Reading John Gunther, Inside U.S.A. (New York: Harper Brothers, 1947), 701 for my book on financial discrimination when I ran across a discussion of votes vs. representation: "South Carolina has precise equality of representation in the House -- six seats -- with the state of Washington, with 793,833 voters out of a total voting population of 1,123,725! Similarly Georgia gets ten seats for 312,539 votes; Wisconsin gets ten for 1,941,603." That prompted the question posed in the title of this post.
Basing representation in the House on the number of votes cast, rather than on population, it seems to me, is a "market" (really incentive-based) solution to the problem of states trying (once again) to restrict voting by members of certain groups, e.g. Amerindians, Hispanics, or African Americans. Successful attempts to keep people from voting would hurt the states that allowed it by reducing the number of reps they could send to the House of Representatives and thereby also their impact on presidential elections through the electoral college.
Basing representation on votes cast would also give individual voters more incentive to turn out and vote because they would be helping to keep up their representation rather than just picking between frick and frack. Voting, I predict, would get a whole lot easier. We might even see negative poll taxes.