Consensus ranking under the exponential model

Assume that we are given a set of N rankings, a.k.a linear orderings on n objects. For instance, the rankings represent the individual preferences of a panel of N judges, each presented with the same set of n candidate objects. The problem of rank aggregation or of finding a consensus ranking, is formulated as finding a single ranking π0 that best agrees with all the N rankings. Kendall’s correlation [Fligner and Verducci, 1986] is a widely used models of agreement [Ailon et al., 2005, Lebanon and Lafferty, 2003, Cohen et al., 1999]. The Kendall distance is defined as dK(π, π0) = ∑