Steve Watson

Preliminaries

We have already defined I(x) = {i₁, …, i_n} to be the Interests of the individual x.
We have noted that there are scalars to account for the Weight of Interest for each of x’s interests:
W(x) = {W_j(x): j ∈ I(x)}
At any time there are a range of possible behaviours of x:
B(x = {b₁, …, b_m}
Each possible behavior b of x would result in a different social situation for x, which we call the Outcome of behaviour b of x. We write this as

C(b, x) = c,

• c is the Context of x. It is the set of relevant parameters describing the social context of x. The relevant parameters are only those that feature in the satisfaction function S, and this will be a very restricted set of all possible parameters.
• The same notation can be used unambiguously to refer to the outcomes of a range of x’s possible behaviours; thus:
  

  C(B(x), x) = {C(b₁, x), …, C(b_m, x)} = {c₁, …, c_m}

The different possible outcomes of x’s behaviour are responsible for differential advancement of x’s interests.

• They indicate/consist of changes to the relevant parameters of the satisfaction function described above.
• To record the fact that the satisfaction function is dependent upon the outcomes of particular behaviours of x, we include those outcomes as one of the arguments.

The outcomes of the behaviour b of x, yield the following satisfactions:

{S(C(b, x), j, x): b ∈ B(x), j ∈ I(x)}, or
{S(c, j, x): c ∈ C(B(x), x), j ∈ I(x)}

The perfectly informed actor will attempt to maximize the total satisfaction function by producing the specific behaviour b_out, such that:

TS(C(b_out, x), I(x), x) = max{TS(C(b, x), I(x), x): b ∈ B(x)}
= max{∑_j∈I(x)w_j(x)S(C(b, x), j, x): b ∈ B(x)}