The gist of it, to steal both men’s thunder, is that by giving the election to the candidate who got the most votes even when that count is not a majority, one ensures that in many cases the electorate’s second-favorite candidate gets elected. George W. is a recent example in American politics. Even though he received less than 50% of the vote, he was elected, because the people voting against him split their votes among other candidates.
The proposed solution? Change elections from a “pick one candidate” system to a “rate each candidate on a scale of 1 to 5” system. Poundstone asserts that this is both constitutional and feasible, and would provide far superior election results. Sounds like very interesting grist for the mill; I’ve added his book to my reading list.