Science Corner: One Button, Two Button, Red Button, Blue Button

Right now, there are generally two types of people on social media: those awash in red button/blue button discourse, and those blissfully unaware of it. For those second types, at the heart of the conversation is the following thought experiment. Everyone in the world has to privately choose to press a red button or a blue button. If a majority of people press blue, everyone lives. If a majority of people press red, only red-pressers live. The current conversation apparently kicked off a few weeks ago with this X poll; a similar conversation was stirred up a few years ago with a similar poll phrased in terms of pills rather than buttons. Both times, blue prevailed in the non-random polls, albeit by a smaller margin this time around.¹ Unsurprisingly, lots of people have strong feelings about why their choice is correct. I’m less concerned about your choice of button; I want to talk about math.

If the extent of your relationship with math is the typical arithmetic-to-calculus-through-algebra journey with a geometry side quest, followed by adulthood accounting and maybe the odd DIY project, you might see math as largely about performing calculations to achieve the single correct answer. There’s a case to be made that this is why we invented math (and writing)–to resolve questions of who owes what to whom in a way that both parties will agree. Things can get messy quickly if I, the monarch of grilled beef patties, think that $5.69 for a burger and $3.09 for onion rings adds up to $8.78 and you, my royal customer, think it’s $4.12 (or worse, beleventy christophthree). But nothing everything in life is financial; as we apply the mathematics we’ve developed over the millennia, we find that sometimes “Under what conditions does each answer make sense?” is a better question to ask than “What is the right answer?”

For example, going to the hassle of carving clay (other storage media are available) with records of business transactions and account balances presumes that you are going to be dealing with the same people over and over again. If I’m only going to trade with you once, we just make whatever deal we are both comfortable walking away with and that’s the end of it. Maybe that means we work out a deal we both think is fair. Or maybe I decide it is worthwhile to skew things in my favor, getting you to accept less either by trickery or coercion. If I know I’m never going to see you again, what do I care if you think I owe you something? And what good does it do you to record that debt?

But now suppose we aren’t so nomadic that we can count on mutual ghosting. On the one hand, I have an extra incentive to deal more fairly because I know you can come find me if you feel aggrieved. On the other hand, you might be willing to take the short end of a deal this time knowing that you can make it up next time, so long as we both agree on what’s owed. If we are asking the question “What’s the maximum value I can get out of this deal?” the “right” answer will depend on which scenario we’re in and what I believe I can get away with.

We’ve since developed math beyond accounting to investigate various such questions, creating fields like economics and game theory. A classic example is the Prisoner’s Dilemma. Two people are imprisoned for a crime and each privately given the chance to testify against the other; testifying means getting set free while the other is penalized, unless both testify, in which case both are penalized to a lesser degree. The best possible outcome for either prisoner is to testify when the other doesn’t, but if both choose that option, they both get a worse outcome than if they had collectively said nothing. It turns out that the best strategy to use changes if you are in this scenario once or if you face the same deal repeatedly with the same person. The repetition creates the opportunity to essentially coordinate without coordinating (that is, without directly discussing your plans with the other person). You can demonstrate that you can be counted on to stay silent, your partner can do the same, and thus you can both take the risk of not testifying and have some confidence that your counterpart will do likewise, earning that better outcome than both testifying.

Martin Nowak covers this and related findings in his book SuperCooperators about what conditions can lead to altruism. Many have written on similar topics, but Nowak also brings his Catholic beliefs into the conversation in a way that might be of more interest than other takes. Here again, the question is not “Is altruism the correct answer?” but rather “Under what conditions is altruism the correct answer and under what conditions is ego the correct answer?” Because the reality is that either one can be the correct answer under different circumstances. One general finding is that groups of altruists can succeed better than groups of egoists in a variety of settings, yet it can often be personally more beneficial to act in an egoist way as a member of a group of altruists–provided enough of the rest of the group remains altruistic.

As a result, having an altruistic group is not a stable state, meaning a situation where no one has an incentive to act differently. The challenge then becomes how to maintain an altruistic group against the incentives to gain even more by putting oneself first. One way or another, the answer basically involves making egoism more costly, whether through monetary penalties, loss of status, loss of freedom, or other measures. Groups that don’t have some means to encourage altruism run the risk of losing their group advantage. At the same time, human psychology is complex. If individuals perceive, accurately or otherwise, that they are incurring those penalties no matter what they do may feel justified in therefore taking the egoist route so that they at least get the maximum benefit to offset the penalty.

I wonder if some amount of this is manifesting in the button discourse, particularly among those defending their choice of red. In this particular framing, the self-interested selection of red does not intrinsically come at a cost to anyone else; it is possible for everyone to press red and live. Sure, one might make the assumption that someone will wind up pressing blue for any number of reasons, but in a thought experiment like this it is also valid to make some “spherical cow”-style assumptions and assume everyone understands the instructions and the implications perfectly, is able to perfectly execute their intention, and knows the same is true for everyone else. Since it is thus possible to construct red button scenarios where everyone lives, it may be worth exploring what assumptions and values someone brought to the analysis instead of just going by the single bit of information available from their color selection. You may still disagree with their choice or their reasoning, or think that they scenarios they are considering aren’t the right ones. But at least you’ll understand better where the differences lie.

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¹I don’t think much can be inferred from the differing outcomes. There are just too many ways that social media polls can be biased in a statistical sense–the two pollers could have very different audiences, the algorithm can make different decisions at different times about who is shown the poll in their feed, etc.–for them to be taken as anything more than curiosities.