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Why the Next President Might not be a Condorcet Winner:

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.

Related Posts (on one page):

  1. Should We Care if Condorcet Winners Lose Presidential Elections?
  2. Why the Next President Might not be a Condorcet Winner:
Kovarsky (mail):
ilya,

i don't think that candidate C is a condorcet winner because he beats candidates A and B, with A being from C's party and B being from the other. your data would need to show that C would be a condorcet winner against all the candidates in B's (the other) party that lost out on the nomination. i doubt the data supports that (although i would be ineterested in seeing it).

if you believe that A won the nomination because he prevailed in pairwise contests with the other primary candidates in his party, then whether A wins the general or not is a fairly good proxy for who occupies a strong point (the person most likely to prevail in a contest with a random selection of opponents).
12.19.2007 12:04am
randal (mail):
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.

This statement is misleading. It's quite possible for the Condorcet winner to win, yet the majority of voters prefer somebody else.

The Condorcet winner isn't even the candidate who is the plurality's first choice.

The Condorcet winner is only exactly what you said: the candidate that no other candidate could beat head-to-head. The colloquial term for this person is "everybody's second choice".
12.19.2007 12:06am
highway61:
Do you mean George Romney?
12.19.2007 12:09am
Oren:
The problem with Condorcet is that it is prone to tactical voting. Of course, FPP is the epitome of strategic voting but the calculus for the individual voter is much simpler. Even worse, all Condorcet methods (IIRC) fail at the participation criterion which is a total brainf**k for voters.

Try explaining to Aunti Mae from Iowa City that voting for Bush over Kerry could make Kerry win. This is after you've already assuaged her doubts about "putting the preferences in a matrix and computing the optimal result" does not mean "rig the system so my candidate always wins by a fluke".

Furthermore, Condorcet winners tend to be the lowest common denominator. The election ceases to be about which candidate has the strongest support but rather which has the fewest number of detractors. I'd rather suffer through presidents I don't like than have to elect people without any vision at all.

Finally, in our reality, the two parties would quickly put together pamphlets encouraging their supports to rank the party nominee top and the other party nominee bottom. If a substantial number of people did this, we'd be back to FPP (except convoluted).
12.19.2007 12:09am
Ilya Somin:
Do you mean George Romney?

Yes.
12.19.2007 12:13am
Ilya Somin:
i don't think that candidate C is a condorcet winner because he beats candidates A and B, with A being from C's party and B being from the other. your data would need to show that C would be a condorcet winner against all the candidates in B's (the other) party that lost out on the nomination. i doubt the data supports that (although i would be ineterested in seeing it).

In the stylized example, this is true by definition because A, B, and C are the only candidates. In the real world cases I mentioned (2000 and 2004), this also held true. In 2000, polls showed that McCain would have beaten Bradley (Gore's only rival for the Democratic nomination) in a general election. In 2004, Bush was the only Republican candidate, so if Lieberman or some other moderate Democrat could have beaten him, that by definition means they could beat the entire Republican field.

if you believe that A won the nomination because he prevailed in pairwise contests with the other primary candidates in his party, then whether A wins the general or not is a fairly good proxy for who occupies a strong point (the person most likely to prevail in a contest with a random selection of opponents).

Not necessarily true. A wins his party's nomination because he could win a pair wise contest against all the other candidates from his party before the primary electorate. But my whole point is that the primary electorate differs in important ways from the general electorate. Therefore, there is no guarantee that if A defeats B in his party's primaries, he would also have defeated him in a head to head general election matchup.
12.19.2007 12:20am
cathyf:
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.
What is artificial about the whole idea is that is based upon the premise that campaigns don't matter. Those of us who think democracy is a process of people making decisions as well as a process of communicating those decisions would argue that what those polls showed was not particularly relevant, because the people being polled were not being exposed to a compaign based upon either of those matchups.

Because primary voters are more knowledgeable about the candidates, they make decisions based upon things which the general electorate doesn't know about. So when you do some hypothetical poll back in early 2000 of the general population of voters, they answer according to what they know, and to most general election voters, they have only a vague sense of who McCain is and what he believes. So they are favorably disposed to him based upon ignorance. The primary voters are not nearly so ignorant, and so they eliminate him from the race without having to educate the non-primary-but-general voters as to McCain's failings.

When actual conservatives talk about what they do or don't like about McCain (as opposed to liberals imagining what conservatives do or don't like about McCain) the focus is on his substantial failings of character. This is a man who projects blame for his own ethical failings upon the human race as a whole, and actively goes out and punishes everyone for those failings. For lots of conservatives, the character failings more than override the fact that McCain has genuine conservative beliefs. If McCain had been more successful in the primaries, then the conservative voters repelled by McCain's character failings would have actively gone out and pointed out the character failings to the less-informed voters, and it's plausible that this would have damaged McCain's poll standings to the extent that he could not have beaten either Bush or Gore. But since McCain's candidacy failed rather early on, there was no need to point out his flaws to the ignorant.
12.19.2007 12:36am
Elliot Reed (mail):
Oren--indeed. The voters wouldn't even be able to understand the mechanics of a Condorcet system, much less work out the implications for strategic voting. Can you imagine the American public, most of which doesn't know what a "set" is, making sense of sequential Schwartz dropping? Heck, I have trouble with sequential Schwartz dropping.

Then again, a Condorcet system might inadvertantly promote sincere voting because nobody would be able to make enough sense of the system to vote strategically.
12.19.2007 1:36am
Thorley Winston (mail) (www):
When actual conservatives talk about what they do or don't like about McCain (as opposed to liberals imagining what conservatives do or don't like about McCain) the focus is on his substantial failings of character. This is a man who projects blame for his own ethical failings upon the human race as a whole, and actively goes out and punishes everyone for those failings.


