tag:blogger.com,1999:blog-4978426466915379555.post1743392862571641987..comments2015-12-24T10:17:39.421-05:00Comments on Formal Methods in Political Philosophy: COLLECTIVE CHOICE THEORY THIRD INSTALLMENTRobert Paul Wolffhttp://www.blogger.com/profile/11970360952872431856noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-4978426466915379555.post-75748150578140519432010-07-23T16:58:23.629-04:002010-07-23T16:58:23.629-04:00The definition of `i is decisive for (x,y)' is...The definition of `i is decisive for (x,y)' is satisfied under several circumstances that I find very counterintuitive: <br />* when yPi x; <br />* when there's a distinct individual j such that xPj y; and most counterintuitively<br />* when xPy. <br /><br />But then the antecedent of Lemma 3 is satisfied just by the fact that P is complete.Noumenahttp://www.blogger.com/profile/02442204504120141558noreply@blogger.comtag:blogger.com,1999:blog-4978426466915379555.post-36836857426143790892010-07-23T04:51:03.127-04:002010-07-23T04:51:03.127-04:00Thanks for picking up the typo. I have corrected ...Thanks for picking up the typo. I have corrected it. I don't really know why Arrow chose "decisive," except that he already was using "dictates" and "is a dictator," so he needed some term that sounds like "dictates." But what do I know?Robert Paul Wolffhttp://www.blogger.com/profile/11970360952872431856noreply@blogger.comtag:blogger.com,1999:blog-4978426466915379555.post-37437270144029771952010-07-21T10:21:38.529-04:002010-07-21T10:21:38.529-04:00Quick typo: Lemma 3: If xDy for i, the*n* zḎw for ...Quick typo: Lemma 3: If xDy for i, the*n* zḎw for i, for all z,w in S.<br /><br />I'm not sure this will make much of a difference, but I'm curious why Arrow chooses to call the relation xDy "decisive". Maybe I just don't know what the word means (possible!) but I only think of someone being decisive when she is able to, for example, break a deadlock. If you want to say that someone is decisive whenever their choice decides the social welfare function, that obviously includes cases where everyone else is against them.J.Vlasitshttp://www.blogger.com/profile/10340794410334308312noreply@blogger.com