What Does A Trump Plurality Mean?

by Don Boudreaux on May 3, 2016

in Myths and Fallacies, Politics, Seen and Unseen

Suppose that at the end of the 2016 Republican primary cycle Donald Trump has a plurality of the popular vote – say, 40 percent.  The remaining 60 percent of the primary vote is spread out over the dozen or so other candidates who were at one time, and some of whom remain, in the race for the GOP presidential nomination.

Contrary to much of what is now being said in the press and on the web, it would not necessarily be (as I heard one person on the radio put it) “a crime against democracy” for GOPers to deny Donald Trump the nomination.  The reason is simple and straightforward: most primary voters (in my example, 60 percent) voted against Trump.

It’s a common (and understandable) mistake to read a vote cast for candidate A as being only a vote for candidate A.  But a vote cast for candidate A might well be – and in practice certainly often is – motivated more by opposition to candidate B than one motivated by enthusiasm for candidate A.  If candidate A wins an outright majority, this reality creates no problem under the rules of majoritarian democracy, for even if all votes cast for candidates B, C, … N are motivated exclusively by utter hatred of candidate A rather than as enthusiasm or support for the candidates who received those votes, the fact remains that a majority of the voters prefer candidate A over all other available candidates.  But if candidate A wins only a plurality and not a majority of the votes, then – as students of collective decision-making have long known – there is no good reason to declare the plurality vote-getter as the winner.  Again, the reason is that the chances are high enough that those who voted for the other candidates did so more to keep A out of office than to install in office one of the candidates B, C, … N.  And given Trump’s huge negatives, this possibility is even more likely with him than with more quotidian candidates who win only pluralities.

Put more succinctly (and ignoring the countless other flaws that infect all collective-decision-making processes), a candidate who wins a majority of the votes can at least be said to be preferred over any of the other candidates by most of the voters.  The same cannot be said of a candidate who wins only a plurality.  Most of the voters might well prefer above all to keep that candidate (A) out of office even if most of the voters have no clear preference for which of the other candidates (B, C, … N) is the best option in place of A.

Here’s an example of ten voters and four candidates (A, B, C, & D).  The example follows the rules of the method that many U.S. states use to choose governors.  That method is the “general election, runoff election.”  The rules are simple.  If a candidate wins a majority of votes in the general election, that candidate wins the election.  But if no candidate wins a majority of the votes, the plurality winner is pitted in a runoff election against the candidate who got the second-highest percentage of the votes in the general election.

Each voter’s preference is shown below in descending order.  For example, voter 1 prefers candidate A above all, and she prefers D to C and C to B.
Screen Shot 2016-05-03 at 10.09.42 AM

In the general election, candidate A will win 40 percent of the votes; candidate B will win 30 percent; candidate C will win 20 percent; and candidate D – seemingly a fringe candidate – will win only 10 percent.

So in the runoff election candidate A is pitted against candidate B.  (Candidates C and D are ousted from the race.)  Below is the very same preference ordering, but with candidates C and D excluded.

Screen Shot 2016-05-03 at 10.17.13 AM

B wins the runoff with 60 percent of the votes.

But, just for kicks, let’s see what happens if that fringe candidate D were to be pitted in a runoff election against B.  Surely D would get trounced, right?  Wrong.  If you look at the first preference table above (the one with all the candidates included), you’ll find that 60 percent of the voters prefer candidate D over candidate B!  You’ll find also that 60 percent of the voters prefer candidate D over candidate A.  (And, to continue a bit further with the exercise: 70 percent of the voters prefer candidate D over candidate C; 60 percent of the voters prefer candidate C over candidate B – the ultimate winner of the election; and 60 percent of the voters prefer candidate C over candidate A – the plurality winner in the general election.)

The main point of the above exercise – which involves a perfectly reasonable representative example of reality – is to reveal that a candidate who wins a plurality of the votes but who does not win a majority of the votes in fact is not at all clearly the most preferred candidate of all the voters.  Trump very well might be the real-world equivalent of candidate A in this example.

(Again, other problems – many equally eye-opening as this one – affect collective-decision-making schemes.  But this post is already too long.)

Bottom line: if Trump wins only a plurality of GOP primary votes, that fact is not evidence that Trump is, among all the candidates, the one most preferred by GOP primary voters.


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