Evidence please.
12.19.2007 1:39am
Thorley Winston (mail) (www):
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.


As someone who if he had to do it over again would have voted for McCain over Bush in 2000, I don't find the argument that because a poll of people who could have voted for Candidate A claim to have preferred him but ultimately whey they had the chance didn't vote for Candidate A* that somehow the preferences of the majority were thwarted all that persuasive. At the end of the day, polls don't mean s*** but actually turning out to vote means everything.

* Either in an open-primary or in a State with a closed primary by registering for that party for the purpose of voting for Candidate A.
12.19.2007 1:46am
Ilya Somin:
I don't find the argument that because a poll of people who could have voted for Candidate A claim to have preferred him but ultimately whey they had the chance didn't vote for Candidate A* that somehow the preferences of the majority were thwarted all that persuasive.

The point, however, is that they DIDN'T have the chance to vote for A, because he was defeated in a primary before they would have gotten that chance.
12.19.2007 1:59am
Thorley Winston (mail) (www):

The point, however, is that they DIDN'T have the chance to vote for A, because he was defeated in a primary before they would have gotten that chance.


Um, Illya did you miss the part where I said:


* Either in an open-primary or in a State with a closed primary by registering for that party for the purpose of voting for Candidate A


I stand by my statement, if these supposed "Condorcet winners" really had the actual support of a majority of voters (as opposed to merely appearing that way in some meaningless poll) then people would have turned to vote for them in the primaries to ensure that they were the nominee and then elect them in the general election.
12.19.2007 2:13am
David M. Nieporent (www):
I stand by my statement, if these supposed "Condorcet winners" really had the actual support of a majority of voters (as opposed to merely appearing that way in some meaningless poll) then people would have turned to vote for them in the primaries to ensure that they were the nominee and then elect them in the general election.
Well, that's just... stupid. You think that the fact that a registered Democrat in February 2000 voted for, e.g., Bradley over Gore shows that he didn't favor McCain over Gore because he didn't change his registration to Republican to vote for him?

That doesn't even address the fact that many states don't let you "register for that party for the purpose of voting for Candidate A" unless you do it far in advance -- New Jersey requires 50 days notice, for instance.
12.19.2007 3:49am
arrow theroem fan:
A better (nonpolitical) explanation of why this happens is that the US voting system simply doesn't have independence of irrelevant alternatives as one of its properties.

Also this doesn't just happen because of primaries. It happens in general elections too (think of how third party candidates can swing an election to a candidate that would have lost 1 on 1).
12.19.2007 4:58am
rarango (mail):
Arrow theorem fan has nailed it--The electoral process can be modeled by economic theory, but the current electoral process doesnt have the elegance and parsimony of an economic model. Moreover, using polling data to specify who the winner might be is not appropriate; the only test is a genuine head to head election, and current polling data isnt precise enough to measure that--it would take an actual election to determine and our system doesnt do that.
12.19.2007 9:03am
The NJ Annuitant (mail):
It all boils down to winning a pluarlity of the votes in enough states to produce a majority in the electoral college. The motivated, primary election voters are, I would think, more likely to vote in the general election than the general public, and therfore,it strikes me as altogether fair that they have much more say in which candidate is nominated Putting together an elecotral college majority would, I think, have little to do with being a Condorcet winner. I do not see this as a cloud on our democracy.
12.19.2007 9:24am
Tracy Johnson (www):
Perhaps putting them in an octagonal "Ultimate Fighting" cage may work better?
12.19.2007 10:32am
Bob from Ohio (mail):

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 all three examples, plus 2000, the party of the Condorcet winner was the party that won the election. So, why does it matter?
12.19.2007 11:11am
CWuestefeld (mail) (www):
the party of the Condorcet winner was the party that won the election. So, why does it matter?

Ummm... because we elect individuals and not parties?

Whether you like or despise either one, do you think that GB and McCain are equivalent?

(I don't think that it matters, but the issue of party affinity is not the reason that it doesn't matter)
12.19.2007 12:33pm
Justin (mail):
" In 2000, John McCain (whose candidacy, by the way, I don't have much sympathy for) was almost certainly the Condorcet winner."

But - better than Bush? This is game theory, so there are no absolutes: do you have sympathy for McCain's candidacy relative to Bush's candidacy, at least in hindsight?
12.19.2007 12:51pm
KeithK (mail):

the party of the Condorcet winner was the party that won the election. So, why does it matter?


I suspect the world would be a different place had either Scoop Jackson won in '76 or Heorge H. W. Bush won in '80.
12.19.2007 2:13pm
Dilan Esper (mail) (www):
What is artificial about the whole idea is that is based upon the premise that campaigns don't matter.

From the left, I agree with the point cathyf made from the right.

Look at Ilya's example, Lieberman. Yes, he might have been more electable. But if he had been elected, he would have continued the Iraq War for 4 more years (as Bush did) and then either been reelected or replaced by a Republican who would also likely continue the Iraq War for another 4 years.

Instead, the Democratic primary electorate has slowly made it more and more clear that it is not acceptable for the party to continue to support the Iraq War. Yes, that may mean losing a winnable election. But in the long term, if this is a principle the party's base cares about and which defines it, the primary electorate may decide that it is worth the cost.

The Republican base does the same thing, and it is just as legitimate on that side of the aisle.
12.19.2007 5:03pm