Noncompliance of the Condorcet Criterion: Does Plurality Voting Justify a Contested Convention?

In the current election, spectators have often wondered why someone like Trump, who has a 64% negative rating by likely voters according to the latest WSJ/NBC poll, has been dominating the primary season so far. For political scientists the answer is simple: plurality voting is not Condorcet compliant. In political science, a Condorcet method, is one in which a candidate that wins in a 1v1 matchup with each of the other candidates wins overall. If such a candidate exists, that person is called the Condorcet winner. Furthermore, a Condorcet loser is a candidate who loses to each opposing candidate in a 1v1 matchup, and the Condorcet criterion says that if such a candidate exists, he cannot win. If these criterion are satisfied, then the voting system is what is known as Condorcet consistent. Trump is a Condorcet loser because he loses to every other candidate in a head-to-head matchup. The question thus arises, do the flaws of plurality voting justify losing candidates remaining in the race past their point of feasible victory, in pursuit of a contested convention? First, I digress.


Condorcet winners and losers are very simple concepts in their most basic sense but are really difficult to apply to the United States system. The Condorcet criterion is an extension on majority rule and is compliant in majoritarian voting systems. In terms of this election the Condorcet loser violates the majority loser criterion because a majority of voters prefers every candidate one-on-one to Trump but Trump still wins. This is a great example of noncompliance of plurality voting to the Condorcet method. Here it doesn’t work because of the plurality. Trump can beat the lot when the entire field of candidates exists (by a margin of about 14 points).

The U.S. has a single-winner plurality voting system in which voters select one candidate to vote for and the candidate with a plurality (or the most) votes wins. The issue with this is that the least preferred candidate overall can win the election. Let’s examine the table below:


600 voters 300 voters 500 voters 200 voters
1. Trump 1. Rubio 1. Cruz 1. Kasich
2. Rubio 2. Cruz 2. Kasich 2. Cruz
3. Cruz 3. Kasich 3. Rubio 3. Rubio
4. Kasich 4. Trump 4. Trump 4. Trump


Now, this is a fictionalized account of the preferences of 1600 likely GOP primary voters. The WSJ/NBC poll used as the basis for this article, says that one-on-one, Cruz would beat Trump 57-40, Rubio would beat Trump 56-43, and Kasich would beat Trump 57-40. However, because we don’t have polling information as to 1v1 matchups between the other GOP contenders such as Kasich versus Rubio, it’s almost impossible to make a completely accurate table. Nonetheless, the table does represent a possible scenario in terms of being representative of the entire population of U.S. voters.


As one can see in the table, Cruz is preferred to Trump by 1000 – 600 voters, Rubio is preferred to Trump by 1000 – 600 voters and Kasich is preferred to Trump by 1000 – 600 voters. Thus, according to the Condorcet criterion, Trump should lose, but he does not (he wins 600 – 500 – 300 – 200), so this violates the majority loser criterion which states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win and more specifically it violates the Condorcet loser criterion which stipulates that any candidate that loses in a head-to-head match up with every other candidate (the Condorcet loser) cannot win. Stated simply, if the election were narrowed down to any one of the three remaining candidates and Trump, Trump would lose, but because of all the candidates in play, he wins, a phenomenon called the “spoiler effect”.


So  it’s fair to say that plurality voting has its issues; it does. However, a plurality voting system is extremely useful in a giant country like America, with diverse communities and the need to educate a large, spread out, dissimilar population on the voting rules and processes. Basically, plurality voting is an easy to understand system, especially compared to majority systems in which candidates have to beat the rest of the candidates combined. It makes things efficient and avoids the need to form coalitions. Plurality systems are less costly and provide quick and clear results that people can understand as opposed to other systems that include runoffs and party-list proportional representation, and other voting methods. Furthermore, in theory it forces voters to value their vote and not vote for extreme candidates, unlikely to win, as voters only have one vote for one candidate. That said, again, plurality voting has so many issues, from wasted votes (as often the majority of votes are cast for losing candidates) to being handcuffed by two political parties as proposed in Duverger’s Law. I’m going to stop here as far as voting systems go, because this could be (and has been) the subject of entire anthologies.


So back to the point: as some would say, because of the flaws of plurality voting, pursuing a contested convention as a losing candidate is justified in order to beat a Condorcet loser. However, as far as plurality flaws necessitating a contested convention goes, well, this doesn’t make sense because the convention voting process isn’t any more Condorcet consistent than the voting process in the primary season. In a contested convention, the delegates basically decide at will at that point as to which candidate to vote for, and are subject to wooing, political promises, and manipulation all the same. The delegates do not remain representative of the population or to the vote of the people, and that’s why it is such an egregious way to solve things, though it works better with two candidates with strong support going in, as this leaves the Party in less shambles a la Reagan v. Ford 1976, in which Ford came out on top in the first round of voting at the Republican National Convention.


In terms of this election, though I sympathize with the candidates hurt by plurality voting itself, John Kasich has no chance of winning anyway. As theorists would say, Kasich voters who are anti-Trump should be tactically moving away from Kasich and onto Cruz, (though this might seem to conflict somewhat with the median voter theory, my argument would be that Trump is the median candidate in a way). Basically, noncompliance of the Condorcet criterion is exactly why Kasich cannot win and should drop out. Kasich beats Trump, Cruz beats Trump, Rubio beats Trump but Trump wins. Voters in plurality systems thus, have to initiate tactics before they vote, which in the anti-Trump Republicans case would call for switching allegiances to Cruz.


Furthermore, a politician shouldn’t stay in the race because he doesn’t believe in the plurality voting system; how ludicrous is that? For Cruz, I think it’s a lot more justified to push for a contested Convention so long as he stays close to Trump. But for someone like Kasich who has not picked up a single victory outside of his home state of Ohio, he needs to accept the will of the people to not make him their top choice and Rubio needs to follow. A contested Convention would only take more of a voice away from the people. What’s worse, in terms of being a Republican, it will greatly hurt the party’s chance to beat Hillary. A few weeks ago Kasich was calling himself his “own man” and now he’s campaigning with Romney, so don’t be confused, he is just another politician. The one other thing one can argue, re: Ohio, is that the ordering of the primaries needs to be changed or done differently. I would be willing to hear arguments to that effect.



One thought on “Noncompliance of the Condorcet Criterion: Does Plurality Voting Justify a Contested Convention?

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s