Consensus and the ideal observer

Wagner and I set out to articulate a theory of rational consensus that supplements standard models of aggregation of information and value. Some of the criticism contained in the articles contained in this volume is based on misunderstanding. This may be due to the novelty of our approach. No matter how clearly one articulates a new position, the reader brings his standard expectations with him and interpolates them into the text. I think that the article by Nurmi, as Wagner explains, contains this sort of error. We were not defending the position he attacks. This is not to suggest that such misunderstanding vitiates the value of such criticism. The untoward formal consequences of reinterpreting our model within the standard framework illustrates the importance of adopting the unconventional model we presented. A number of the articles raise challenging philosophical points. I shall at tempt to reply to them in some detail. I shall not comment on formal matters as Wagner has dealt with those issues in his reply. The various authors in this volume have represented our model of consensus in summary form. The more detailed and axiomatic version of our theory is contained in our book to which the reader should refer in evaluating the merits of our views and those of our critics. I shall not present our theory here nor shall I comment on the presentation of the model by our critics except to note that we do not preclude the assignment of zero weights, nor do we preclude shifting of weights as one proceeds to higher levels. We argue that, under realistic conditions, some assignment of zero weights and some shifting of weights at higher levels will not destroy consensus. I now turn to a philosophical discussion of the work of our critics. Some articles suggest that finding a weighted average is motivated by an interest in compromise, Baird, or collegiality, Levi. That was not our intention. Our critics do not cite any passages from our work in support of that interpretation of our work. In a scientific context, basing probabilities on considerations of collegiality or an interest in compromise would be subversive of the goals of inquiry. We suggest a different motivation entirely.