I think that you’re asking when would you check that your graph is complete in a real world case, sorry if I misunderstood.
If so, take the question of whether global warming is anthropogenic. There are people who claim to have evidence that it is and people who claim to have evidence that it isn’t so the basic diagram that we have for this case is a paradox diagram similar to that in figure 2 of the article above. Now there are a number of possible responses to this: Some people could be stuck on the paradox diagram and be unsure as to the right answer, some people may have invalidated one or the other side of the argument and may have decided one or the other claim is true, and some may be adding more and more proofs to one side or the other—countering rather than invalidating.
I think there’s also a fourth group who’s belief graph will look the same as those who have invalidated one side and have hence reached a conclusion. However, these will be people who, while they may technically know that arguments exist for the negation of their belief, have not taken opposing notions into account in their belief graph. So to them, it will look like a graph demonstrating the truth of their belief but, in fact, it’s simply an incomplete paradox graph and they have some distance to go to figure out the truth of the matter.
So to summarise: I think there are people on both sides of the anthropogenic global warming debate who know that purported proofs against their beliefs exist on one level but who don’t factor these into their belief graphs. I think they could benefit from asking themselves whether their graph is complete.
I should mention that this particular case isn’t what motivated the post—in some ways I worry that by providing specific examples people stop judging an idea on its merit and start judging it based on their beliefs regarding the example mentioned and how they feel this is meant to tie in with the idea. Regardless, I could be mistaken. Is it considered a good idea to always provide real world example in LW posts on rationality techniques?
Or if you meant a more personal example then at my work there’s currently a debate over whether a proposed electronic system will work. I’m one of the few people that thinks it won’t (and I have some arguments to support that) but I haven’t invalidated any arguments that show it will work, I simply haven’t come across any such arguments. But it’s a circumstance where I might benefit from asking, is my graph complete?
As a side note, I think the technique can also be extended to other circumstances. For example, some aspects of Eliezer’s Guessing the teacher’s password could be modelled by a “Password Graph” a graph like those above but where the truth of both A and not-A go through the same proof (say P1 for example). If you have a proof for A then you could ask if you have an incomplete Password graph because, if so, you could be in trouble. So you could extend the circumstances where the question applies by asking if you have completed any of a number of graphs. Of course, doing so comes at the cost of simplicity.
I think that you’re asking when would you check that your graph is complete in a real world case, sorry if I misunderstood.
If so, take the question of whether global warming is anthropogenic. There are people who claim to have evidence that it is and people who claim to have evidence that it isn’t so the basic diagram that we have for this case is a paradox diagram similar to that in figure 2 of the article above. Now there are a number of possible responses to this: Some people could be stuck on the paradox diagram and be unsure as to the right answer, some people may have invalidated one or the other side of the argument and may have decided one or the other claim is true, and some may be adding more and more proofs to one side or the other—countering rather than invalidating.
I think there’s also a fourth group who’s belief graph will look the same as those who have invalidated one side and have hence reached a conclusion. However, these will be people who, while they may technically know that arguments exist for the negation of their belief, have not taken opposing notions into account in their belief graph. So to them, it will look like a graph demonstrating the truth of their belief but, in fact, it’s simply an incomplete paradox graph and they have some distance to go to figure out the truth of the matter.
So to summarise: I think there are people on both sides of the anthropogenic global warming debate who know that purported proofs against their beliefs exist on one level but who don’t factor these into their belief graphs. I think they could benefit from asking themselves whether their graph is complete.
I should mention that this particular case isn’t what motivated the post—in some ways I worry that by providing specific examples people stop judging an idea on its merit and start judging it based on their beliefs regarding the example mentioned and how they feel this is meant to tie in with the idea. Regardless, I could be mistaken. Is it considered a good idea to always provide real world example in LW posts on rationality techniques?
Or if you meant a more personal example then at my work there’s currently a debate over whether a proposed electronic system will work. I’m one of the few people that thinks it won’t (and I have some arguments to support that) but I haven’t invalidated any arguments that show it will work, I simply haven’t come across any such arguments. But it’s a circumstance where I might benefit from asking, is my graph complete?
As a side note, I think the technique can also be extended to other circumstances. For example, some aspects of Eliezer’s Guessing the teacher’s password could be modelled by a “Password Graph” a graph like those above but where the truth of both A and not-A go through the same proof (say P1 for example). If you have a proof for A then you could ask if you have an incomplete Password graph because, if so, you could be in trouble. So you could extend the circumstances where the question applies by asking if you have completed any of a number of graphs. Of course, doing so comes at the cost of simplicity.