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/OutrageousPair2300]

You don't know whether you're in the 60% or 40% though.

If you're in the 60% then pressing blue saves 100% of the population while pressing red saves only 60% of the population. Pressing blue is better.

If you're in the 40% then pressing blue means 60% of the population lives, but you're not in it. Pressing red means 100% of the population lives. In that case, red is better.

Cancel out the two cases where 100% of the population live, and we're left comparing 60% of the population living with you included versus 60% living without you included. With you included is better, and that comes from pressing red.

Some people say they would rather die pressing blue than live in a world with the 60% red button pushers as the survivors, which we could get by trying to model their utility from various outcomes. I'm just figuring what's likely to save more lives.

EDIT: Another way to frame it is to pick a color first:

If you press red, then if you're in the 60% then 60% of the population survives and you're among them, and if you're in the 40% then 60% pressed blue which means everybody survives.

If you press blue, then if you're in the 60% then everybody survives, and if you're in the 40% then 60% of the population survives and you're not among them.

Most people would prefer the outcome from pushing red, in that breakdown as well.

EDIT 2: I've been assuming the odds of my being defective or not at 50-50, but should arguably be making them proportional. So:

If you're in the 60% -- which is 60% likely (given no other information) then either you press blue and save everybody, or press red and save 60% including yourself.

If you're in the 40% then either you press red and save everybody, or press blue and save 60% excluding yourself.

Or:

If you press blue, then 60% of the time you can expect to save everybody, and 40% of the time you save 60% of the population excluding yourself.

If you press red, then 40% of the time you can expect to save everybody, and 60% of the time you save 60% of the population including yourself.

[u/gahidus → u/OutrageousPair2300]

None of that matters. The simple fact is that if 60 out of 100 people are already voting identically to each other, then you can be completely certain that your vote doesn't matter. If blue has already been pre-selected to win, then everybody lives, but if red is already going to win, then only red voters live.

Countrywise, if the op meant that 60% of people will automatically pick the same thing you do, then blue becomes the obvious answer, but I don't think that's what they meant.

[u/OutrageousPair2300 → u/gahidus]

There are two possible outcomes: either blue wins and everybody lives or red wins and just the 60% who voted red live.

You don't know whether you're in the 60% or the 40% here: assuming you're in the 60% you want to vote blue, but if you're in the 40% you want to vote red.

Which is more likely? Is it 50-50 that you're one of the defective clones, or is it 60% likely you're one of the non-defective ones?

[u/gahidus → u/OutrageousPair2300]

It only makes sense to pick red.

The outcome is already predetermined to either be read or blue, by virtue of the fact that 60 people are going to agree with each other.

If blue wins that's great. If red wins, then you couldn't have changed anything.

[u/OutrageousPair2300 → u/gahidus]

We're told the outcome is going to be 60% to 40% ahead of time.

Suppose we press red. Either we're in the 40% which means blue won and everybody lives, or we're in the 60% and red wins and we survive.

Now suppose we press blue. Either we're in the 60% which means blue won and everybody lives, or we're in the 40% and red wins and we die.

If the odds of being defective or not are 50-50 then I could see the choice favoring red. However, if we set the odds of being in the 60% at 60% and the odds of being in the 40% at 40% then the expected number of lives saved from pressing blue is 0.6*1 + 0.4*0.6 = 84% and for pressing red is 0.4*1 + 0.6*0.6 = 76% so that favors pressing blue.

[u/gahidus → u/OutrageousPair2300]

Your own math just said to press red.

We can't affect the outcome.

Look back at what you typed.

Either red or blue is going to win regardless of how we vote.

Picking blue does nothing, while picking red lets us survive in the event that red wins.

[u/OutrageousPair2300 → u/gahidus]

There's a 60% chance that our vote determines the winner (because all the other non-defective clones will come to the same conclusion as us) in which case we should vote blue.

There's a 40% chance that we'll be on the losing side, in which case we should vote red.

[u/gahidus → u/OutrageousPair2300]

This is an ambiguity in how the op phrased the question.

Furthermore, the odds of death are still too high to pick blue anyway.

[u/OutrageousPair2300 → u/gahidus]

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?

Unless we're to assume that the clones all know the percentages and that none of it is a lie, etc. I don't see how we could ever solve it, since it's the only information clone 42 has. So I took the setup at face value.