tag:blogger.com,1999:blog-11367545.post3581217070958515245..comments2021-01-25T04:00:36.502-05:00Comments on EricHerboso.org: The Double-Crux GameEric Herbosohttp://www.blogger.com/profile/07888413471076959781noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-11367545.post-21457529700886838642018-07-09T13:40:11.627-04:002018-07-09T13:40:11.627-04:00There is an updated version of that prezi with som...There is an updated version of that prezi with some additional rationality techniques/concepts outlined, rationalist taboo, steel-manning and inferential distance<br /><br />I'll hopefully be fixing some typos etc and including a link some exercises I put together for when I deliver this presentation as a workshop at some point.<br /><br />https://prezi.com/_er3ebasdwr5/better-disagreement-2/<br /><br />(I did actually remove the slide you used from by old presentation as I found the formalish logic was bit intimidating for some in my audiences)<br /><br />glad to see someone found my prezi useful - only just found this post ~2yrs after the factRichard J. Actonhttps://www.blogger.com/profile/16122308422217420449noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-41153875003931214342016-07-12T15:32:08.897-04:002016-07-12T15:32:08.897-04:00Whoops, I'm not sure where I got A<=>B f...Whoops, I'm not sure where I got A<=>B from. Sorry about that. Anyway, it sounds as if I was right to take it that a crux of A is something you think is implied by A.<br /><br />The fully-calculated Bayesian version of double-cruxing sounds like a lot of Not Fun in general, so I endorse your suggestion of not bothering with intermediate degrees of credence for propositions other than the original -- in which case, it seems like the thing to look for is propositions that we're *very confident* are necessary for our positions on the contentious proposition to be right.<br /><br />An obvious difficulty here is that there's a reason why those probabilities tend to come out not-very-different: nontrivial chains of reasoning where all the steps are uncertain aren't, and shouldn't be, very convincing. What it should take to convince you in such cases is different in shape from what it takes to convince you when you have a watertight chain of logical inference.<br /><br />(In other words, if you can't find suitable propositions that follow almost-certainly from the thing you disagree on, double-cruxing probably isn't actually the best way to resolve your disagreement.)<br /><br />I'm not sure I understand your use of the term "confidence interval" here, by the way. Those things in your calculations look to me like probabilities, not confidence intervals.ghttps://www.mccaughan.org.uk/g/noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-71862160108161924742016-07-11T01:28:43.569-04:002016-07-11T01:28:43.569-04:00The problem that you pointed out is that the p(C) ...The problem that you pointed out is that the p(C) values aren’t the same, so it’s at first unclear how to treat C as a double crux. However, you can still use C as a double crux — you just have to multiply out the confidence interval. Using the values that I provided (on purpose) here, this makes the end result somewhat unsatisfactory, as the disagreement on p(C) is .89 for me and .81 for you, which is quite similar to each other. If you were to nest a few additional double cruxes in, you may find that the difference between your confidence in some future proposition p(Z) and my confidence in that same proposition might be nearly identical.<br /><br />To correct for this, there’s an additional rule in finding a double crux: it has to result in a significant difference in confidence intervals between the two players. This is harder to do than it sounds, and it doesn’t exactly sound easy to do.<br /><br />Because I enjoy the double crux game as a social game to help resolve disagreements, I tend to just stick to only using confidence intervals in the first proposition, but not subsequent ones. That way it is easier to explain to people, it’s more fun to play, and it makes finding shared cruxes much easier. When I play, it’s more likely to get people to understand each others’ differences than to actually change someone’s mind, mostly because finding double cruxes is hard enough in the boolean version of the game.<br /><br />If you find a better explanation of how to play the double crux game using confidence intervals somewhere online, please link it here so that future people can see it as well.Eric Herbosohttps://www.blogger.com/profile/07888413471076959781noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-47223549065191557382016-07-11T01:28:16.389-04:002016-07-11T01:28:16.389-04:00Your second question is much more complicated to a...Your second question is much more complicated to answer. It involves confidence intervals of nested propositions that you have to calculate twice at each step, so that when you find the final proposition Z that you can look up, you can see which of the two probability estimates is closer to reality. The domino-falling effect of changing confidence levels still occurs, but it rarely resolves to completely changing one’s mind on the original proposition; it just modifies the confidence interval by some calculated amount. Plus it requires an additional rule to finding a good double crux at each step.