A short calculation about a Twitter poll

Note that another way of phrasing the poll is:

Everyone responding to this poll chooses between a blue pill or red pill.

• if you choose red pill, you live
• if you choose blue pill, you die unless >50% of ppl choose blue pill

Which do you choose?

I bet the poll results would be very different if it was phrased this way.

A bit less than game-theoretical argument here.

Note that a significant consideration is that one does not want to be "morally responsible" for "those clueless bluepillers" dying. Absent uniformity or perfect coordination, PEOPLE DIE!!!111. 

Another note: people are often willing to risk their own lives in order to avoid this guilt. Survivor's guilt is a thing you can't easily logic away. These people will vote blue, because the alternative is unthinkable. 

Finally, if you care about these people, even though you realize that redpilling is the safe personal choice, bluepilling is a decision worth considering seriously.

It seems like everyone will pick red pill, so everyone will live.  Simple deciders will minimize risk to self by picking red, complex deciders will realize simple deciders exist and pick red, extravagant theorists will realize that the universal red accomplishes the same thing as universal blue.

I suspect the self-selection of participants outweighs all other parts of the calculation.  The choices are actually red, blue, or no response (with an undefined outcome, but I'd expect that the vast majority of humans on earth chose it, or had it chosen for them because they didn't even see the poll).   Followed by the confounder that the setup is a lie - it's FAR more likely that the pollster is faffing about and nobody will be killed as a result of any outcome.  I don't think there's anything to learn from this setup - some participants may make the calculation, but the vast majority will ignore it, or choose for signaling or amusement value.

If you did this with forced participation, and actual belief that it worked as claimed, the vast majority of humans would choose red.  In fact, why would anyone choose blue?  100% red means everyone lives, and it doesn't require any trust or coordination to achieve.

If you change it so there are hostages (people who don't get to choose, but will die if the blue threshold isn't met), then it becomes interesting.  But still not that interesting - coordination and trust become the primary questions, and your setup doesn't mention anything about what mechanisms are available or what population is voting.  Basically, the "depending on your beliefs about how the rest of the population will vote" dominates, and you don't provide any evidence to update those beliefs upon.

Embarrassingly minor nitpick I'm too neurotic to not mention: It's the ceil of N/2 instead of floor.

The poll is interesting insofar as it generates discussion and analysis, but meaningless as an evaluation of human empathy. This would be true even if done in standard laboratory conditions. Stated preferences, particularly for issues of morality and self-sacrifice, map poorly to revealed preferences. A study evaluated how many people said they would donate blood freely in the UK vs how many actually did, with tragically predictable poor matching (https://onlinelibrary.wiley.com/doi/full/10.1002/hec.4246). 

The actually interesting study would be to complete this poll to people who truly believed that the poll was real. How would people respond. How would parents recommend their children to respond? Would the father really tell his daughter to potentially step into the blender when she could have a guaranteed survival ticket?

I would state with 95% probability that if a) if those polled truly believed that the poll were real; b) that there were families involved; and c) that they could not communicate beforehand then nearly all (if not all) respondents would press red. This may even be true if they could communicate beforehand. 

Looks about right to me. Of course, the hard part is actually estimating $P(B<\lfloor N/2\rfloor )$ for a given population under specific conditions, and the even harder part is figuring out what you can do in general to create populations where this probability tends to be very low. In such populations where the probability of a red victory is negligible, choosing blue is a way of protecting the tiny fraction of people who misread or misclick, suffer from a temporary bout of insanity, or just aren't smart enough to comprehend the choice at all, at negligible risk to yourself.

Among earthlings, I think the issue would be more about a lack of coherence and understanding of decision theory and a desire to solve coordination problems, as well as common knowledge that such knowledge and desire was common (if it were in fact common), rather than a lack of altruism or any social pressure issues.

I would comfortably choose blue in dath ilan [? · GW]; on Earth under most conditions, I'd pick red for basically the reasons you give, but feel pretty sad about it.

I think my minimum condition for choosing blue would be if a supermajority of the population could pass a competence test, i.e. demonstrate understanding and independently generate valid explanations about games like this at at least the quality level in this post. 

Judging from twitter, this is a condition which doesn't hold even among rationalists, unfortunately. A further condition would be that there is no one playing who is confidently spouting wrong / crazy explanations and getting people to agree with them, whether they're arguing for red or blue. (On a binary question, there will be lots of people who arrive at the right answer by chance; but that's only relevant if they arrive at the right answer for actually-valid reasons, and if everyone can immediately see and validly refute invalid reasoning.)

 

You are offered the investment of a lifetime! If only enough people each chip in $10000, then they'll all get their money back! Otherwise they'll all lose it!

There's a monster at the top of that mountain. It doesn't hunt people, but it will eat anyone who walks into its mouth. Unless enough people walk in at once. Come on, we've got to walk into its mouth to save the people who are going to walk into its mouth!

I expect that other voters correlate with my choice, and so I am not just deciding 1 vote, but actually a significant fraction of votes.

If the number of uncorrelated blue voters, plus the number of people who vote identical to me exceeds 50%, then I can save the uncorrelated blue voters.

More formally: let R, B, C denote the fraction of uncorrelated red, uncorrelated blue and correlated voters that will vote the same as you do. Let S be how large a fraction of people you'd let die in order to save yourself (i.e. some measure of selfishness).

Then choosing blue over red gives you extra utility/lives saved depending on what R,B,C,S are.

If B>0.5 then the utility difference is 0.

If B<0.5 and B+C>0.5 then the difference is +B.

If B+C<0.5 then the difference is -(C+S).

By taking the expectation over your uncertainties about what B,R,C might be, for example by averaging across some randomly chosen scenarios that seem like they properly cover your uncertainty, you get the difference in expected utility between voting blue and red.

Estimating C,R,B can be done by guessing which algorithms other voters use to decide their votes, and how much those algorithms equal your own. Getting good precision on the latter part probably involves also guessing the epistemic state of other voters, i.e. their guesses for C,R,B, and doing some more complicated game theory and solving for equilibria.

Kickstarter version:

Everyone who takes a red pill lives.

If enough people take a blue pill, they live. If fewer than that, they regurgitate the pill and live.

Tangential, but my response to the dilemma differs massively depending on the mechanism I imagine.

I bet an individual's red pill or blue pill selection correlates extremely well with red tribe or blue tribe affiliation.