{"id":65,"date":"2012-06-20T15:30:09","date_gmt":"2012-06-20T05:30:09","guid":{"rendered":"http:\/\/stevewatson.info\/blog\/2012\/06\/20\/rudimentary-dominance-structure-in-organizations\/"},"modified":"2012-06-20T15:36:43","modified_gmt":"2012-06-20T05:36:43","slug":"rudimentary-dominance-structure-in-organizations","status":"publish","type":"post","link":"https:\/\/stevewatson.info\/blog\/2012\/06\/20\/rudimentary-dominance-structure-in-organizations\/","title":{"rendered":"Rudimentary Dominance Structure in Organizations"},"content":{"rendered":"

Previously, we have said that groups are organized wrt subsets of the membership, thus:<\/p>\n

\n\tO(G) = {r1<\/sub>, \u2026, rn<\/sub>} ∈ 2|G|<\/sup> is the Organization<\/u> of G, where ri<\/sub> are the roles in G, satisfying<\/p>\n

    \n
  1. (∀x ∈ |G|)(∃r ∈ O(G)) [x ∈ r]<\/li>\n
  2. (∀x ∈ |G|)(∀ri<\/sub>, rj<\/sub> ∈ O(G)) [x ∈ ri<\/sub> & x ∈ rj<\/sub> → ri<\/sub> = rj<\/sub>]<\/li>\n<\/ol>\n<\/blockquote>\n

    Of course, merely defining a subset of subsets does not suffice to characterize an organization or the structure of a group. <\/p>\n

    The point of a group, we noted before, was to assist in the achievement of the interests of its members. Socially relevant groups, which are actors in the social realm, will have a structure that coordinates the actions of its members towards some end. Such coordination is achieved through the imposition of a system of dominance relations. The point of the roles is in large part that the dominance relations that are relevant to the function of the group are defined wrt the roles. We wish, therefore, to note the existence of a characteristic set of dominance relations amongst the roles in the organization, which can be done by referencing the dominance relationship defined between agents. First define a dominance relationship amongst sets of agents as follows:<\/p>\n

    \nLet X, Y be disjoint sets of agents. Y dominates X iff (∀x ∈ X) (∃y ∈ Y) [y\/x].\n<\/p><\/blockquote>\n

    We now apply this relation to the roles of a group, and claim that all the roles are involved in dominance relationships. We also need to specify some roles as being special in the sense that though they dominate others they are not themselves necessarily dominated by any other roles in the group. These are the Leadership Roles<\/u> in an organization. In fact, we shall assume there is just one leadership role. This is certainly the case in most forms of organization, and certainly in the standard hierarchical organization. Let the leadership role be denoted rL<\/sub>. Then we say that<\/p>\n

    \n
      \n
    1. (∀ri<\/sub> ∈ O(G)-rL<\/sub>) (∃rj<\/sub> ∈ O(G)) [rj<\/sub> \/ ri<\/sub>]<\/li>\n<\/ol>\n
        \n
      • We should also distinguish leadership roles from Strict Leadership Roles<\/u>. Strict leadership roles are undominated leadership roles. Not all LR are SLR. Every group has a LR but not every group has an SLR \u2013 in fact it\u2019s likely that there are very few of the latter. The existence of an SLR is described thus:
        \n

        \n\t\t\t(∃rSL<\/sub> ∈ O(G)) (∀r ∈ O(G)-rSL<\/sub>) [~(r\/rSL<\/sub>)]\n\t\t<\/p><\/blockquote>\n<\/li>\n<\/ul>\n<\/blockquote>\n

        Setting that possibility to one side for now, there are many different structures possible under this minimal definition. It\u2019s possible, for example, to have the leadership role entirely detached from the rest of the group roles. This is unacceptable \u2013 meaning just that it is not characteristic of significant social formations. We need to expand the definition of the leadership role to eliminate this possibility. <\/p>\n

        We say that there is a Domination Sequence<\/u> (or a chain of command) in O(G) subordinating role p to role q iff (∃ < ri<\/sub>: i=1, \u2026,n > ∈ O(G)n<\/sup>) [r1<\/sub>\/p & r2<\/sub>\/r1<\/sub> & \u2026 & q\/rn<\/sub>], and we write q\/\/p and read that as q Superdominates<\/u> p<\/p>\n

        A reasonable suggestion, then, would be that for any other role in the group, the leadership role superdominates that role; thus:<\/p>\n

        \n
          \n
        1. (∀r ∈ O(G)-rL<\/sub>) [rL<\/sub>\/\/rn<\/sub>]<\/li>\n<\/ol>\n<\/blockquote>\n

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

          Previously, we have said that groups are organized wrt subsets of the membership, thus: O(G) = {r1, \u2026, rn} ∈ 2|G| is the Organization of G, where ri are the roles in G, satisfying (∀x ∈ |G|)(∃r ∈ O(G)) [x ∈ r] (∀x ∈ |G|)(∀ri, rj ∈ O(G)) [x ∈ ri & x ∈ rj […]<\/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-65","post","type-post","status-publish","format-standard","hentry","category-sociology"],"_links":{"self":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/65","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=65"}],"version-history":[{"count":0,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/65\/revisions"}],"wp:attachment":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/media?parent=65"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/categories?post=65"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/tags?post=65"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}