Given Donald Trump’s continuing electoral success, it appears increasingly likely that only a “brokered convention” can prevent a Trump nomination.

Various voices have begun to suggest that such an outcome would be an illegitimate, undemocratic maneuver — essentially, the party establishment’s “stealing” the nomination (see Newt Gingrich’s comments). Party leaders “should not be able to use conventions as a way to subvert the will of the people” (see the Atlantic, for example).  Even those who favor this route apologetically acknowledge a brokered convention as an “anachronistic, undemocratic” means to an end.

Such arguments represent a fundamental confusion about the nature of democratic decision-making. A little reflection shows that concepts like “the will of the people” are quite slippery – and that Trump has no special claim on that title.

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Of course, what voters want is important in a democracy. But the results of elections are not simply a reflection of “the people’s will.” They derive from the combination of three factors: voter preferences, the rules that define how citizens can vote and how votes are counted, and the choices that are presented to voters.

Here’s the key point: Exactly the same voter preferences can result in widely different election results under alternative (and equally democratic) election procedures. As a result, it is not at all clear what “the will of the people” might mean.

A simple example illustrates this. The following table lists the preferences of 100 voters over three candidates — for example, 34 voters prefer Lopez to Lee to Lewis, and so on.

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34 voters 30 voters 26 voters 10 voters
Lopez Lee Lewis Lewis
Lee Lopez Lee Lopez
Lewis Lewis Lopez Lee

Plurality rule — the person with the most votes wins — is standard for most elections in the United States. By this rule, the candidate who secures the most votes is declared the “winner” of a presidential primary (leaving aside the much more complicated question of delegate allocation). Under plurality rule, candidate Lewis wins with 36 percent of the vote.

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But of course plurality rule is not the only plausible election procedure; many other procedures are used around the world and in the United States.

Consider, for example, an instant run-off procedure, used in some state and local elections in the U.S. Under this procedure, candidate Lee – who receives the fewest votes – would be eliminated in the first round, her votes would be transferred to her voters’ second choice (Lopez), and Lopez would win the election with a comfortable two-thirds majority (64-36) against Lewis. A majority run-off system (used, for example, to elect the president of France) would result in the same outcome.

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Or consider the Borda count, which is used to elect the winner of the Heisman Trophy and baseball’s most valuable player, among others. Under this system, each voter ranks the candidates from best to worst, assigning one point for first place, two points for second place, and so forth. The points are totaled, and the candidate with the lowest score wins. In this case, Lee (180 points) beats both Lopez (192 points) and Lewis (238 points).

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Finally, note that Lee is preferred by a majority of voters to both Lewis and Lopez – and thus would win a “round-robin” tournament between the candidates.

What is the point here? What the example underscores is that there is no straightforward or self-evident way to think about “what the people want” or what “the voters’ choice” is.

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Step back for a moment. Does Lewis really reflect “the will of the people”? Sure, he secures the most votes if citizens can only choose one candidate. But two-thirds of the voters would prefer either of the other candidates!

Is Lopez “the people’s choice”? Almost as many voters place him first as Lewis, and he is second for many more. But Lopez would lose decisively to Lee!

So perhaps Lee represents “the people’s will”? Maybe. Lee seems to be a compromise candidate — but of course Lee is also the first choice of the smallest number of voters.

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In short, it is not at all clear who voters prefer in a situation like this. The winner is determined as much by electoral rules as it is by the preferences of voters.

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This fact — that aggregating the preferences of  individuals is a vexing problem — is one of the most important insights of the social sciences of the past 50 years. It earned Kenneth Arrow a Nobel Prize, and William Riker wrote powerfully about its implications for democratic theory.

Of course, these results do not imply that votes cast are meaningless, or should be ignored. This is why it is important to specify electoral procedures ahead of time, and not to change them “midstream.” By this logic, should Trump win a majority of delegates, the Republican Party should accept this outcome.

But if Trump fails to win a majority of delegates, the logic is equally clear: securing a plurality of the vote (or delegates) does not provide Trump with any special claim to legitimacy, nor does it give him the mantle of “the people’s choice.”

In this case, a brokered convention that denies him the nomination is not a coup in which the party’s establishment thumbs its nose at the electorate. On the contrary, such an outcome can represent the preferences of many voters, and have an equally powerful claim to be “democratic.”

Georg Vanberg is a professor of political science at Duke University.

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