‘double or nothing!’
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.
I think the calculus comes down to “will I feel 5x worse if five people die than if just one dies?” Chances are, no, it is more of a binary yes/no for feeling guilty. So from a purely selfish standpoint I want to minimize the chances I will walk away regretting my decision. That means pulling the lever.
No it’s 1 either way, right?
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
You’d also have to consider the value of the lives saved by not sending the train to the 5 person track.
I thought that information would be encoded when you assign -5 to it (value of the outcome of losing 5 lives) and -1 for 1 life lose doing nothing.
But the logic would be doing something and saving life is a plus, doing something and getting more people killed is a huge negative
So basically, you’re saying that the two tracks with people tied to them are valued at -1 and -5, while the empty tracks have some positive non-zero value?
Uhg you could read what I wrote
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?
It ain’t my life being risked, so I’ll be a high roller in this scenario.
I think I liked another commenter’s explanation that the value of saving everyone is much higher than the value of merely saving 5.
See if I can’t get dad’s Parkinsons to pay off
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.
Is this math accurate?
what company manufactured the trolley ? it is injured ?
this is a stats problem. you have a 2 in 5 chance of someone getting killed.
without doing the math I’d say you have a 20% chance of killing someone by pulling the lever but have a 100% chance by doing nothing.
I’ll take my chances and pull the lever three times which should reduce that 20% to about 10%.
That’s game theory though. Fun statistics.
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 can choose a ready guide in some celestial voice
If you choose not to decide, you still have made a choice
You can choose from phantom fears and kindness that can kill
I will choose a path that’s clear, I will choose Freewill
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 = 0.25people.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’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.
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.
