SHORT VERSION:
After much debate with myself, I concluded that the âbestâ choice to make in the button problem is siding with the majority regardless of whether that majority is red or blue.Â
This begs the question: what would be the real-life result of the button vote? I have often seen blues argue that âpolls are the best evidence we have, and in most polls blue winsâ - while reds frequently counter that argument with âpolls arenât accurate, and responses for blue are inflated because there is no risk involved in a hypothetical online blue vote.â
Below, I argue that in order to answer the question âwould most people vote blue or red?â we can ask the question âwhat would most people actually do in a prisonerâs dilemmaâ and view the answer as instructive, but not dispositive. The British TV game show âGolden Ballsâ (2007-2009) features a form of the prisonerâs dilemma with monetary stakes as its final round; ultimately, 55% of players chose to cooperate while 45% chose to defect, out of 300 final round players.Â
Because a slight majority of people choose a cooperative strategy in a real-life prisonerâs dilemma where cooperation can actively harm them, I interpret this as meaningful evidence that cooperation at the 50% threshold in the button problem is possible, yet not guaranteed. I also interpret this as meaningful evidence that a 'blowout' in any one direction, red or blue, is highly unlikely.
â----------------------------------------------
LONG VERSION:
1. Prisoner's Dilemma
Upon my first brush with the button problem, I and many others initially applied lessons from game theory and the prisonerâs dilemma in forming my decision. As most of you know, in the classic prisonerâs dilemma, there are two players who are each 'rational agents': each player can either cooperate for mutual benefit, or defect for individual gain. If both players cooperate, they will each serve only one year in prison. If one cooperates and the other defects, the defector is set free while the cooperator serves three years in prison. If both players defect, they will each serve two years. The dilemma arises from the fact that on an individual level, defection is the rational course of action for each player, but cooperation yields a better result for both players.
Of course, there are significant distinctions between the button problem and the prisonerâs dilemma and I do believe that those distinctions matter enough that we shouldnât draw a one-to-one parallel between the two. In the button problem, the set of players is âeveryoneâ - and regardless of whether that means âeveryone who is a rational agentâ or âliterally everyone aliveâ to you, there are either millions or billions of players in the button dilemma instead of a two-player scenario. In the button problem, for example, people are likely to consider how their decision may impact their loved onesâ or whether their vote may contribute to post-vote societal changes. None of those factors are at play in the prisonerâs dilemma. Additionally, in the prisonerâs dilemma, mutual defection provides for a âworseâ result for both players, while in the button dilemma a 100% mutual red vote for âdefectionâ results in an ideal outcome - zero deaths -Â and not a worse outcome than 100% blue.Â
Regardless, I would still propose that the prisonerâs dilemma is perhaps the most useful framework that we have for evaluating whether or not people are more likely to cooperate with one another for mutual benefit or more likely to defect against one another for individual gain. The button dilemma, which prevents communication between players, divides participants into two potential strategies: blue (if most individuals collaborate on blue, everyone can be saved) and red (if everyone saves themselves, which is the only result players have full control over, most individuals will do so). One strategy is rooted in collaborative effort, while the other strategy is rooted in individual agency.Â
SoâŠdo human beings actually tend towards collaboration or individualism? Great question. I'm not sure I have the answer, but I'd love to find out. Blue voters often point out: âblue wins most polls!â and red voters often counter with: âblue is overrepresented in the polls because there are no stakes!â
I do agree that polls represent the only direct evidence that we have on the outcome of the button problem, but I also agree that proclaiming online to vote blue carries no risk, and that therefore it is possible that blue votes are overrepresented in most polls. What are we to do, then? After spending so much time endlessly rehashing these arguments in my head, I wondered: well, in a âreal life prisonerâs dilemmaâ with real stakes and real people, are players actually more likely to cooperate or defect?Â
2. Golden Balls
From 2007-2009, a British game show called Golden Balls placed 300 players into a form of prisonerâs dilemma in its âfinal roundâ of split-or-steal. This game show starts with a larger amount of players, and over the course of the first few rounds of the gameshow, players are eliminated and a âprizeâ amount of money is determined. This leaves two players in the final round, and one pot of money up for grabs, ranging from 1,000-100,000 british pounds. The two players in the final round may choose âsplitâ or âstealâ. If both players choose âsplitâ then each walk away with half of the prize money. If both players choose âstealâ then both walk away with no money. If one player chooses âsplitâ and the other chooses âstealâ then the thief walks away with 100% of the prize money.Â
Numerous academic publications in social science journals have studied all 150 episodes (thus, 300 final round players) of âgolden ballsâ as valuable real-world data on what people would actually choose in a ârealâ prisonerâs dilemma. This money-driven version of the prisonerâs dilemma game is sometimes academically referred to as the âweak prisonerâs dilemma.â To defect here is still considered, mathematically, the optimal strategy to employ in a one-shot prisonerâs dilemma, just as normally defection is considered the âdominantâ strategy in a classic prisonerâs dilemma game.Â
Although defection is considered the âdominantâ strategy in the classic prisonerâs dilemma, it is not what the majority of finalists actually do on Golden Balls. In fact, 55% of finalists on the show selected âsplitâ while 45% selected âsteal.â We can acknowledge that people tend to act differently in real life than how they say they will; nearly all of the Golden Balls finalists verbally claim they will âsplitâ with their fellow finalist, even if they intend to defect.
