Often a group of people need to find a consensus. One strategy for finding a consensus is to try to reach unanimous agreement by a process of exchange of information and rational argument. But where that fails we need to find a consensus without reaching unanimity. A special but important case occurs when the people in the group are making estimates of some numerical quantity, for example, a probability. In that case there is an especially simple procedure: take the arithmetic mean of the estimates. An equally simple procedure would be to take the median. But neither procedure takes into account differences in the expertise of the members of the group, which differences might, in a favorable case, be agreed upon by members of the group. In order to take these differences into consideration it has been proposed by Lehrer and Wagner,1 that the consensual estimate, Pc be the sum of the products of the individual estimates, Px.... ,Pn multiplied by weights, Wi,... ,wn which reflect the expertise of the individuals. Thus