I regret naming that graph The Decision Theory Befuddler, because in retrospect I think it’s likely that a population of perfectly rational FDT agents would all independently settle on the coin toss strategy.
In a population of irrational agents, I’d assume that you’re just trying to vote against whichever side you expect to be the majority.
I feel like this might be a valid strategy if you’ve reasoned that the total population breakdown will land right at 50⁄50.
If you have any expectation to the contrary, then your best strategy is to select the color that you think will receive the fewest votes from your peers.
Edit: Ah, maybe you’re saying that the best FDT strategy is to just flip a coin? (assuming you expect your peers to all have similar decision making functions to your own)
Thank you! I spent hours just staring at what the Threshold looks like in various sawtooth problems and still managed to miss the frequency-magnitude tradeoff.
If you expect the average choice to land right at the Threshold, it does begin to feel similar to the 2-player version for arbitrary values of N. The only difference is that 100% successful Red coordination ceases to be a target you can aim for.
Really interesting stuff happening around the Threshold.
If my post acts as an attempt to persuade others to join the Blue team, or if it carries a subtext of that flavor, then I need to improve my communication skills.
While writing this post, I would regularly notice little phrases, graph choices, etc. which communicated an unnecessary Blue bias. To the best of my ability I’ve tried to minimize all of that. Alas, eliminating one’s bias from one’s communication is a continuous process. There will always be more.
I’ve raised my Blue heart to the sky, that any bias I’ve overlooked might be made obvious to others. If you’ve found it, then I’ll at least consider that last part a success.
Still, I’d like to emphasize: I do not want to persuade you to change sides. Adjusting the outcome of a sawtooth problem might be but one path toward safe resolution. If there are other paths, I expect them to be much easier to walk—provided we can find them.
I meant it when I described Red as a kind of fallback strategy for the overall population. For most of my life, I’ve seen a world drowning in Blue coordination failure. By looking at it through the framework of sawtooth space, I feel like I now see vast swaths of Red picking up the pieces of Blue hubris.
I think safely resolving a dangerous sawtooth problem essentially involves smoothing it out, such that the Threshold disappears and our choice of color becomes irrelevant.
Would I like it if you voted Blue? Of course I would. I’m a Blue. But I really don’t want you to change your vote. It feels like it would be dangerous for me to want you to change your vote. If I succeed in persuading you, and Blues nevertheless fail, then all I’ve managed to do is drag everyone a little further into the Threshold. Stay Red. The world might need you.