So if there’s a crux 1⁄3 of the time, and if my having a crux and your having a crux are independent (they surely aren’t, but it’s not obvious to me which way the correlation goes), we expect there to be cruxes on both sides about 10% of the time, which means it seems like it would be surprising if there were an available double-crux more than about 5% of the time. Does that seem plausible in view of CFAR experience?
Of course double-cruxing could be a valuable technique in many cases where there isn’t actually a double-crux to be found: it encourages both participants to understand the structure of their beliefs better, to go out of the way to look for things that might refute or weaken them, to pay attention to one another’s positions … What do you say to the idea that the real value in double-cruxing isn’t so much that sometimes you find double-cruxes, as that even when you don’t it usually helps you both understand the disagreement better and engage productively with one another?
Actually finding a legit double crux (i.e. a B that both parties disagree on, that is a crux for A that both parties disagree on) happening in the neighborhood of 5% of the time sounds about right.
More and more, CFAR leaned toward “the spirit of double crux,” i.e. seek to move toward getting resolution on your own cruxes, look for more concrete and more falsifiable things, assume your partner has reasons for their beliefs, try to do less adversarial obscuring of your belief structure, rather than “literally play the double crux game.”
Interesting.
So if there’s a crux 1⁄3 of the time, and if my having a crux and your having a crux are independent (they surely aren’t, but it’s not obvious to me which way the correlation goes), we expect there to be cruxes on both sides about 10% of the time, which means it seems like it would be surprising if there were an available double-crux more than about 5% of the time. Does that seem plausible in view of CFAR experience?
Of course double-cruxing could be a valuable technique in many cases where there isn’t actually a double-crux to be found: it encourages both participants to understand the structure of their beliefs better, to go out of the way to look for things that might refute or weaken them, to pay attention to one another’s positions … What do you say to the idea that the real value in double-cruxing isn’t so much that sometimes you find double-cruxes, as that even when you don’t it usually helps you both understand the disagreement better and engage productively with one another?
Actually finding a legit double crux (i.e. a B that both parties disagree on, that is a crux for A that both parties disagree on) happening in the neighborhood of 5% of the time sounds about right.
More and more, CFAR leaned toward “the spirit of double crux,” i.e. seek to move toward getting resolution on your own cruxes, look for more concrete and more falsifiable things, assume your partner has reasons for their beliefs, try to do less adversarial obscuring of your belief structure, rather than “literally play the double crux game.”