Integrating contributions received from other agents is an essential activity in multi-agent systems (MASs). Not only must related contributions be integrated together, but the confidence in each integrated contribution must be determined. In this paper we look specifically at the issue of confidence determination and its effect on developing "principled," highly collaborating MASs. Confidence determination is often masked by ad hoc contribution-integration techniques, viewed as being addressed by agent trust and reputation models, or simply assumed away. We present a domain-independent analysis model that can be used to measure the sensitivity of a collaborative problem-solving system to potentially incorrect confidence-integration assumptions. In analyses performed using our model, we focus on the typical assumption of independence among contributions and the effect that unaccounted-for dependencies have on the expected error in the confidence that the answers produced by the MAS are correct. We then demonstrate how the analysis model can be used to determine confidence bounds on integrated contributions and to identify where efforts to improve contribution-dependency estimates lead to the greatest improvement in solution-confidence accuracy.