{"id":61,"date":"2012-06-14T21:17:31","date_gmt":"2012-06-14T11:17:31","guid":{"rendered":"http:\/\/stevewatson.info\/blog\/2012\/06\/14\/modelling-a-social-agent\/"},"modified":"2012-06-14T21:26:35","modified_gmt":"2012-06-14T11:26:35","slug":"modelling-a-social-agent","status":"publish","type":"post","link":"https:\/\/stevewatson.info\/blog\/2012\/06\/14\/modelling-a-social-agent\/","title":{"rendered":"Modelling a Social Agent: Part 1 (Preliminaries)"},"content":{"rendered":"<p><font color=\"#000000\">The fundamental atom of social theory must be the individual agent.<br \/>\nWe are interested in those aspects of the agent that are relevant to its role in the social world.<br \/>\nThe agent is first of all an actor, acting to improve the degree of satisfaction of its interests.<br \/>\nThe model for the agent should be a (simplified) model of processes that we believe are important in the decision procedure for any actual agent.<\/p>\n<p><b>Preliminaries<\/b><\/p>\n<p>We have already defined <i>I<\/i>(<i>x<\/i>) = {<i>i<sub>1<\/sub><\/i>, \u2026, <i>i<sub>n<\/sub><\/i>} to be the <u>Interests<\/u> of the individual <i>x<\/i>.<br \/>\nWe have noted that there are scalars to account for the <u>Weight of Interest<\/u> for each of <i>x<\/i>\u2019s interests:<br \/>\n\t<i>W<\/i>(<i>x<\/i>) = {<i>W<sub>j<\/sub><\/i>(<i>x<\/i>): <i>j<\/i> &isin; <i>I<\/i>(<i>x<\/i>)}<br \/>\nAt any time there are a range of possible behaviours of <i>x<\/i>:<br \/>\n\t<i>B<\/i>(<i>x<\/i> = {<i>b<sub>1<\/sub><\/i>, \u2026, <i>b<sub>m<\/sub><\/i>}<br \/>\nEach possible behavior <i>b<\/i> of <i>x<\/i> would result in a different social situation for <i>x<\/i>, which we call the <u>Outcome<\/u> of behaviour <i>b<\/i> of <i>x<\/i>. We write this as<\/p>\n<blockquote><p>\n\t<i>C<\/i>(<i>b<\/i>, <i>x<\/i>) = <i>c<\/i>,\n<\/p><\/blockquote>\n<ul>\n<li><i>c<\/i> is the <u>Context<\/u> of <i>x<\/i>. It is the set of relevant parameters describing the social context of <i>x<\/i>. The relevant parameters are only those that feature in the satisfaction function <i>S<\/i>, and this will be a very restricted set of all possible parameters. <\/li>\n<li>The same notation can be used unambiguously to refer to the outcomes of a range of <i>x<\/i>\u2019s possible behaviours; thus:<br \/>\n<blockquote><p>\n\t\t<i>C<\/i>(<i>B<\/i>(<i>x<\/i>), <i>x<\/i>) = {<i>C<\/i>(<i>b<sub>1<\/sub><\/i>, <i>x<\/i>), \u2026, <i>C<\/i>(<i>b<sub>m<\/sub><\/i>, <i>x<\/i>)} = {<i>c<sub>1<\/sub><\/i>, \u2026, <i>c<sub>m<\/sub><\/i>}<\/li>\n<\/blockquote>\n<\/ul>\n<p>The different possible outcomes of <i>x<\/i>\u2019s behaviour are responsible for differential advancement of <i>x<\/i>\u2019s interests. <\/p>\n<ul>\n<li>They indicate\/consist of changes to the relevant parameters of the satisfaction function described above. <\/li>\n<li>To record the fact that the satisfaction function is dependent upon the outcomes of particular behaviours of <i>x<\/i>, we include those outcomes as one of the arguments.<\/li>\n<\/ul>\n<p>The outcomes of the behaviour <i>b<\/i> of <i>x<\/i>, yield the following satisfactions:<\/p>\n<blockquote><p>\n\t{<i>S<\/i>(<i>C<\/i>(<i>b<\/i>, <i>x<\/i>), <i>j<\/i>, <i>x<\/i>): <i>b<\/i> &isin; <i>B<\/i>(<i>x<\/i>), <i>j<\/i> &isin; <i>I<\/i>(<i>x<\/i>)}, or<br \/>\n\t{<i>S<\/i>(<i>c<\/i>, <i>j<\/i>, <i>x<\/i>): <i>c<\/i> &isin; <i>C<\/i>(<i>B<\/i>(<i>x<\/i>), <i>x<\/i>),  <i>j<\/i> &isin; <i>I<\/i>(<i>x<\/i>)}\n<\/p><\/blockquote>\n<p>The perfectly informed actor will attempt to maximize the total satisfaction function by producing the specific behaviour <i>b<sub>out<\/sub><\/i>, such that:<\/p>\n<blockquote><p>\n\t<i>TS<\/i>(<i>C<\/i>(<i>b<sub>out<\/sub><\/i>, <i>x<\/i>), <i>I<\/i>(<i>x<\/i>), <i>x<\/i>) = max{<i>TS<\/i>(<i>C<\/i>(<i>b<\/i>, <i>x<\/i>), <i>I<\/i>(<i>x<\/i>), <i>x<\/i>): <i>b<\/i> &isin; <i>B<\/i>(<i>x<\/i>)}<br \/>\n\t\t\t= max{&sum;<sub><i>j<\/i>&isin;<i>I<\/i>(<i>x<\/i>)<\/sub><i>w<sub>j<\/sub><\/i>(<i>x<\/i>)<i>S<\/i>(<i>C<\/i>(<i>b<\/i>, <i>x<\/i>), <i>j<\/i>, <i>x<\/i>): <i>b<\/i> &isin; <i>B<\/i>(<i>x<\/i>)}\n<\/p><\/blockquote>\n<p><\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The fundamental atom of social theory must be the individual agent. We are interested in those aspects of the agent that are relevant to its role in the social world. The agent is first of all an actor, acting to improve the degree of satisfaction of its interests. The model for the agent should be [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28],"tags":[],"class_list":["post-61","post","type-post","status-publish","format-standard","hentry","category-sociology"],"_links":{"self":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/61","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/comments?post=61"}],"version-history":[{"count":0,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/61\/revisions"}],"wp:attachment":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/media?parent=61"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/categories?post=61"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/tags?post=61"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}