One issue is that people often spend a lot of time arguing about things that aren’t cruxes for either of them. Two people who disagree about whether to increase the top marignal tax rate might get into a back-and-forth about the extent to the higher rate will lead to rich people hiding their money in offshore banks, when the answer to that question wouldn’t shift either of their views. Maybe they’re talking about that topic because it seems like a it should be an important consideration (even though it isn’t crucial for either of them). Maybe one of them mentioned the topic briefly as part of a longer argument, and said something about it that the other person disagreed with and therefore responded to. Maybe one of them guessed that it was a crux for the other person and therefore chose to bring it up. Whatever the reason, this subtopic is mostly a waste of time and a distraction from a potentially more interesting conversation that they could be having. Focusing on cruxes helps to avoid these sidetracks because each person is frequently checking “is this a crux for me?” and occasionally asking “is that a crux for you?” (or some reduced-jargon alternative, like “So if you imagine one world where raising the top rate would mostly just lead to rich people hiding their money in offshore banks, and another world where that didn’t happen, would your view on raising the rate be the same in both of those worlds?”).
Focusing on your cruxes also flips around the typical dynamic of a disagreement. Normally, if Alice and Bob disagree about something, then for the most part Alice is trying to change Bob’s mind and Bob is trying to change Alice’s mind. If Alice is used to thinking about her cruxes, Alice can instead mostly be trying to change Alice’s mind. “Raising the top marginal tax rate seems to me like a good idea, but Bob thinks otherwise—maybe there’s something I’m missing?” Alice understands Alice’s mind a lot better than Bob does, so she has the advantage in looking for what sorts of information might shift her views. Bob is helping her doing it, collaboratively, noticing the places where her thinking seems funny, or where she seems to be missing information, or where her model of the world is different from his, and so on. But this looks very different from Bob taking the lead on changing Alice’s views by taking his best guesses, often going mainly on his priors about what things tax-rate-increasers tend to be wrong about.
Obviously this is not the best way to approach every disagreement. In cases like negotiation you have other goals besides “improve my model of this aspect of the world”, if you don’t have much respect for Bob’s thinking then it may not be worth the trouble, and in online discussions with many people and lots of time lag this approach may be impractical. But in cases where you really care about getting the right answer (e.g., because your career success depends on it), and where the other person’s head seems like one of the better sources of information available to you, focusing on your cruxes in a conversation about disagreements can be a valuable approach to take.
(I still haven’t gotten into “double crux”, and am not planning to.)
How are cruxes relevant in disagreements?
One issue is that people often spend a lot of time arguing about things that aren’t cruxes for either of them. Two people who disagree about whether to increase the top marignal tax rate might get into a back-and-forth about the extent to the higher rate will lead to rich people hiding their money in offshore banks, when the answer to that question wouldn’t shift either of their views. Maybe they’re talking about that topic because it seems like a it should be an important consideration (even though it isn’t crucial for either of them). Maybe one of them mentioned the topic briefly as part of a longer argument, and said something about it that the other person disagreed with and therefore responded to. Maybe one of them guessed that it was a crux for the other person and therefore chose to bring it up. Whatever the reason, this subtopic is mostly a waste of time and a distraction from a potentially more interesting conversation that they could be having. Focusing on cruxes helps to avoid these sidetracks because each person is frequently checking “is this a crux for me?” and occasionally asking “is that a crux for you?” (or some reduced-jargon alternative, like “So if you imagine one world where raising the top rate would mostly just lead to rich people hiding their money in offshore banks, and another world where that didn’t happen, would your view on raising the rate be the same in both of those worlds?”).
Focusing on your cruxes also flips around the typical dynamic of a disagreement. Normally, if Alice and Bob disagree about something, then for the most part Alice is trying to change Bob’s mind and Bob is trying to change Alice’s mind. If Alice is used to thinking about her cruxes, Alice can instead mostly be trying to change Alice’s mind. “Raising the top marginal tax rate seems to me like a good idea, but Bob thinks otherwise—maybe there’s something I’m missing?” Alice understands Alice’s mind a lot better than Bob does, so she has the advantage in looking for what sorts of information might shift her views. Bob is helping her doing it, collaboratively, noticing the places where her thinking seems funny, or where she seems to be missing information, or where her model of the world is different from his, and so on. But this looks very different from Bob taking the lead on changing Alice’s views by taking his best guesses, often going mainly on his priors about what things tax-rate-increasers tend to be wrong about.
Obviously this is not the best way to approach every disagreement. In cases like negotiation you have other goals besides “improve my model of this aspect of the world”, if you don’t have much respect for Bob’s thinking then it may not be worth the trouble, and in online discussions with many people and lots of time lag this approach may be impractical. But in cases where you really care about getting the right answer (e.g., because your career success depends on it), and where the other person’s head seems like one of the better sources of information available to you, focusing on your cruxes in a conversation about disagreements can be a valuable approach to take.
(I still haven’t gotten into “double crux”, and am not planning to.)