By Iain McLean, Haidee Lorrey and Josep M. Colomer
Electronic Journ@l for History of Probability and Statistics, Vol.4:1 (2008)
Abstract: We take institutions seriously as both a rational response to dilemmas in which agents found themselves and a frame to which later rational agents adapted their behaviour in turn. Medieval corporate bodies knew that they needed choice procedures. Although the social choice advances of ancient Greece and Rome were not rediscovered until the high middle ages, the rational design of choice institutions predated their rediscovery and took some new paths. Both Ramon Llull (ca 1232-1316) and Nicolaus of Cusa (Cusanus; 1401-64) made contributions which had been believed to be centuries more recent. Llull promotes the method of pairwise comparison, and proposes the Copeland rule to select a winner. Cusanus proposes the Borda rule, which should properly be renamed the Cusanus rule.
Voting might be needed in any institution ruled by more than one person, where decisions could not simply be handed down from above. Medieval theologians no doubt believed that God’s word was handed down from above; but they well knew that they often had to decide among rival human interpretations of it. The Church faced its own decision problem every time a new Pope needed to be elected. Bodies not directly in the hierarchy of the Church had to evolve their own decision procedures. The chief such bodies were commercial and urban corporations; religious orders; and universities.
The disagreement between Llull and Cusanus raises the issue: should voting be regarded as a method of aggregating judgments or as a method of aggregating interests? In the former interpretation (only), voting procedures are a solution to a problem of approximate reasoning. There is an unknown, true state of affairs (for medieval thinkers, divine will). A voting procedure aggregates unreliable individual perceptions of the will of God to a more reliable group judgment of it. In the rougher world of Cusanus, and probably of electors to the papacy and to Dogeships, only at most lip service is paid to the will of God, and voting is a process of aggregating interests.