A terrible way to forecast the 2016 contest is to gauge whose supporters are the loudest. Presidential elections are not decided by partisans or ideologues.

The arithmetic is pretty simple: 41% of voters in the 2012 presidential election described themselves as moderates, and 29% as independents. Almost all Republicans (93%) and self-described conservatives (82%) voted for Mitt Romney, but that wasn’t enough. Even if Mr. Romney had won every Republican or conservative voter, it still wouldn’t have been enough.

Because there are roughly 5% more Democrats than Republicans, the GOP needs a solid majority of independents to win a national election. In 2012 Mitt Romney outpolled Barack Obama among independents, 50% to 45%. But that didn’t take him across the electoral college finish line.

It is safe to predict that the proportions that held in 2012 will be about the same this year. About two-thirds of the voters will not be Republicans. Thus it is vital to pay early attention to how each of the candidates is doing among independents. A long, drawn-out primary that forces candidates to make strong appeals to the party’s ideological base can hurt the eventual nominee in November.

There are two ways that we can measure how independents see the Republican contenders. On the positive side, we can ask whether voters hold favorable views about a candidate. Or, on the negative side, we can ask whether they would rule out voting for a candidate. Those White House hopefuls with high favorability ratings among swing voters have good prospects for winning a general election. Those whom independents and moderates say they would not even consider supporting start with a deep, probably insurmountable, deficit.

The Internet polling organization YouGov has been tracking, since May 2015, a sample of 5,000 Americans, who have been asked roughly every six weeks about the presidential race. Although Donald Trump is leading in GOP primary polls, his ratings among independents are the worst of any candidate in the field.

In YouGov’s three most recent surveys, Mr. Trump was viewed “very unfavorably” by an average of 43% of independents. How does he fare among moderate voters? In August, only 17% of moderates had a “very favorable” opinion of him; 47% had a “very unfavorable” opinion. Those figures have hardly budged since.

Ted Cruz doesn’t do much better. Only 13% to 16% of independents had a very favorable view of him in YouGov’s three most recent surveys; 28% to 32% viewed him very unfavorably. Among moderates, almost no one (6% to 7%) feels “very favorable” about Mr. Cruz; many (28% to 35%) feel “very unfavorable.”

The problem for Messrs. Trump and Cruz is not that voters don’t know who they are. Mr. Trump started out with nearly everyone being able to rate him; only about 5% said they didn’t know or didn’t have an opinion. As for Mr. Cruz, in June about a quarter of independents did not know enough about him. But over the past six months that figure has dropped to 4%—and most of those voters moved into the “unfavorable” camp. Not a good sign.

Already, large proportions of independents and moderates say that they have made up their minds about the two Republican front-runners. A full 58% of moderates and 51% of independents told YouGov in December that they “would never vote for” Mr. Trump. The figures are a little better for Mr. Cruz, but still about half of moderates (47%) and almost as many independents (41%) say they would never pull the lever for him.

How can anyone, under the circumstances, expect either of these two to win a general election? For the GOP to regain the White House, it will have to do much better, particularly given Hillary Clinton’s better ratings. In December, 48% of moderates said they would consider voting for Mrs. Clinton—a full 16 percentage points better than Mr. Trump and 22 points better than Mr. Cruz.

Many of the other Republicans running for the 2016 nomination beat Mrs. Clinton’s numbers, and unlike Mr. Trump, none starts with more than half of swing voters unwilling to consider him. Marco Rubio is the most competitive among independents: 37% said in December that they would consider voting for him; only 32% ruled him out. All the other GOP candidates are under water. Forty-seven percent of independents said they would never vote for Jeb Bush, and 43% said the same about Chris Christie.

Moderates are a little harder on the GOP contenders. Mr. Rubio again comes in first: 35% would consider voting for him, and 36% wouldn’t. Thirty-five percent of moderates would also consider voting for Mr. Bush and Mr. Christie, but their negatives are much higher: 48% have ruled out Mr. Bush, and 44% Mr. Christie.

The candidate with the lowest negatives among swing voters is John Kasich: Only 30% of moderates and independents say they would never vote for him. The problem for Mr. Kasich is that about a fifth of these voters say they have never heard of him.

With a large field, the percentage of people who say they intend to vote for a candidate is less relevant than the percentage who say they will not vote for him. By this measure, the current GOP front-runners are doing very badly. As the Iowa caucus and New Hampshire primary approach, Republicans may want to consider this if they are serious about one of their own becoming president.

Mr. Brady is a professor of political economy in the Stanford University Graduate School of Business and a senior fellow at the Hoover Institution.

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