Yale Law Professor Akhil Reed Amar has suggested:
Divide the state into one hundred equally populous single-member districts, as under the current system. Give each person one ballot and one vote, but within each district, after the votes are cast, don't just add up the votes and in effect waste or ignore the votes of those of the minority party or parties– the “losers.” Instead, treat all voters, all ballots, equally, but in a different way. Suppose we put all of the ballots from a given district in a twirling drum, pull one ballot out in a lottery, and declare the candidate listed on that ballot the winner from that district. Ex ante, each ballot has an equal chance of casting the winning vote. If you get 20 percent of the vote in a district, you have a 20 percent chance of winning the election even if someone else got more votes. Like the current system, lottery voting uses small single-member districts, but because of the law of averages, lottery voting generates an overall legislature that looks much more like the one generated by cumulative voting. A geographically dispersed 20 percent minority party will win around twenty of the one hundred seats. Each party will get its fair share–its proportionate share–of legislative representation, tracking pretty closely the overall percentage of the vote it received statewide.
During a nice conversation about alternative voting schemes last night at the Amsterdam Falafelshop with my friend Clark, I got thinking about just how little most Americans are aware of the degree to which the democratic rules of the game constrain the range of the politically possible. We blithely believe that since we have some scheme of universal suffrage that the government must reflect the “will of the people.” But this is utterly fallacious. There are probably an uncountable number of different voting schemes that are equivalently “democratic,” but which would produce wildly different legislatures, policies, and civic cultures. Amar's ingenious idea is just one example of an alternative democratic scheme that would give quite different results from our current system.
The interesting normative question is whether a political community can truly exemplify the ideal of republican self-governance if they do not understand the extent to which the rules of collective decision-making limit their choices, some possibilities being ruled out of bounds simply in virtue of being governed by one set of rules rather then another.
Amar speaks of law schools, but I think his point is general:
Too few of us–citizens and lawyers–recognize that a choice exists. This is largely a failure of education, especially in law schools where professors train students much better in the arts of textual and doctrinal analysis, and now even in certain law and economics and statistical techniques, than in the basic rudiments of social choice theory. Plain meaning, expressio unius, judicial review, the Coase theorem, regression analysis, and T tests–these are all part of law school vocabulary. But the Condorcet Paradox, agenda manipulation, May's Theorem, single peakedness, Downsian equilibrium, Black's Theorem and the like, are not–not yet, at least.
I think our attitude toward democracy would undergo a fairly radical change if it was broadly understood just how much we are ruled by the rules.