  Weighted Majority Voting (WMV) is a well-known optimal decision rule for
collective decision making, given the probability of sources to provide
accurate information (trustworthiness). However, in reality, the
trustworthiness is not a known quantity to the decision maker - they have to
rely on an estimate called trust. A (machine learning) algorithm that computes
trust is called unbiased when it has the property that it does not
systematically overestimate or underestimate the trustworthiness. To formally
analyse the uncertainty to the decision process, we introduce and analyse two
important properties of such unbiased trust values: stability of correctness
and stability of optimality. Stability of correctness means that the decision
accuracy that the decision maker believes they achieved is equal to the actual
accuracy. We prove stability of correctness holds. Stability of optimality
means that the decisions made based on trust, are equally good as they would
have been if they were based on trustworthiness. Stability of optimality does
not hold. We analyse the difference between the two, and bounds thereon. We
also present an overview of how sensitive decision correctness is to changes in
trust and trustworthiness.
