tag:blogger.com,1999:blog-4978426466915379555.post1590470039689836920..comments2015-12-24T10:17:39.421-05:00Comments on Formal Methods in Political Philosophy: COLLECTIVE CHOICE THEORY FIRST INSTALLMENTRobert Paul Wolffhttp://www.blogger.com/profile/11970360952872431856noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-4978426466915379555.post-8794685539513095672011-02-10T09:21:53.755-05:002011-02-10T09:21:53.755-05:00What's a preference order? And how do I know ...What's a preference order? And how do I know that I have one? It's supposed to play a role in the rational decision making that I make: in my beliefs about what I should do, or what I shouldn't, if I am to be a rational agent. And, of course, I want to be a rational agent. Should I pay for the beer that I just bought at the bar, or not? Should I vote in the upcoming election, or not?thealcoholicshttp://www.blogger.com/profile/02542234961775042666noreply@blogger.comtag:blogger.com,1999:blog-4978426466915379555.post-33482715149226108552010-07-17T11:33:35.243-04:002010-07-17T11:33:35.243-04:00Marinus, that is a really funny typo. I am almost...Marinus, that is a really funny typo. I am almost tempted to leave it, but I guess I better fix it. Vlasits, you are of course correct. For the paradox, the number of alternatives must be greater than 2.Robert Paul Wolffhttp://www.blogger.com/profile/11970360952872431856noreply@blogger.comtag:blogger.com,1999:blog-4978426466915379555.post-72893507793868697992010-07-17T11:19:08.277-04:002010-07-17T11:19:08.277-04:00Question (maybe this should be answered later): it...Question (maybe this should be answered later): it seems from the kind of preferences needed for the paradox majority voting, the cardinality of S must be greater than 2. Could there be proof that when voting over two options, all of the population's preferences can map into a social preference order satisfying all of the desired axioms? I know that this case is so particular that it would rarely (never) apply, but it would be an interesting formal result nonetheless.J.Vlasitshttp://www.blogger.com/profile/10340794410334308312noreply@blogger.comtag:blogger.com,1999:blog-4978426466915379555.post-49175039560813923892010-07-16T20:13:06.110-04:002010-07-16T20:13:06.110-04:00There's a small typo where you introduce the C...There's a small typo where you introduce the Condorcet example:<br /><br />"X prefers a to <b>be</b> and b to c. Since X is minimally rational, he also prefers a to c."<br /><br />I had a double take there till I realised 'be' should be 'b'.Marinushttp://www.blogger.com/profile/13492009758043047531noreply@blogger.comtag:blogger.com,1999:blog-4978426466915379555.post-40150325247584938892010-07-16T18:22:39.905-04:002010-07-16T18:22:39.905-04:00For the second vote in the paradox, why is their p...For the second vote in the paradox, why is their preference about the ordering of {b,c} used to determine how they will vote? They already know that they have voted for a ahead of b. So, you would think that their second vote would be determined by their preferences between (a,b,c), (a,c,b), and (c,a,b). But you haven't said anything about their preferences between those.<br /><br />On a related note, why is preference only treated as a binary relation?Brianhttp://www.blogger.com/profile/05521670453253394589noreply@blogger.comtag:blogger.com,1999:blog-4978426466915379555.post-86321119748974840092010-07-16T09:20:27.540-04:002010-07-16T09:20:27.540-04:00OK. I have changed it. Check it to make sure it ...OK. I have changed it. Check it to make sure it makes sense now.Robert Paul Wolffhttp://www.blogger.com/profile/11970360952872431856noreply@blogger.comtag:blogger.com,1999:blog-4978426466915379555.post-84623733703914580812010-07-16T09:18:07.747-04:002010-07-16T09:18:07.747-04:00Rats. yes, that is right. I will fix it right aw...Rats. yes, that is right. I will fix it right away. Sorry about thatRobert Paul Wolffhttp://www.blogger.com/profile/11970360952872431856noreply@blogger.comtag:blogger.com,1999:blog-4978426466915379555.post-46667426806263643262010-07-16T06:55:33.873-04:002010-07-16T06:55:33.873-04:00C(S) is the set of all alternatives in the Environ...<em>C(S) is the set of all alternatives in the Environment S such that, for every x and y in S, xRy.</em><br /><br />This seems garbled. For one thing, nothing after the `such that' appears to depend on C(S) in any way. For another, the definition implies that everything is S is ranked as good or as better than everything in S, which rules out transitivity right off the bat. <br /><br />Perhaps it's supposed to be something like this: C(S) is a subset of the environment S such that, for every x in C(S) and y in S, xRy?Noumenahttp://www.blogger.com/profile/02442204504120141558noreply@blogger.com