<br /><br />My best recommendation is to go in-person to a CFAR event that teaches the double crux algorithm (like the one Amodei taught at EAG Oxford: <a href="https://docs.google.com/presentation/d/1CDA5GWVvM0ioIpRTJ83N4QNeXSV7l1TRPA50xVXEmUU" rel="nofollow">https://docs.google.com/presentation/d/1CDA5GWVvM0ioIpRTJ83N4QNeXSV7l1TRPA50xVXEmUU</a>), as I’m not sure how to effectively convey what I know in a blog post comment. But I’ll try to post a few thoughts anyway, just in case some of it helps you or another reader detail the idea in full.<br /><br />First, ensure that both players have calibrated their credence well. See <a href="http://acritch.com/credence-game/" rel="nofollow">http://acritch.com/credence-game/</a> or <a href="http://lesswrong.com/lw/hak/link_how_to_calibrate_your_confidence_intervals/" rel="nofollow">http://lesswrong.com/lw/hak/link_how_to_calibrate_your_confidence_intervals/</a>. Then try it out first with only using a confidence interval for the initial proposition A, not other propositions. This makes the math easier.<br /><br />Example: I’m 70% confident in A; you’re 30%. We find a double crux B such that A→B for me and ¬A→¬B for you. Therefore here are our beliefs:<br /><br />Eric: <b>p(A)=.7</b> ; <b>A→B</b> ; <b>p(B|A)=1</b>. Therefore: <b>p(B)=.7</b>.<br /><br />G: <b>p(¬A)=.7</b> ; <b>¬A→¬B</b> ; <b>p(¬B|¬A)=1</b>. Therefore: <b>p(¬B)=.7</b>.<br /><br />Then, once you’re able to do the above well, you can move on to allowing confidence intervals on nested propositions, but require forced agreement on supporting facts. For example, let’s say we find a double crux C such that follows from A 75% of the time if A is false, but 95% of the time if A is true. This would mean the beliefs would be:<br /><br />Shared beliefs: <b>p(C|¬A)=.75</b> ; <b>p(C|A)=.95</b><br /><br />Eric: <b>p(A)=.7</b> ; <b>p(C)=.89</b> (calculated)) ; <b>A→C</b> (per shared beliefs).<br /><br />G: <b>p(¬A)=.7</b> ; <b>p(¬C)=.19</b> (calculated) ; <b>¬A→¬C</b> (per shared beliefs).<br /><br />The p(C) values for each of us would be found by multiplying out the confidence intervals, like so: <em>(.75)(.3)+(.95)(.7) = .89</em>.Eric Herbosohttps://www.blogger.com/profile/07888413471076959781noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-39902635471321868452016-07-11T01:21:13.301-04:002016-07-11T01:21:13.301-04:00Regarding your first question:
No one needs to be...Regarding your first question:<br /><br />No one needs to believe A↔B. We’re only looking for sufficient conditions, not necessary ones. One person believes A→B and another believes B→A, but neither need believe both simultaneously. If Peter and Dorek are playing, then these are the beliefs they’d need to have:<br /><br />Peter: <b>A</b> ; <b>B</b> ; <b>A→B</b>. By modus tollens, Peter would also believe <b>¬B→¬A</b>.<br /><br />Dorek: <b>¬A</b> ; <b>¬B</b> ; <b>¬A→¬B</b>. By modus tollens, Dorek would also believe <b>B→A</b>.<br /><br />An example may help here. Let’s say Peter believes traditional Greek mythology is true, whereas Dorek believes Roman mythology is true. So Peter and Dorek decide to play the double crux game with the proposition A: “traditional Greek mythology is true”. To start with, Peter believes A and Dorek believes ¬A.<br /><br />Now the two of them individually start looking for (single) cruxes of their belief. This means Peter is looking for a new statement B such that A→B. Once found, modus tollens will inform Peter that ¬B→¬A as well.<br /><br />So Peter thinks: if greek myths are true, then Zeus is the king of all gods. This will be Peter’s single crux B: “Zeus is the king of all gods.” Peter believes both B and A→B, so this works as a single crux. Peter mentions this as a possible double crux for Dorek.<br /><br />So Dorek thinks: Zeus is not the king of all gods; Jupiter is. So Dorek believes ¬B. Also, if greek myths are not true, then zeus is unlikely to be the king of all gods. So ¬A→¬B. (<em>Note that this uses a probability estimate, not a logical certainty, but that nevertheless works for the double crux game.</em>) By modus tollens, Dorek also believes B→A.<br /><br />Thus they have found their double crux: B. Peter believes A, B, and ¬B→¬A; while Dorek believes ¬A, ¬B, and B→A.<br /><br />To finish the game, they visit a trusted oracle and ask if Zeus is the king of all gods. The oracle says no, so they now know ¬B. Because Peter already agreed that ¬B→¬A, Peter updates his belief from A to ¬A.Eric Herbosohttps://www.blogger.com/profile/07888413471076959781noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-7182090936784405962016-07-10T19:37:34.366-04:002016-07-10T19:37:34.366-04:00(Sorry, I'm coming to this long after it was p...(Sorry, I'm coming to this long after it was posted. Perhaps no one's reading any more.)<br /><br />Could someone clarify a couple of things?<br /><br />1. If I understand right, a "double crux" of a proposition A means another proposition B for which you think A => B and B => A. But the post also refers to a "crux" and doesn't explain its terminology. Does it mean a proposition B for which you think A => B? (So that not-B => not-A, so that refuting B would require you to abandon belief in A.) Or something else?