As part of an AHRC network grant, the LSE Choice Group organises a series of master classes by leading researchers on topics related to decision and game theory, social choice and decision-making.
The first of those was given by Carl Wagner, Professor of Mathematics and Adjunct Professor of Philosophy at the University of Tennessee, and co-author with Keith Lehrer of the 1981 monograph “Rational Consensus in Science and Society” The two master classes focused on the mathematical foundations of the model, introducing the method of iterated averaging in the first lecture and providing its axiomatic foundations in the second lecture.
The first lecture entitled “The French-DeGroot-Lehrer Model of Consensus” introduced a number of different interpretations of the method of iterated weighted averaging. The main idea of this method is that individuals assign weights to each other that reflect how much the opinion of the individual should count in group decision-making. The result is a weight matrix. If the matrix itself is repeatedly mutiplied through by the weights, the product will converge to a unanimous assignment of weights to all individuals in the group, provided there are suitable patterns of respect between individuals.
The second lecture entitled “The Axiomatics of Aggregation” provided an axiomatic characterisation of weighted means with independence of alternatives (a separability condition) and zero preservation (a unanimity condition) axioms playing the central role. The approach allowed discussionn of the implications of several axioms in allocation aggregation problems as well as in aggregating probability measures.
In the evening, Carl Wagner also gave a Choice Group seminar talk on “Independence Preservation in Expert Judgment Synthesis”, in which he argued against requiring “universal” application of independence, showing several reasonable ways of preserving epistemically significant cases of independence when probability pooling is conceived in analogy with the single profile social welfare theory of Bergson and Samuelson.
The rational consensus emerging was that the activities of the day formed a perfect start for the series of master classes, providing many students and researchers with very useful formal background to the Lehrer/Wagner model and group decision-making more generally.
LSE Choice Group