  A new game-theoretic approach for combining multiple classifiers is proposed.
A short introduction in Game Theory and coalitions illustrate the way any
collective decision scheme can be viewed as a competitive game of coalitions
that are formed naturally when players state their preferences. The winning
conditions and the voting power of each player are studied under the scope of
voting power indices, as well and the collective competence of the group.
Coalitions and power indices are presented in relation to the Condorcet
criterion of optimality in voting systems, and weighted Borda count models are
asserted as a way to implement them in practice. A special case of coalition
games, the weighted majority games (WMG) are presented as a restricted
realization in dichotomy choice situations. As a result, the weighted majority
rules (WMR), an extended version of the simple majority rules, are asserted as
the theoretically optimal and complete solution to this type of coalition
gaming. Subsequently, a generalized version of WMRs is suggested as the means
to design a voting system that is optimal in the sense of both the correct
classification criterion and the Condorcet efficiency criterion. In the scope
of Pattern Recognition, a generalized risk-based approach is proposed as the
framework upon which any classifier combination scheme can be applied. A new
fully adaptive version of WMRs is proposed as a statistically invariant way of
adjusting the design process of the optimal WMR to the arbitrary
non-symmetrical properties of the underlying feature space. SVM theory is
associated with properties and conclusions that emerge from the game-theoretic
approach of the classification in general, while the theoretical and practical
implications of employing SVM experts in WMR combination schemes are briefly
discussed. Finally, a summary of the most important issues for further research
is presented.
