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Considering a network with $n$ nodes, where each node initially votes for one(or more) choices out of $K$ possible choices, we present a DistributedMulti-choice Voting/Ranking (DMVR) algorithm to determine either the choicewith maximum vote (the voting problem) or to rank all the choices in terms oftheir acquired votes (the ranking problem). The algorithm consolidates nodevotes across the network by updating the states of interacting nodes using twokey operations, the union and the intersection. The proposed algorithm issimple, independent from network size, and easily scalable in terms of thenumber of choices $K$, using only $K\times 2^{K-1}$ nodal states for voting,and $K\times K!$ nodal states for ranking. We prove the number of states to beoptimal in the ranking case, this optimality is conjectured to also apply tothe voting case. The time complexity of the algorithm is analyzed in completegraphs. We show that the time complexity for both ranking and voting is$O(\log(n))$ for given vote percentages, and is inversely proportional to theminimum of the vote percentage differences among various choices.

Distributed Voting/Ranking with Optimal Number of States per Node