  We investigate an iterative deliberation process for an agent community
wishing to make a joint decision. We develop a general model consisting of a
community of n agents, each with their initial ideal point in some metric space
(X, d), such that in each iteration of the iterative deliberation process, all
agents move slightly closer to the current winner, according to some voting
rule R. For several natural metric spaces and suitable voting rules for them,
we identify conditions under which such an iterative deliberation process is
guaranteed to converge.
