Which button?

May 2026 · code on github. The essay and the model in one place: every number and figure is computed live from the attached dataset.

Everyone in the world has to take a private vote by pressing a red or blue button. If more than 50% of people press the blue button, everyone survives. If less than 50% of people press the blue button, only people who pressed the red button survive. Which button would you press?

– Tim Urban · @waitbutwhy

Like all good internet dilemmas, it's an obviously non-obvious problem. The less one thinks about it, the sooner one arrives at an answer, and the harder it is to be talked out of it. Logical people find no logical argument against red; moral people find no moral argument against blue. In the end it's not clear which way things would go.

The first error everyone makes is thinking the dilemma has only one right answer. That misidentifies the kind of dilemma this is. There are three outcomes: you are saved, you save yourself, or you die. So there are really two equilibria: collaborative risk or individual salvation. This is not a prisoner's dilemma[1], since there is no Faustian bargain. It is a coordination game[2]. There is no us or them. We can all try to save everyone, or we can all save ourselves. The more we agree, the fewer die.

An equal error is assuming we all share a goal, or even read a shared goal the same way. The most common goal is to maximize survivors or minimize casualties, two sides of the same coin. Directly opposing it is the also-popular argument for dying. Both arguments hold that some deaths are justified, either those of others or their own: "some will inevitably die" and "I don't want to live in a cruel world," respectively. It's one's desire to help against one's survival sense, wrapped up in whatever framework we subscribe to.

To approach anything like an objective answer, we first have to level the playing field. Rule out the colorblind, slips, mistakes, communication, coercion and similar exits, and we can look at the case for each choice.

Game theory is a good place to start because it is simple and visual. Two options and two scenarios give four outcomes. Two of them are equal, so there are three in the end:

One can trust that they will be saved while knowing they could be killed, or guarantee their own survival. Any one person's blue press is insignificant, while a red press is exclusively for the presser[3]. This only accounts for rational outcomes. Someone who values the choice over the outcome will press blue regardless, but they are a rare minority.

Philosophy offers some insight into the morality, though not every framework helps. Because this is a coordination game, Kant's imperative[4] instantly renders the dilemma moot (even in a red world there are no blue-pressers to die). The hinge is where we believe we lie: what we think others will press. Assuming blue is twice as likely because it needs half as much agreement confuses the threshold with the odds of clearing it. Both may be equally impossible, with one a much narrower miss. Or one may be far more likely for reasons that aren't obvious.

Back to the post. I left out one part at the start, the attached poll:

Tim's poll, final results · 98,539 votes · final results on x.com

Netizens[5] generally trend blue, narrowly blue, as in the poll above from the original tweet. Unlike in the dilemma, people could see prior votes (even if only by cheating), and they definitely discussed it, extensively. This is one of the places I saw the rationalizations above[6].

The nature of the problem, this unstable rhetoric and the narrow wins across polls made me question where we would really land. They only made me doubt the polls more. So I set out to estimate the outcome from data, or from analogs to the data.

The first step is to establish the variables at play: trust and altruism. That is, how much you believe in others and how much you value them. As stated earlier, if you count only altruism, the choice is immediately blue.

Altruism is hard to estimate. For a lower bound I looked at organ donation rates. These range from fractions of a percent for essential organs to a few percentage points for things like blood. For the upper bound I used dictator-game meta-studies, which gave me the generous bound[7] of 28%[8].

Trust is the key variable of the two. It varies wildly between nations and drives the choice. My primary source is World Values Survey[9] data, corroborated by behavioral trust games[10]. Trust ranges from a low of 5% in Colombia to around 74% in Denmark, and most countries sit in the lower half of the distribution.

The data

One row per surveyed nation plus a rest-of-world bucket for the ~2.7B people not individually surveyed. The column dictionary and full provenance are on the dataset page. Loaded and sorted by trust:

The model

To simulate this I ran ~7.0B agents per run, based on population data for the countries with trust data plus an estimate[11]. They ranged from 5.1 million agents for New Zealand to over 1.4 billion for China[12].

Each agent gets a random trust and altruism, sampled from its nation's ranges, and one rule:

$$\text{press blue if}\quad \text{trust} \times (1 + \text{altruism}) \ge 1$$

The per-country blue share has a closed form, so the notebook computes it exactly by quadrature. The ~7B-agent Monte-Carlo run that confirms it is at the end, behind a flag. Below, blue_fraction evaluates the closed form for one nation. world plays the single global game across all of them. The critical_* functions find the thresholds where an outcome flips.

