<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="">The wiki page <a href="https://wiki.electorama.com/wiki/Maximal_elements_algorithms" class="">https://wiki.electorama.com/wiki/Maximal_elements_algorithms</a> confused me because it says (as you paraphrased) “X beats Y pairwise for the Schwartz set, X beat or ties Y pairwise for the Smith Set”.</div><div class=""><br class=""></div><div class="">Isn’t that backwards? I thought the Smith set was the smallest set of candidates who all *defeat* candidates outside of the set (as wikipedia says), while Schwartz set was the one that allowed ties.</div><div class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Mar 8, 2018, at 11:28 AM, Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de" class="">km_elmet@t-online.de</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class="">On 03/07/2018 04:48 AM, Curt wrote:<br class=""><br class="">Sets like Schwartz and Smith are usually maximal elements of a partially ordered set. <a href="https://wiki.electorama.com/wiki/Maximal_elements_algorithms" class="">https://wiki.electorama.com/wiki/Maximal_elements_algorithms</a> gives more information about this, as well as how to use Floyd-Warshall or Kosaraju's algorithms to find maximal elements.<br class=""><br class="">In graph theory terms, we're interested in the smallest set so that there's a cycle from any candidate in that set to any other candidate in that set, according to a relation (X beats Y pairwise for the Schwartz set, X beats or ties Y pairwise for the Smith set). Any strongly connected components algorithm should work, if given a directed graph where there's an edge from X to Y iff X is ranked ahead of Y according to the relation being used.<br class=""></div></div></blockquote></div><br class=""></div></body></html>