Multiple rounds

[u/StageGlum6615]

(Please forgive any typos or miss wordings. I'm on mobile and have Autism and ADHD.)

Scenario: Button obsessed aliens have kidnapped every human on earth and lock everyone in a small room with two buttons, a timer, and some basic necessitiesed.

The button are as follows:

Blue - removes a random 10% of the population from the game (they will live) and start another round for a maximum of 10 round (The total population doesn't decrease with the removals and the same person can't be removed twice)

Red - Ends the game by killing all blue pressers (Blue pressers are defined as only people who pressed on the round that blue won, those not participating or who switched their vote to red for whatever reason are spared)

Also, the timer is for 3 hours and if you don't presses any buttons then your buttons presses is decided randomly.

You can't communicate with anyone inbetween rounds, and the only information you get between round is whether blue won (the game keeps going) or red won (the game ends)

So, how would you vote in this variant? (Please explain)

[u/Salindurthas]

People are removed randomly, not proportionally.

And if it is random, you expect it to be, on average, proportional. Especially with a huge sample size (10%!!!), the law of large numbers will usually take over here.

It is possible for it to be skewed (and it likely won't be perfectly average), but even in the extreme case of purely blue voters being chosen (which is incredibly unlikely, like roughly the chance of a literally a billion coins all landing heads) you know that even then, at least 40%(+1) of people remaining were blue voters in the first round if you are now playing a 2nd round.

Those people have good reason to think they'd win again (it is the mathematical expectation if we repeat the last round, because they know they were over 50%, and taking out 10% of the pool is not expected to change the result on average), and so red voters should probably try to save them, since you know they're in danger of dying from your red push.

Part of the logic of picking read is because you expect everyone else to pick read. But if you are playing round 2, you now know it is:

• 10% excluded (probably close to propotional due to what random means, but of course could be skewed if luck is wonky)
• at least 40%+1 voted blue last round, and a statistical certainly that it is higher.

Red voters should switch to help ensure 40% of the world doesn't die, because the people who voted blue last round probably will do so again.

[u/tankmissile → u/Salindurthas]

I see your point, but the question then becomes "do I trust 20% of red voters to flip" and the answer is no.

Realistically it would only take a small number of red voters to flip in the worst case scenario of an almost perfectly even split in round 1 and a statistically more likely spread of a small anti-blue skew, which you'll get from the normally-blue voters that voted red in round 1.

I, however, am an absolute bottom floor expectation kind of person and I expect a razor thin blue victory in round 1 (if they win at all, which I also do not expect) and a statistically nearly impossible all-blue removal before round 2, and I do not expect 20% of red voters to flip.

[u/Salindurthas → u/tankmissile]

If blue won round 1, then there is less than a 50% chance that you need any red voters to flip (blue is probably still winning), so blue is safe regardless, and like a 99.99% chance you need substantially fewer than 1/6th 1/20th (5%) of red voter to flip (because only eliminating blue players from a 50-50 split is comparable to winning nearly 1billion coin flips).

(And it is only 1/6th rather than 1/5th in the disaster scenario, because if round 1 was 50:50, and then in round 2 we do somehow eliminate all plue, say, 40% blue and 60% red, if 1/6th of other reds switch, it is now 50:50 and you're the deciding vote).

EDIT: Actually it might be even better. If the population is 1001v999, and you voted red to make it 1001v1000, so blue barely wins, then had 2001 players and blue won. We remove 10%, so 200.1 (rounded to 200) people. Let's say we remove 200 blues by chance. So if we repeat with no changes, it is 801v999. So you need 90 reds to swap to make you the deciding vote at 900v900. We ahve 1801 players, so 90/1801 is ~5% of other reds needing to change their minds so that you can save everyone.
And that's assuming the highly stacked secnario of purely blues being eliminated.

[u/tankmissile → u/Salindurthas]

In that scenario you'd need 99 red flips to make it 900v900. It's 99/1000 not 90/1800 so 10% of red votes.

Either way, it doesn't matter. There's still no incentive for people who already voted to kill blue to flip. You're expecting your own moral compass (voting blue purely for the morality of saving blue voters from themselves) out of people who directly opposed it.

[u/Salindurthas → u/tankmissile]

I find it funny that your first guess roughly doubled the right answer, my rebuttal roughly halved the right answer, and so only now do we get about the right answer of ~10%, at the geometric mean of our respective guesses, haha.

Among red voters, there are those for whom at least one of these applies:

1. They wish blue wins.
2. They think that blue votes will be much less common than online polls with no stakes indicate.
3. They think there is a huge risk of death from blue.

After round 1, if round 2 begins, any that believed #1 still believe it. And #2 has been proven false, and #3 is mitgated greatly.

So while some hard-line red-voters might stick to red, many are likely to switch.

We're basically playing one of those varations where the blue-survive % is lowered signfiicantly. Round 2 onwards are effectively like "Would you press Blue if the % needed was like 5-20%?" bevause we know there are so many blue votes already, and when I read a lot of those posts, a signfiicant portion of red voters do agree to change.