http://peteg.org/blog en http://peteg.org/blog/2008/11/09#2008-11-09-MaysTheorem /choice/social-choice <p> <a href="http://www4.in.tum.de/~nipkow/">Tobias Nipkow</a> has written an <a href="http://www4.informatik.tu-muenchen.de/~nipkow/pubs/arrow.html">article</a> about mechanising some recent proofs of <a href="http://en.wikipedia.org/wiki/Arrow's_impossibility_theorem">Arrow's Theorem</a> and <a href="http://en.wikipedia.org/wiki/Gibbard-Satterthwaite_theorem">Gibbard-Satterthwaite</a> in <a href="http://isabelle.in.tum.de/">Isabelle</a>, and has kindly cited my clumsy attempts at similar things. In an attempt at differentiation I have polished up my proofs from Sen's magnum opus and added one of <a href="http://en.wikipedia.org/wiki/May%E2%80%99s_theorem">May's Theorem</a>. As one might expect from a positive result in social choice theory there are endless reworkings of the original conditions in the literature since 1952, and I am not entirely sure what the state of the art is. </p><p> The proof itself is fairly straightfoward, although Sen makes an uncharacteristic slip by unnecessarily arguing by contradition in his proof of my <code>anonymous_neutral_indifference</code>. When I'm next bored and idle I'll see if that makes any difference in the bigger scheme of things. </p><p> The hope is to get all of this into the <a href="http://afp.sourceforge.net/" class="title">Archive of Formal Proofs</a> and obtain some feedback on the nastier parts of the mechanisation. </p><p> Once more: </p><dl> <dt><a href="http://peteg.org//static/arrows_theorem.pdf">arrows_theorem.pdf</a> </dt> <dd>An <a href="http://isabelle.in.tum.de/">Isabelle</a>-generated document of the development.</dd> <dt><code>darcs get http://peteg.org/isabelle/arrows_theorem/</code> </dt> <dd>A <a href="http://darcs.net/">darcs</a> repository for the development. </dd> </dl> <p> An interested soul has written a great <a href="http://www66.homepage.villanova.edu/thomas.bartlow/history/SocialChoice/KOMay.htm">overview of May's life work</a>. </p> http://peteg.org/blog/2008/05/05#2008-05-05-ArrowBook /choice/social-choice <p> Amazing stuff, one can now get a whole pile of old economics monographs for free off the internet. The drawcard is <a href="http://nobelprize.org/nobel_prizes/economics/laureates/1972/arrow-autobio.html">Kenneth Arrow</a>'s <a href="http://cowles.econ.yale.edu/P/cm/m12-2/index.htm" class="title">Social Choice and Individual Values</a>. <em>Pulls the spare life out of the back pocket and is not seen for the next twenty years.</em> </p>