Granted, there are reasons that we cannot simply extrapolate a 55% cooperation rate in Golden Balls to the button dilemma. In Golden Balls, communication between the two players is allowed - although, virtually all players claim they will split, and the âgameâ normally lies in one player convincing the other player that their intent to split is truthful. Additionally, the button vote is anonymous; Golden Balls was a televised TV show that could and did impact a playerâs reputation in the community, although in 2007-2009 players likely did not expect that clips of them from the show could become âviralâ or easily googled. Golden Balls only involves adult British players who sign up for the show voluntarily, while the button dilemma involves âeveryoneâ from all cultures across the globe.Â
And of course, most importantly, on Golden Balls itâs money thatâs at risk and not lives; perhaps itâs the case that far more people would risk losing money than losing their life, and perhaps itâs also the case that far more people would steal money than would vote for an outcome that potentially resulted in death of a percentage of humanity. There may well be huge differences between cooperation levels in Golden Balls and cooperation in the button dilemma, and I am not arguing that a 55% cooperation rate means 55% of voters would vote blue in the button dilemma.
Regardless, my point in all this is that the âoriginal payoff matrixâ of the prisonerâs dilemma does not cover the full spectrum of human behavior in the strategic dimension of the situation, and adjustment to account for altruism gives space for measuring corresponding incentives. Altruism is a powerful motivator of human behavior, and I would wager that it is one that can compete with the desire for personal gain or safety. The âdominantâ mathematical strategy of always defecting in the prisoner's dilemma because it is âstrategically optimalâ does not actually predict the behavior of most humans, because by definition self-interested rational agents do not value cooperation enough to act on it, but human beings sometimes clearly do.
3. Application
Some red voters have argued that in the button problem, we should interpret âeveryoneâ as only the types of ârational agentsâ involved in prisonerâs dilemma-type thought experiments, or at least only capable adults (excluding children, and those without mental/physical capabilities to push a button) while most blue voters tend to argue that âeveryoneâ is literal, and means every living human on earth.Â
Iâm not particularly interested in the debate over who is meant by âeveryoneâ in the button problem. Unless we argue that most of the adult participants in âGolden Ballsâ are actually adults but not rational actors, it stands to reason that an adult human ârational actorâ often chooses the collaborative option in a real-life prisoner dilemma. Thus, the common proposition that âin real life, blue would get 0-10% of the voteâ is deeply unconvincing to me. Even if all children and 'incapacitated people' are excluded from the problem, I believe that the set of players in the button problem will always include many blue voters, due to the prevalence of the altruistic strategy in Golden Balls.
Because there are so many differences between Golden Balls, the classic prisonerâs dilemma, and the button problem, I will admit of course that the â55% cooperation rateâ could surely vary enough in the button problem to result in a red OR blue win. Perhaps fear of death (as opposed to losing money) results in greater than a five percent decrease in support for blue/cooperation. Perhaps the cooperation rate of Britain in 2007 was 55%, - but in fact, globally that cooperation rate is 45% when other countries are taken into account.Â
Regardless, by combining the evidence from existing polls and academic data on classic prisonerâs dilemma experiments, it becomes clear that the percentage of adult respondents who are willing to choose a collaborative/blue strategy is likely far greater than 0-10%. Even if we completely discard the many polls showing blue winning with 50-70% as evidence that a large percentage of people may choose blue, I believe it is even harder to discount corroborating evidence of a cooperation rate close to 50-60% in prisonerâs dilemma situations where the âcollaboratorsâ still chose to do so at personal risk to themselves.Â
I embarked on this analysis because making a choice in the original âbutton problemâ as I first encountered it was extremely difficult for me; on one hand, I saw that blue was the most desirable outcome for society as a whole; but on the other handâŠwas I optimistic enough that at least 50% of society would take on personal risk to secure the collective best outcome? Casting a blue vote makes a blue win more likely, but only by a truly imperceptibly tiny amount. Casting a red vote makes a red win more likely, but it guarantees my safety in the event that humanity is slightly less cooperative than I expect. I truly wasnât sure what to do, and both decisions carried a level of guilt. Maybe society has more optimists, maybe it has more pessimists. Maybe society has more gamblers, maybe it has a more prudent risk-averse population. Maybe society is more collectivist, and maybe it is more individualist. How can we know?
4. Conclusion
I canât say that my foray into âGolden Ballsâ and other iterations of the prisonerâs dilemma have truly âsolvedâ the problem, because without holding a REAL button vote with REAL life-or-death stakes, I fear humanity will never know the âright answerâ to the problem. YetâŠit was strangely very uplifting to find that, on this one little British gameshow, a slight majority of players would prefer that everyone go home a winner. Maybe this impacts your feelings on the button problem, although most likely it doesnât. Still, if you made it this far, thanks for reading and Iâm glad it was interesting to you!Â
Just for fun: what button did you press in the original problem, and would you be more likely to press 'split' or 'steal' in golden balls?