• (Meanwhile, doublecrux is not guaranteed to be faster for 3+ people to converge but I still expect it to be faster for smallish groups with particularly confusing disagreements)

Conjecture: The amount of time it takes to use double crux as a group can be lower bounded by the amount of time it takes every pair to double crux. If we assume the amount of time for every pair is the same (which it isn’t), and call that amount of time t, then the lower bound is t*n(n-1)/​2. (Because n choose 2 = n(n-1)/​2.)

If 10 people tried this and 6 of them told me it didn’t feel useful, even superficially, I’d probably change my mind significantly. If they tried it continuously for a year and there weren’t at least 3 of them that could point to transparently useful outcomes, (such as disagreements taking much less time than they’d naively predict), I’d also significantly change my beliefs here.

There’s also the possibility that it turns out to be a) useful for some people, but not others, b) useful**, but for something other than double crux*, c) this is an area where gains take time—perhaps past some threshold of low hanging fruit.

*Perhaps calibration, or understanding one’s own beliefs better.

**The real question is if the effects are strong enough to be useful.

EDIT: I meant to write “upper bound”.

• To me that n choose 2 is more of an upper bound. If each 1-on-1 didn’t hear each other and they were not ordered then the time to do those would be the same as randomly picking people to discuss. But in a group discussion the discussion can hear each others. In a simple case where there are only 2 true factions but each faction has 50 members you could have the whole group crux if 1 member from different factions cruxed and others listened and the chosen ones were perfectly representative of their factions. To the extent there is faction internal strife you can’t reuse per se the previous discussion. The least copyfriendly case is when everything needs to be done fresh for each member in which case it doesn’ t matter if 1-on-1 discussion do not hear the group discussion.

On one hand adding additonal participant means it’s another dice throw from what random position they start from which can be in additional dimensions not yet exhibited. On the other hand each thing said can be listened multiple times in the same time frame (or reverse each listener can only receive 1/​n amount of talk that is relevant to their beliefs).

• Conjecture: The amount of time it takes to use double crux as a group can be lower bounded by the amount of time it takes every pair to double crux. If we assume the amount of time for every pair is the same (which it isn’t), and call that amount of time t, then the lower bound is t*n(n-1)/​2. (Because n choose 2 = n(n-1)/​2.)

“How much time it’d take to pairwise doublecrux” seems like a useful detail, but doesn’t seem like either an upper or lower bound. (I think it works as “this is approximately how long you should expect things to take on average”, with some debates taking longer and some shorter)

Things might take longer, because maybe if everyone pairwise doublecruxes, each pair ends up disagreeing with other pairs due to idiosyncratic beliefs or personal-history that other pairs didn’t share.

Things might take less time, because multiple people in the group might share enough beliefs that they can functionally share updates.

i.e. if Alice, Bob, Catherine and Doug all doublecrux, it might be that once Alice and Bob have doublecruxed, Alice can easily say to Catherine (who has a similar worldview ‘Bob explained this to me, it works like X’, where X uses some shorthand that Alice and Catherine already share.

• There’s also the possibility that it turns out to be a) useful for some people, but not others, b) useful**, but for something other than double crux*, c) this is an area where gains take time—perhaps past some threshold of low hanging fruit.

Yup. The cruxes I listed there would not shift me to “this is useless”, but they would shift me to “I retract my blanket endorsement of this strategy for everyone who reads LessWrong.”

• By useful I primarily* meant “worth a blanket endorsement of this strategy for everyone who reads LessWrong” but for different reasons.

*This was “b”