{"id":66,"date":"2012-06-22T22:37:49","date_gmt":"2012-06-22T12:37:49","guid":{"rendered":"http:\/\/stevewatson.info\/blog\/2012\/06\/22\/recruitment-retirement-retention-and-resistance\/"},"modified":"2012-06-22T22:42:02","modified_gmt":"2012-06-22T12:42:02","slug":"recruitment-retirement-retention-and-resistance","status":"publish","type":"post","link":"https:\/\/stevewatson.info\/blog\/2012\/06\/22\/recruitment-retirement-retention-and-resistance\/","title":{"rendered":"Recruitment, Retirement, Retention, and Resistance"},"content":{"rendered":"

In order for G to retain its membership it needs to be the case that continuing membership of G is believed to be more likely to advance the salient and weighty interests of x than relinquishing membership of G. This Retention Condition<\/u> may be expressed as follows:<\/p>\n

\n\tFor x ∈ |G|,
\n\tLet Bstat<\/sub>(x) ⊂ B(x) be all actions that constitute remaining in the group
\n\tLet Bexit<\/sub>(x) ⊂ B(x) be all actions that constitute leaving the group <\/p>\n

\t(∀x ∈ |G|)[ E<\/b>[ TS(C(Bstat<\/sub>(x), x), I(x), x) ] ≥ E<\/b>[ TS(C(Bexit<\/sub>(x), x), I(x), x) ] → A(x)∈Bstat<\/sub>(x) ]<\/p>\n

\tWhere [ E<\/b>[ TS(C(Bstat<\/sub>(x), x), I(x), x) ]
\n\t\t= ∑b∈E<\/b>[ Bstat<\/sub>(x) ]<\/sub> E<\/b>[ P(b) ] (∑j∈E<\/b>[I(x)]<\/sub>wj<\/sub>(x) ∑c∈E<\/b>[C(b, x)]<\/sub> E<\/b>[ P(c) ]E<\/b>[ S(c, j, x) ])
\n\tand\t[ E<\/b>[ TS(C(Bexit<\/sub>(x), x), I(x), x) ]
\n\t\t= ∑b∈E<\/b>[ Bexit<\/sub>(x) ]<\/sub> E<\/b>[ P(b) ] (∑j∈E<\/b>[I(x)]<\/sub>wj<\/sub>(x) ∑c∈E<\/b>[C(b, x)]<\/sub> E<\/b>[ P(c) ]E<\/b>[ S(c, j, x) ])\n<\/p><\/blockquote>\n

We may similarly define a Recruitment Condition<\/u> that needs to be satisfied in order that x should become a member of G:<\/p>\n

\n\tFor x ∈ |G|,
\n\tLet Bstat<\/sub>(x) ⊂ B(x) be all actions that constitute remaining outside the group
\n\tLet Bintrat<\/sub>(x) ⊂ B(x) be all actions that constitute joining the group <\/p>\n

\t(∀x ∈ |G|)[ E<\/b>[ TS(C(Bintrat<\/sub>(x), x), I(x), x) ] > E<\/b>[ TS(C(Bstat<\/sub>(x), x), I(x), x) ] → A(x)∈Bintrat<\/sub>(x) ]<\/p>\n

\tWhere [ E<\/b>[ TS(C(Bstat<\/sub>(x), x), I(x), x) ]
\n\t\t= ∑b∈E<\/b>[ Bstat<\/sub>(x) ]<\/sub> E<\/b>[ P(b) ] (∑j∈E<\/b>[I(x)]<\/sub>wj<\/sub>(x) ∑c∈E<\/b>[C(b, x)]<\/sub> E<\/b>[ P(c) ]E<\/b>[ S(c, j, x) ])
\n\tand\t[ E<\/b>[ TS(C(Bintrat<\/sub>(x), x), I(x), x) ]
\n\t\t= ∑b∈E<\/b>[ Bintrat<\/sub>(x) ]<\/sub> E<\/b>[ P(b) ] (∑j∈E<\/b>[I(x)]<\/sub>wj<\/sub>(x) ∑c∈E<\/b>[C(b, x)]<\/sub> E<\/b>[ P(c) ]E<\/b>[ S(c, j, x) ])\n<\/p><\/blockquote>\n

Just for the sake of completeness, we\u2019ll note two other conditions, which are perfectly obvious given the preceding. First, the Retirement Condition<\/u>: <\/p>\n

\n\t(∀x ∈ |G|)[ E<\/b>[ TS(C(Bstat<\/sub>(x), x), I(x), x) ] < E<\/b>[ TS(C(Bexit<\/sub>(x), x), I(x), x) ] → A(x)∈Bexit<\/sub>(x) ]\n<\/p><\/blockquote>\n

And, second, the Resistance Condition<\/u>:<\/p>\n

\n\t(∀x ∈ |G|)[ E<\/b>[ TS(C(Bintrat<\/sub>(x), x), I(x), x) ] ≤ E<\/b>[ TS(C(Bstat<\/sub>(x), x), I(x), x) ] → A(x)∈Bstat<\/sub>(x) ]\n<\/p><\/blockquote>\n

    \n
  • The condition of equality between the two estimated total satisfactions will be taken to favour continuation of the status quo. It is assumed that inertia is preferred where we find ourselves in the position of Buridan\u2019s Ass.<\/li>\n
  • It is not here assumed that (∀x ∈ |G|) [Bstat<\/sub>(x) = Bintrat<\/sub>(x)c<\/sup>] or that (∀x ∈ |G|) [Bstat<\/sub>(x) = Bexit<\/sub>(x)c<\/sup>], but that does seem like a reasonable assumption to make.<\/li>\n<\/ul>\n

    <\/font><\/p>\n","protected":false},"excerpt":{"rendered":"

    In order for G to retain its membership it needs to be the case that continuing membership of G is believed to be more likely to advance the salient and weighty interests of x than relinquishing membership of G. This Retention Condition may be expressed as follows: For x ∈ |G|, Let Bstat(x) ⊂ B(x) […]<\/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-66","post","type-post","status-publish","format-standard","hentry","category-sociology"],"_links":{"self":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/66","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=66"}],"version-history":[{"count":0,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/66\/revisions"}],"wp:attachment":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/media?parent=66"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/categories?post=66"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/tags?post=66"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}