In this chapter an analysis of the behavior of an arbitrary
(perhaps massive) collective of computational processes in terms of
an associated "world" utility function is presented We concentrate
on the situation where each process in the collective can be viewed
as though it were striving to maximize its own private utility
function. For such situations the central design issue is how to
initialize/update the collective's structure, and in particular the
private utility functions, so as to induce the overall collective
to behave in a way that has large values of the world utility.
Traditional "team game" approaches to this problem simply set each
private utility function equal to the world utility function. The
"Collective Intelligence" (COIN) framework is a semi-formal set of
heuristics that recently have been used to construct private
utility. functions that in many experiments have resulted in world
utility values up to orders of magnitude superior to that ensuing
from use of the team game utility. In this paper we introduce a
formal mathematics for analyzing and designing collectives. We also
use this mathematics to suggest new private utilities that should
outperform the COIN heuristics in certain kinds of domains. In
accompanying work we use that mathematics to explain previous
experimental results concerning the superiority of COIN heuristics.
In that accompanying work we also use the mathematics to make
numerical predictions, some of which we then test. In this way
these two papers establish the study of collectives as a proper
science, involving theory, explanation of old experiments,
prediction concerning new experiments, and engineering insights.
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