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#decisionTheory

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AnthonyMy half-baked deep thought of the weekend:<br><br>Arrow’s Impossibility Theorem should be renamed Arrow's Context-Sensitivity Theorem, and re-interpreted as saying a social choice function that neglects context leads to dictators.<br><br>I say this because the axiom of independence from irrelevant alternatives--one of the assumptions behind the theorem--states that a social choice function should be such that the relationship between A and B is not changed once a new alternative C is introduced. Unpacked, this means the choice function should be insensitive to any context C might bring with it.<br><br>Arrow's theorem essentially says that a social choice function satisfying this and a couple other axioms leads to dictators (meaning, one individual's preferences dictate the social choice function's preferences, overruling everyone else involved in the choice who might disagree). Hence the re-interpretation: neglecting context in social choice leads to dictators.<br><br><a href="https://buc.ci?t=economics" class="mention hashtag" rel="nofollow noopener" target="_blank">#economics</a> <a href="https://buc.ci?t=socialwelfare" class="mention hashtag" rel="nofollow noopener" target="_blank">#SocialWelfare</a> <a href="https://buc.ci?t=socialchoice" class="mention hashtag" rel="nofollow noopener" target="_blank">#SocialChoice</a> <a href="https://buc.ci?t=welfareeconomics" class="mention hashtag" rel="nofollow noopener" target="_blank">#WelfareEconomics</a> <a href="https://buc.ci?t=decisiontheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#DecisionTheory</a> <a href="https://buc.ci?t=arrowstheorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#ArrowsTheorem</a><br>
Nick Byrd, Ph.D.<p>Jon Baron shared Peter Wakker's annotated bibliography of <a href="https://nerdculture.de/tags/decisionTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decisionTheory</span></a></p><p>&gt; 9000 entries!</p><p>DocX <a href="http://personal.eur.nl/wakker/refs/webrfrncs.docx" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">personal.eur.nl/wakker/refs/we</span><span class="invisible">brfrncs.docx</span></a></p><p>PDF <a href="http://personal.eur.nl/wakker/refs/webrfrncs.pdf" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">personal.eur.nl/wakker/refs/we</span><span class="invisible">brfrncs.pdf</span></a></p><p>BibTeX (no annotations, I merged redundancies) <a href="https://www.dropbox.com/scl/fi/vbkki82h62ydq0fol1g8d/Decision-Theory.bib?rlkey=84m8zx3tyaa4uy6p0zptkybnx&amp;st=qx9myebb&amp;dl=0" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">dropbox.com/scl/fi/vbkki82h62y</span><span class="invisible">dq0fol1g8d/Decision-Theory.bib?rlkey=84m8zx3tyaa4uy6p0zptkybnx&amp;st=qx9myebb&amp;dl=0</span></a></p><p><a href="https://nerdculture.de/tags/cogSci" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>cogSci</span></a> <a href="https://nerdculture.de/tags/decisionScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decisionScience</span></a> <a href="https://nerdculture.de/tags/epistemology" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>epistemology</span></a> <a href="https://nerdculture.de/tags/philSci" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>philSci</span></a> <a href="https://nerdculture.de/tags/library" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>library</span></a></p>
AnthonyToday I heard an anecdote about the <a href="https://en.wikipedia.org/wiki/Monty_Hall_problem" rel="nofollow noopener" target="_blank">Monty Hall problem</a>. Apparently Monty Hall himself was once asked his thoughts about the formal version of the problem, and his response was that it was in no way faithful to the game show problem from which it takes its name.<br><br>Where does the formal version fall short? Monty himself actively tried to mislead the contestant. He knew them, and tried to persuade them. This was a key part of the game. He said the formal model kills all the suspense. It'd be too boring to watch.<br><br>In other words, Monty Hall operated in a large world and it's in that context the Monty Hall problem is interesting, whereas the formal "Monty Hall problem" chops it down to a small world that is not faithful to the real world version of the problem, and on top of it all is boring.<br><br><a href="https://buc.ci?t=ecologicalrationality" class="mention hashtag" rel="nofollow noopener" target="_blank">#EcologicalRationality</a> <a href="https://buc.ci?t=largeworlds" class="mention hashtag" rel="nofollow noopener" target="_blank">#LargeWorlds</a> <a href="https://buc.ci?t=smallworlds" class="mention hashtag" rel="nofollow noopener" target="_blank">#SmallWorlds</a> <a href="https://buc.ci?t=modeling" class="mention hashtag" rel="nofollow noopener" target="_blank">#modeling</a> <a href="https://buc.ci?t=decisiontheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#DecisionTheory</a> <a href="https://buc.ci?t=choicetheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#ChoiceTheory</a> <a href="https://buc.ci?t=rationalchoicetheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#RationalChoiceTheory</a> <a href="https://buc.ci?t=montyhallproblem" class="mention hashtag" rel="nofollow noopener" target="_blank">#MontyHallProblem</a><br>