{"id":1580,"date":"2009-04-17T20:30:30","date_gmt":"2009-04-18T04:30:30","guid":{"rendered":"http:\/\/www.oeconomist.com\/blogs\/daniel\/?p=1580"},"modified":"2009-06-13T01:26:49","modified_gmt":"2009-06-13T09:26:49","slug":"tweak-of-the-weak","status":"publish","type":"post","link":"https:\/\/www.oeconomist.com\/blogs\/daniel\/?p=1580","title":{"rendered":"Tweak of the Weak"},"content":{"rendered":"<p>In ordinary decision theory, the name <q>weak preference<\/q> is used for a relation that could be defined as <span style=\"font-style: italic ;\">the complement of the inverse of <span style=\"font-style: italic ;\">strict preference<\/span><\/span>, or as <span style=\"font-style: italic ;\">the union of <span style=\"font-style: italic ;\">strict preference<\/span> with <span style=\"font-style: italic ;\">indifference<\/span><\/span>.  In ordinary decision theory, these two are equivalent.  Typical symbols used for this relationship are <q>&#8829;<\/q>, <q>&#8831;<\/q> and <q>&#10928;<\/q>.<\/p><p>In my paper, I noted the conventional conception of <span style=\"font-style: italic ;\">weak preference<\/span> as the aforementioned union; later, I defined it for my purposes such that <blockquote>(<var>X<sub>1<\/sub><\/var> &#8829; <var>X<sub>2<\/sub><\/var>) &#8801; [{<var>X<sub>1<\/sub><\/var>} &#8838; C({<var>X<sub>1<\/sub><\/var>, <var>X<sub>2<\/sub><\/var>})]<\/blockquote> which is the complement of the inverse of <span style=\"font-style: italic ;\">strict preference<\/span>.<\/p><p>Well, I've decided that I was just asking for trouble using that name and that symbol, because people would have trouble not thinking of it as the union of <span style=\"font-style: italic ;\">strict preference<\/span> with <span style=\"font-style: italic ;\">indifference<\/span>, and thence think that a distinct relation of indecision is precluded <span style=\"font-style: italic ;\">a priori<\/span>.  So I've switched to the name <q>non-rejection<\/q> and the symbol <q>&#8832;<\/q>.<\/p><p>There will probably still be people who ask how this relation differs from that of <span style=\"font-style: italic ;\">weak preference<\/span>, but that will be more an expression of their <em>cleverness<\/em> than of their <em>confusion<\/em>, and it will be easier to offer an explanation how the relation could be seen as <span style=\"font-style: italic ;\">weak preference<\/span>, how it should <em>not<\/em> be seen as <span style=\"font-style: italic ;\">weak preference<\/span>. (I may try to squeeze some pre&euml;mptive discussion into the paper, though I am bumping-up against size limits.)<\/p><p><span style=\"font-weight: bolder ; font-variant: small-caps ;\">Addendum<\/span> (2009:04\/18)<span style=\"font-weight: bolder ;\">:<\/span> I added a pre&euml;mptive discussion, so that even fewer people will get confused.<\/p>","protected":false},"excerpt":{"rendered":"In ordinary decision theory, the name weak preference is used for a relation that could be defined as the complement of the inverse of strict preference, or as the union of strict preference with indifference. In ordinary decision theory, these two are equivalent. Typical symbols used for this relationship are &#8829;, &#8831; and &#10928;.In my [&hellip;]","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[117,36,5,4],"tags":[299,445,446],"class_list":["post-1580","post","type-post","status-publish","format-standard","hentry","category-communication","category-economics","category-personal","category-public","tag-decision-theory","tag-papers","tag-writing"],"_links":{"self":[{"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=\/wp\/v2\/posts\/1580","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1580"}],"version-history":[{"count":0,"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=\/wp\/v2\/posts\/1580\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1580"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1580"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1580"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}