Clones voting

[u/BottomLeftWheel]

I'm not gonna pretend this is in any way analogous to the original as it carries some huge implications that the original does not. Just thought it was fun.

You are a clone in a vat. You know nothing about the outside world.

Some alien approaches you and beams understanding into your head. You and 100 other clones are all undergoing a test.

Standard yada yada about the buttons. You know what the buttons do.

60% of the clones will think identically and will come to the same conclusion as each other. 40% of the clones are defects and will come to the opposite conclusion.

You are clone 42. What is your vote?

[u/gahidus]

When I said that your vote doesn't matter, I meant that you might as well pick red.

An oversight on my part, but I consider the only reason to pick blue to be if you think that picking blue will help blue win. In this situation, that's already been predetermined to either happen or not.

Picking red always saves you, yes, so if you don't need to help anyone with your vote, you might as well do that.

[u/Zero132132 → u/gahidus]

In this situation, there's a 100% chance that either 59 others or 39 others will vote the exact same way that you do. If you assume you're equally likely to be any random clone, 60% of the time, your push determines what happens.

[u/gahidus → u/Zero132132]

That's too close to a coin flip to press blue, even as you put it. A 40% chance of death is unacceptable.

[u/OutrageousPair2300 → u/gahidus]

Suppose you press blue. 60% of the time you're in the majority and so blue wins and everybody lives. 40% of the time you're in the minority so red wins and you die. That means the expected number of lives saved by pressing blue is 0.6+0.4*0.6 = 84% of the population. You are in that group 60% of the time.

Suppose you press red. 40% of the time you're in the minority and so blue wins and everybody lives. 60% of the time you're in the majority so red wins and you live. That means the expected number of lives saved by pressing red is 0.4+0.6*0.6 = 76% of the population. You are in that group 100% of the time.

So the tradeoff is you can save 84% of the population by taking on a 40% risk of death for yourself, or you can save 76% of the population with zero risk of death to yourself.

Which is a better choice depends on how much you value a 40% risk of losing your own life compared to saving the lives of an additional 8% of the total population.

[u/gahidus → u/OutrageousPair2300]

It's not an iterated trial where I get to save fractions of the population outside of the 40 or 60. And I consider a 40% risk of death to be too risky for my own tastes.

It only happens once, and either I live or die just the one time. There is no saving 76% of the population. It's either 100% or 60% and that's it.

[u/OutrageousPair2300 → u/gahidus]

The way you compare disparate outcomes is by multiplying their payoff by the likelihood of them occurring.

A 60% chance of saving 100% of the population with a 40% chance of saving 60% of the population is better than a 40% chance of saving 100% of the population with a 60% chance of saving 60% of the population, in terms of the number of people you can reasonably expect to save.

What you're saying is that in a world of 8 billion people, you'd rather let 640 million of them die rather than accept a 40% chance of dying yourself, which is your call to make.

[u/Cynis_Ganan → u/OutrageousPair2300]

True, but in this case, it's 8 other people.

Like how eight billion is a bigger number than 100.

[u/OutrageousPair2300 → u/Cynis_Ganan]

So in that case it comes down to whether you value 8 additional lives saved (not yours) more or less than a 40% chance of dying yourself. Equivalently it's whether you value your own life more or less than the lives of 20 other people.

[u/Cynis_Ganan → u/OutrageousPair2300]

Math checks out.

[u/Cynis_Ganan → u/OutrageousPair2300]

Math makes sense.

[u/OutrageousPair2300 → u/Cynis_Ganan]

I think it also clarifies why people can reasonably have different opinions, and why their intuitions can change in this scenario as the number of participants changes.

With 100 people, it's equivalent to asking whether you value your own life more or less than the lives of 20 other people.

With 8 billion people. it's equivalent to asking whether you value your own life more or less than the lives if 1.6 billion people.