{"id":64,"date":"2012-06-17T23:27:06","date_gmt":"2012-06-17T13:27:06","guid":{"rendered":"http:\/\/stevewatson.info\/blog\/2012\/06\/17\/micro-analysis-of-power-relationships\/"},"modified":"2012-06-18T20:24:39","modified_gmt":"2012-06-18T10:24:39","slug":"micro-analysis-of-power-relationships","status":"publish","type":"post","link":"https:\/\/stevewatson.info\/blog\/2012\/06\/17\/micro-analysis-of-power-relationships\/","title":{"rendered":"Micro analysis of power relationships"},"content":{"rendered":"

Blalock and Wilken (Intergroup Processes<\/i>, NY: Free Press, 1979, p. 330) note that there are at least two conceptions of social power that are in play in sociological theorizing. The first conception concerns the actual achievement of goals and may apply more readily to larger scale elements of the sociological ontology; the second conception is at the micro level and is appropriate to interpersonal conceptions of social power. Since our working assumption is that at some stage the macro level analyses will need to be in principle<\/i> explicable (if not actually reducible) to micro level phenomena, and that the attempt to begin at the top level is legitimate but can only proceed in a positivistic fashion until the micro level analysis has proposed a range of adequate theoretical constraints upon macro level speculations, we therefore confine our interest to the second form of conception of social power.<\/p>\n

As an example of the kind of definition that is proposed to cover the latter conception they offer the following: \u201cA has power over B when A can change B\u2019s actions, or sanction B, and so forth.\u201d This definition is only offered as an indicator<\/i> by those authors, and it is, of course, unsatisfactory as it stands. For example, it does not distinguish between power and mere influence. To distinguish \u2018power\u2019 in the sense that it is usually used \u2013 and in which sense it has a special significance in informal sociological explanations \u2013 from \u2018power\u2019 as the mere existence of the effect of one agent on another, we need to concentrate on the implied coercive capabilities of A over B. Thus we would need to include the fact that B changes his behaviours because he believes that A has the ability to<\/i> punish him if he fails to comply. Moreover, he believes that A actually will<\/i> punish him if he fails to comply. <\/p>\n

We can attempt a definition using the established formalism as follows:<\/p>\n

\n\tx has power over y iff (∃bresponse<\/sub> ∈ E<\/b>(y))[ B(x) ] which satisfies the conditions<\/p>\n

    \n
  1. E<\/b>(y)[ C(bresponse<\/sub>, x) ] = cresponse<\/sub><\/li>\n
  2. E<\/b>(y)[ TS(cresponse<\/sub>, I(y), y) ] << E<\/b>(y)[ TS(cnow<\/sub>, I(y), y) ]<\/li>\n
  3. (∃b ∈ E<\/b>(y)[ B(y) ]) [(E<\/b>(y)[ A<\/b>(y)=b → A<\/b>(x)=bresponse<\/sub> ] & (E<\/b>(y)[ (A<\/b>(y)≠b → A<\/b>(x)≠bresponse<\/sub>) ]]<\/li>\n<\/ol>\n<\/blockquote>\n
      \n
    • Whenever x and y are in a relationship such as this we say that x Dominates<\/u> y and write x\/y<\/li>\n
    • As presented the relationship of dominance appears to have no essential structure. It is not necessarily transitive, and it is not necessarily non-symmetric.<\/li>\n
    • Degrees of power can be traced back to the degrees by which the total satisfaction functions are altered in 2.<\/li>\n
    • Note that E<\/b>(y)[ statement ] in condition 3 is to be read as the subjective estimation of the fuzzy truth value of \u2018statement,\u2019 or the subjective degree of belief of y in \u2018statement.\u2019<\/li>\n
    • Complexity can be added by noting that in most cases bresponse<\/sub> is merely one of a class of behaviours that are available to x which can punish y in various degrees, that b in condition 3 is merely one of a class of behaviours that are available to y which can prompt the response from x.<\/li>\n
    • cnow<\/sub> in condition 2 is the context at the time of consideration, but it should really refer to the context that exists when x does not respond punitively to the b in condition 3.<\/li>\n
    • Note that this is power through punishment, but there is a similar definition available for power through reward: simply replace condition 2 with the condition
      \n

      \n\t\tE<\/b>(y)[ TS(cresponse<\/sub>, I(y), y) ] >> E<\/b>(y)[ TS(cnow<\/sub>, I(y), y) ]\n\t<\/p><\/blockquote>\n<\/li>\n<\/ul>\n

      In the light of the notes above, refine the original definition thus:<\/p>\n

      \n\tx dominates y iff
      \n\t(∃Bresponse<\/sub>(x) ∈ E<\/b>(y)[ B(x) ])
      \n\t(∃Bneutral<\/sub>(x) ∈ E<\/b>(y)[ B(x) ]-Bresponse<\/sub>(x))
      \n\t(∃Bstimulus<\/sub>(y) ∈ E<\/b>(y)[ B(y) ])
      \n\t\tthe following conditions are satisfied:<\/p>\n

        \n
      1. (∀bstimulus<\/sub> ∈ Bstimulus<\/sub>(y)) (∀bresponse<\/sub> ∈ Bresponse<\/sub>(x))
        E<\/b>(y)[ P(Bneutral<\/sub>, x) | A<\/b>(y)=bstimulus<\/sub> & A<\/b>(x)≠bresponse<\/sub> ] ~ 1<\/li>\n
      2. ∀bstimulus<\/sub> ∈ Bstimulus<\/sub>(y)) (∃bresponse<\/sub> ∈ Bresponse<\/sub>(x))
        [(E<\/b>(y)[ A<\/b>(y)=bstimulus<\/sub> → A<\/b>(x)=bresponse<\/sub> ]<\/li>\n
      3. ∀bresponse<\/sub> ∈ Bresponse<\/sub>(x)) (∃bstimulus<\/sub> ∈ Bstimulus<\/sub>(y))
        [(E<\/b>(y)[ A<\/b>(x)=bresponse<\/sub> → A<\/b>(y)=bstimulus<\/sub> ]<\/li>\n
      4. ∀cresponse<\/sub> ∈ E<\/b>(y)[ C(Bresponse<\/sub>, x) ]) (∀cneutral<\/sub> ∈ E<\/b>(y)[ C(Bneutral<\/sub>, x) ])
        [E<\/b>(y)[ TS(cresponse<\/sub>, I(y), y) ] << E<\/b>(y)[ TS(cneutral<\/sub>, I(y), y) ]<\/li>\n<\/ol>\n<\/blockquote>\n

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

        Blalock and Wilken (Intergroup Processes, NY: Free Press, 1979, p. 330) note that there are at least two conceptions of social power that are in play in sociological theorizing. The first conception concerns the actual achievement of goals and may apply more readily to larger scale elements of the sociological ontology; the second conception is […]<\/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-64","post","type-post","status-publish","format-standard","hentry","category-sociology"],"_links":{"self":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/64","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=64"}],"version-history":[{"count":0,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/64\/revisions"}],"wp:attachment":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/media?parent=64"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/categories?post=64"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/tags?post=64"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}