This paper demonstrates that three of the basic approaches to the solution of the social choice problem are in fact equivalent to one another. All will yield the same social decision functions -- a winning set of permutations of the actions. The Combinatorial Optimization criterion of Blin and Whinston is shown to be monotonically related to the Kemeny function criterion proposed by Levenglick. The set covering formulation for the l_1 norm case devised by 

Merchant and Rao is also shown to be equivalent to the other two. The geometrical aspect of the problem is also discussed and an example is provided.