Results

Once every country had run, I merged the results into the world outcome closest to the real population and estimated behavior. That gives the blue presser/death toll numbers. Per one hundred thousand people:

Nearly half the surveyed countries sit below the US on trust, and almost all their presser counts are a rounding error[13]. In every simulation I could run, the most trusting nations were also the most devastated.

xychart
  x-axis "← trust →" ["0", "0.02", "0.04", "0.06", "0.08", "0.1", "0.12", "0.14", "0.16", "0.18", "0.2", "0.22", "0.24", "0.26", "0.28", "0.3", "0.32", "0.34", "0.36", "0.38", "0.4", "0.42", "0.44", "0.46", "0.48", "0.5", "0.52", "0.54", "0.56", "0.58", "0.6", "0.62", "0.64", "0.66", "0.68", "0.7", "0.72", "0.74", "0.76", "0.78"]
  y-axis "death toll"
  line [0, 0, 0, 0, 0, 0, 0, 0, 0.001, 0.001, 0.001, 0.002, 0.003, 0.004, 0.005, 0.007, 0.01, 0.013, 0.016, 0.021, 0.026, 0.033, 0.041, 0.05, 0.061, 0.073, 0.088, 0.105, 0.124, 0.145, 0.169, 0.195, 0.224, 0.256, 0.291, 0.328, 0.368, 0.41, 0.454, 0.5]

Short of clearing the bar, the closer a country is to blue winning, the worse it gets. Small but high-trust countries can stand to lose nearly half their population. Large low-trust countries that would dwarf them in any other category lose but a fraction of theirs. There are, of course, outliers. Taking the trust data at face value, China's mix of population and trust puts its deaths north of 300 million, the bulk of the global toll. That world figure leans on China's contested 64%. Without China, the world's death rate would sit below the US's. At the other end, Colombia, the least trusting nation in the sample, is also quite small and would lose under 2 thousand people in total.

The full table, with the altruism each country would need to save itself:

Half-coordinated optimism kills far more people than selfishness ever could[14]. Getting half of earth on board is no more likely than getting most people to save themselves. But the thought that it may be could doom nearly half the people of certain nations.

In the dilemma where nobody can communicate, if you're undecided, press red. There's no guarantee otherwise. But in our world, where communication does very much happen, blue is the right choice (as we saw in the poll).

Sensitivity

How much the headline moves when the assumptions do. The thresholds first:

Confirmation at real scale

The quadrature is the result; the simulation exists to confirm it. Set CONFIRM = True to redraw every one of the ~7 billion agents (several minutes of runtime). The checked-in run matched the closed form to 0.0004 pp.

Footnotes

1. A prisoner's dilemma has a single dominant move, defect, no matter what the other player does. Its one equilibrium is bad for everyone. Here, pressing red keeps you alive whether blue wins or loses, so red is merely the safe play. The only pull toward blue is the value you place on others. SEP, "Prisoner's Dilemma".
2. In a coordination game, the two outcomes that save everyone (all-red and all-blue) are equally good. But pressing red keeps you alive either way, so landing on all-blue takes trust rather than logic. SEP, "Game Theory".
3. Survivor guilt, the weight of having lived where others did not, was a listed feature of post-traumatic stress in the 1980 DSM-III and dropped from the criteria by 1987. On its diagnostic history.
4. Kant's Formula of Universal Law, from the 1785 Groundwork: act only on a maxim you could at the same time will to be a universal law. A world where everyone presses red, or everyone presses blue, leaves no one to die. The deaths come only from a split world, which no shared maxim produces. So the rule is neutral between the two safe options. SEP, "Kant's Moral Philosophy".
5. A netizen is a citizen of the internet.
6. Cleaned up from the comment sections, with the profanity and the typos taken out and the reasoning left in.
7. The high end on purpose, to give blue the best chance.
8. Engel's meta-study of dictator games (129 papers, 41,433 observations) puts average giving at 28% of the pot. Engel, 2011. The mean flatters: a third of dictators give nothing. Costly altruism toward strangers runs far lower. Non-directed kidney donors, who give a kidney to someone they will never meet, numbered 387 in the entire United States in 2019. OPTN data, Jan et al. 2022.
9. World Values Survey, Wave 7 (2017-2022), Question Q57: "Generally speaking, would you say that most people can be trusted or that you need to be very careful in dealing with people?" worldvaluessurvey.org. Denmark itself is not in Wave 7; its figure comes from the European Values Study 2017, merged into the same series.
10. The corroboration, three different instruments: the Integrated Values Surveys put Denmark at 73.9% (2022, via Our World in Data); the OECD's 2023 Trust Survey at 75%; and a rescaled European Social Survey reading at 77.3% (2018). Behaviorally, in the trust game (the money you hand over is multiplied before the other player decides what to return), senders part with about half across 162 studies. Johnson & Mislin, 2011.
11. Trust and altruism are drawn from Beta distributions around each nation's mean (concentration 7). An agent presses blue when trust × (1 + altruism) ≥ 1, the risk-neutral expected-value rule at altruism a = 0.28. Blue wins only if more than half of everyone presses it. It never did, in any country or the world. The death rate is a closed-form result, confirmed by a Monte-Carlo run at the real population, about 7 billion agents. Code and parameters are in the repository above.
12. This could have been done with a normalized hundred thousand per country, or estimated as an integral, but what's the fun in that?
13. Under the model's preset conditions: no errors, no communication, and no coercion.
14. That is, if you don't argue that the failure is the fault of the majority, and thus always a problem with selfishness.