Stability of Weighted Majority Voting under Estimated Weights

Weighted Majority Voting (WMV) is a well-known decision making rule. The weights of sources are determined by the probabilities that sources provide accurate information (trustworthiness). However, in reality, the trustworthiness is usually not a known quantity to the decision maker-they have to rely on an estimate called trust. An algorithm that computes trust is called unbiased when it has the property that it does not systematically overestimate or underestimate the trustworthiness. To formally analyze the uncertainty to the decision process brought by such unbiased trust values, we introduce and analyze two important properties of WMV: stability of correctness and stability of optimality. We also provide an overview of how sensitive decision accuracy is to the changes in trust and trustworthiness.