Some economists and political theorists argue that electoral systems should be structured so as to maximize the probability that the electoral winner will also be a Condorcet winner.

I. What is a Condorcet Winner?

Note: If you are an economist or otherwise knowledgeable about voting theory, you should skip this section and move on to Part II.

In plain English, the Condorcet winner is the candidate who can defeat every other candidate in a head to head majority vote matchup. If the candidates in the race are Smith, Jones, and Brown, Smith is the Condorcet winner if he can defeat both Jones and Brown in separate head to head votes. Sometimes, there is no Condorcet winner available. For example, if Smith can defeat Jones, Jones would defeat Brown, and Brown would defeat Smith, none of the three is a Condorcet winner (this kind of scenario is known to game theorists as the Condorcet Paradox).

However, our presidential selection system often fails to choose the Condorcet winner even in cases where one does exist. From the standpoint of democratic theory, this might be considered problematic. If the Condorcet winner ends up an electoral loser, that implies that the electoral winner has prevailed despite the fact that a majority of voters prefer somebody else; that outcome seems to go against the notion that democracy is a system of majority rule.

II. Why Condorcet Winners Often Lose Presidential Elections.

Why would a Condorcet winner ever lose a presidential election? Because before a presidential candidate can have a real chance in the general election, he or she has to win the nomination of one of the two major parties. In the modern nomination system, that means he has to win a large enough number of primaries. Primary voters, of course, differ significantly from general election voters. They are more knowledgeable, but also more partisan and ideologically extreme. As a result, a general election Condorcet winner can easily be eliminated in the party primary because he or she isn't ideologically extreme enough for the primary voters.

This is more than just a theoretical possibility. It has actually happened in recent presidential elections. In 2000, John McCain (whose candidacy, by the way, I don't have much sympathy for) was almost certainly the Condorcet winner. Polls showed that he would easily have defeated both George W. Bush and Democratic nominee Al Gore in a head to head general election matchup. But because Republican primary voters believed (quite possibly wrongly, as it turned out) that McCain was less conservative than George W. Bush, McCain never got that chance.

More speculatively, in 2004, a moderate Democrat such as Joe Lieberman might well have defeated either the very liberal Democratic nominee John Kerry or Bush in a head to head general election matchup. However, Lieberman wasn't liberal enough for the Democratic primary electorate, and so his candidacy was doomed from the start.

I won't go through all the relevant history. But there is evidence to suggest that probable Condorcet winners also got eliminated in the primaries in 1968 (George Romney or Nelson Rockefeller, though the evidence is very equivocal), 1976 (Scoop Jackson), and 1980 (George H.W. Bush, who might well have defeated either Reagan or Carter in a general election).

In sum, there is good reason to believe that the presidential nomination system will often eliminate a Condorcet winner. In the next post, I will consider the question of whether this is a bad thing.