In networked systems comprised of many agents, it is often required to reach a common operating point of all agents, termed the network consensus. We consider two iterative methods for reaching a ranking (ordering) consensus over a voter network, where the initial preference of every voter is of the form of a full ranking of candidates. The voters are allowed, one at a time and based on some random scheme, to change their votes to bring them 'closer' to the opinions of selected subsets of peers. The first consensus method is based on changing votes one adjacent swap at a time; the second method is based on changing votes via averaging with the votes of peers, potentially leading to many adjacent swaps at a given time. For the first model, we characterize convergence points and conditions for convergence. For the second model, we prove convergence to a global ranking and derive the rate of convergence to this consensus.