<br /><br />2. The post suggests that you can play the same game when your disagreement is "softer": the two participants assign different probabilities to some proposition, but they aren't 0% and 100%. In this case, what happens to the notions of "crux" and "double-crux"? I mean, suppose we are arguing about whether freebles are glorkish; I say there's a 30% chance they are and you say there's a 70% chance. Am I now looking for other statements logically equivalent to "there's a 30% chance that freebles are glorkish"? That seems impossibly specific. Or am I looking for other statements equivalent to "freebles are glorkish" and to which I assign 30% probability? Or for statements equivalent to something like "there's a less than 50% chance that freebles are glorkish", trying to find a dividing line between my position and yours?ghttps://www.mccaughan.org.uk/g/noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-12553555008946745252016-01-27T05:07:13.478-05:002016-01-27T05:07:13.478-05:00I'd try it.I'd try it.Harmanas Choprahttps://www.facebook.com/mulldrifting/posts/686787250716noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-41449159103335776652016-01-27T05:06:28.017-05:002016-01-27T05:06:28.017-05:00I'm going to do this!I'm going to do this!Lauren Leehttps://www.facebook.com/mulldrifting/posts/686787250716noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-2400592941544845452016-01-27T05:05:34.349-05:002016-01-27T05:05:34.349-05:00Do you have some semi-controversial ideas brainsto...Do you have some semi-controversial ideas brainstormed already? You might pique more targeted, action-ready interest if you share examples.Melanie Heiseyhttps://www.facebook.com/mulldrifting/posts/686787250716noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-47497828550796449562016-01-27T05:04:18.378-05:002016-01-27T05:04:18.378-05:00that sounds fun, poke me sometime to videochatthat sounds fun, poke me sometime to videochatAlice Mondayhttps://www.facebook.com/mulldrifting/posts/686787250716noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-62239843078351978252016-01-27T05:03:21.508-05:002016-01-27T05:03:21.508-05:00Sounds fun/interesting. I am down to try!Sounds fun/interesting. I am down to try!Delen Heismanhttps://www.facebook.com/mulldrifting/posts/686787250716noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-52854942587776823602016-01-27T05:02:25.659-05:002016-01-27T05:02:25.659-05:00Let's.Let's.Dave McCabehttps://www.facebook.com/mulldrifting/posts/686787250716noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-44934451464242284232016-01-27T05:01:26.690-05:002016-01-27T05:01:26.690-05:00It might be interesting to play this with the prop...It might be interesting to play this with the proposition *about* the double crux game.Melanie Heiseyhttps://www.facebook.com/mulldrifting/posts/686787250716noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-32786662938495911372016-01-27T05:00:14.251-05:002016-01-27T05:00:14.251-05:00"Your goal is to find the exact same statemen..."Your goal is to find the exact same statement B that serves as a crux for both you and your partner"<br /><br />I didn't read the preceding sentences carefully enough the first time, so for a second I thought the goal was to find B such that one person thinks B <=> A and the other person thinks B <=> !A. Or to eventually find some analogous Z.<br /><br />I think that would also be a very interesting game, if a very different one.Karl Mazurakhttps://www.facebook.com/mulldrifting/posts/686787250716noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-63651608833930160262016-01-27T04:58:41.016-05:002016-01-27T04:58:41.016-05:00I'd be interestedI'd be interestedChris Masciolihttps://www.facebook.com/mulldrifting/posts/686787250716noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-50939358030081087732016-01-27T04:57:23.206-05:002016-01-27T04:57:23.206-05:00If anyone wants to play the double crux game with ...If anyone wants to play the double crux game with me, I could use the practice!Lauren Leehttps://www.facebook.com/mulldrifting/posts/686787250716noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-30145675088541409332016-01-27T04:56:09.207-05:002016-01-27T04:56:09.207-05:00we can do this for life insurance decisionswe can do this for life insurance decisionsWendolyn Breslyn Trozzohttps://www.facebook.com/eric.trozzo/posts/10208385180650352noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-67813318654562854702016-01-27T04:54:20.758-05:002016-01-27T04:54:20.758-05:00I'm down to play! I'm just gonna say go ah...I'm down to play! I'm just gonna say go ahead and book a skype call with me, anyone who wants to: <a href="https://malcolmocean.youcanbook.me/" rel="nofollow">https://malcolmocean.youcanbook.me/</a>Malcolm Oceanhttps://malcolmocean.youcanbook.me/noreply@blogger.comtag:blogger.com,1999:blog-11367545.post-28448602044472187572016-01-27T04:52:43.823-05:002016-01-27T04:52:43.823-05:00Awesome!Awesome!Kenzi Amodeihttps://www.facebook.com/EricHerboso/posts/756326219729noreply@blogger.com