Collective decision efficiency and optimal voting mechanisms: A comprehensive overview for multi-classifier models

A new game-theoretic approach for combining multiple classifiers is proposed. A short introduction in basic 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 Banzhaf and Shapley numbers, as well and the collective competence of the group in terms of correct collective decision. 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. This report is a compact introduction to the theoretical material upon which a new expert fusion model can be designed.