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Analysis of the Reliability and Behavior of Majority and Plurality Voting Systems

Yacoub, Sherif; Lin, Xiaofan; Burns, John

HPL-2002-118

Keyword(s): majority voting; plurality voting; expert combination; fault-tolerance

Abstract: Voting is a well-known technique used to combine decisions of peer experts. It has wide application in many domains. Voting is used in fault tolerant applications to mask errors from one or more experts using N-Modular Redundancy (NMR) and N-version Programming. It is also used in pattern recognition applications where decisions from several classifiers can lead to better recognition results. There are several strategies for voting including: majority, weighted voting, plurality, instance runoff voting, threshold voting, and the more general weighted k-out- of-n systems. To use a voting schema in any application domain, we have to understand the various tradeoffs and parameters and how they impact the correctness, reliability, and confidence in the final decision made by the voting system. In this paper, we analyze the behavior of two voting schemas: majority voting and plurality voting. We conduct synthetic studies using a simulator that we developed to analyze results from each expert, apply a voting mechanism, and analyze the voting results. The simulator builds a decision tree and uses a depth-first traversal algorithm to obtain reliability of the system and other factors that describe the voting behavior. For this analysis, we define and study the following behaviors of a voting system: 1) the probability of reaching a consensus, "Pc"; 2) reliability of the voting system, "R"; 3) certainly index, "T"; and 4) the confidence index, "C". The parameters controlling the analysis are the number of participating experts (or units), the number of possible output symbols that can be produced by an expert, the probability distribution of each expert's output, and the voting schema. This study unleashes several behaviors of a voting system and introduces a synthetic approach to compute its reliability.

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