Steve Watson

• an agent x is an Acceptant of the norm n iff x accepts the rule n.
  

  K(n) = {x: B(x)[ n ]}

• We can discover whether x accepts a norm by observation of his behaviour

A Norm Formation is a set of norms, N = {n₁, …, n_n}.

• an agent x is an acceptant of the norm formation N iff x accepts the rules in n.
  

  K(N) = {x: B(x)[ N ]}

• Standard classes of norm formations are conventions, traditions, etc. (which may be analysed later.)

An Institution may be formalized as a norm formation which imposes a group structure on K(N)

• This definition results in a particular selection of social structures being called institutions which may differ from the selections made by other theoretical views. This is no great difficulty, since we have the theoretical machinery to deal with all reasonable extensions or restrictions of this concept.

1. An institution imposes an (Institutional) Organization on K(N)
   • N → (∃Q ={r₁, …, r_n} ⊂ 2^K(N))
     

     [((∀x ∈ K(N))(∃r_i ∈ Q) [x ∈ r_i]) &
     ((∀x ∈ K(N))(∀r_i, r_j ∈ Q) [x ∈ r_i & x ∈ r_j → r_i = r_j])]

   • We call the elements of Q the (Institutional) Roles of the organization of N
2. An institution imposes a relation of (Institutional) Dominance on K(N)
   • x institutionally dominates y in N iff
     

     (∃α_response(x) ∈ B(y)[ α(x) ])
     (∃α_neutral(x) ∈ B(y)[ α(x) ] – α_response(x))
     (∃α_challenge(y) ∈ B(y)[ α(y) ])
     the following conditions are satisfied:

     1. (∀a_challenge ∈ α_challenge(y)) (∀a_response ∈ α_response(x)) B(y)[ P(α_neutral(x) | A(y)=a_challenge & A(x)≠a_response ] ≈ 1
     2. (∀a_challenge ∈ α_challenge(y)) (∃a_response ∈ α_response(x)) (∃N’ ⊂ N) [(B(y)[ N’ → (A(y)=a_challenge → A(x)=a_response )]]
     3. (∀a_response ∈ α_response(x)) (∀a_challenge ∈ α_challenge(y)) (∃N’ ⊂ N)[(B(y)[ (A(x)=a_response → A(y)=a_challenge) → N’]
     4. (∀c_response ∈ B(y)[ C(α_response, c_x,0, x) ]) (∀c_neutral ∈ B(y)[ C(α_neutral, c_x,0, x) ])[B(y)[ T(c_response, I(y), y) ] << B(y)[ T(c_neutral, I(y), y) ]

   • This condition differs from the condition for (non-institutional) dominance in parts 2 and 3, which express y’s belief that his action together with the rules of the institution will produce x’s response, and that without those rules there would be no such response. This is, therefore, a special case of the previous definition.
   • Note that since N creates the conditions under which T is degraded for noncompliant agents, N provides the mechanism of enforcing compliance.
   • Express x institutionally dominates y as x/_Ny
3. Let the Group determined by the institution N be denoted G_N = < K(N), R >, where R contains at least
   • O(G_N), the institutional organization as defined on |G_N|,
   • ADD(G_N) = {< x, y >: x, y ∈ |G_N|, x/_Ny}, the (Institutional) Agent Dominance Diagram of G_N, and
   • RDD(G_N) = {< r_i, r_j >: r_i, r_j ∈ O(G_N), r_i/_Nr_j}, the (Institutional) Role Dominance Diagram of G_N, where, for disjoint sets X and Y, Y institutionally dominates X iff (∀x ∈ X) (∀y ∈ Y) [y /_N x].