Red Button, Blue Button

On April 24th, 2026, Tim Urban put forth the following poll on Twitter/X:

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?

I love this dilemma, and I'm exhausted by it. I’ve been thinking about it for two straight weeks, and have spent nearly all that time refining my thoughts by writing this piece. It's consumed me in a way that I've never before experienced with any math problem, and I need to get it out of my head.

Discourse surrounding the Button Dilemma reminds me of polarizingly political topics. In much the same way that political discussions make people go funny in the head, answers to the Button Dilemma tend to elicit vitriol from people of both Red and Blue conviction. Everyone feels their answer is clear, and everyone is confounded by the lack of consensus.

I think this dilemma is pointing to something very important and fundamental about coordination problems. [...]

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Outline:

(00:09) Red Button, Blue Button

(01:46) What Are We Even Arguing About?

(07:24) A Fair Way To Look At It

(12:55) Playing With τ and N

(16:29) Extreme Sawtooth Problems

(18:52) Axiomatic Expansion of Sawtooth Space

(22:02) The Map

(22:18) Our Parameters

(24:00) Regions of the Map