Let there be N nodes. Let a be an agent from the set A of all agents. Let vai be the value agent a places on node i. Let wij be the weight between nodes i and j. Let the “averaged agent” b mean a constructed agent b (not in A) for which vbi = average over all a of vai. Write “the sum over all i and j of S” as sum_{i, j}(S).
Average IC = ICa = - sum_{i, j} [wij x sum_a (vai x vaj)] / |A|
Expected IC from average agent b = ICb = - sum_{i, j} [wij x (sum_a(vai) / |A|) x (sum_a(vaj) / |A|)]
I should have said that |A| means the number of agents in the set A.
sum.a(v.aj) means the sum, over all agents, of the value they place on node j.
‘x’ means multiplication, not a variable. ICa and ICb are variables I defined, and maybe I should have written them on the left like so:
Am I the only one who’s completely lost by this?
I should have said that |A| means the number of agents in the set A. sum.a(v.aj) means the sum, over all agents, of the value they place on node j. ‘x’ means multiplication, not a variable. ICa and ICb are variables I defined, and maybe I should have written them on the left like so:
ICa := Average IC = …