The Anti-Trump Endorsement Game

The mathematical strategy behind endorsing Ted Cruz, as explained by game theory.

In this game, Donald Trump is king.  (Mel Evans / AP)

In 1936, the economist John Maynard Keynes invented a beauty contest. In examining why stock prices fluctuate, he suggested the metaphor of a newspaper pageant, where readers select the six prettiest faces from 100 photographs. But only people who picked the most popular choices would win.

“It is not a case of choosing which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks are the prettiest,” he wrote. “We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be.”

I doubt Keynes was on Jeb Bush’s mind Wednesday, when the former presidential candidate announced his support for Ted Cruz on Facebook. But you’d better believe the beauty pageant was in play. While it’s hard to gauge Bush’s actual feelings for Cruz—it appears he left most of the insults to his brother—he spent only one sentence in his statement praising the Texas senator before moving on. Cruz’s foremost qualification, it appears, was his ability to appeal to voters and win primary contests.”

And so Bush joins a slew of other prominent conservatives—Mitt Romney, Lindsey Graham, Carly Fiorina—who picked not the prettiest in the pageant, but the presumptive favorite. In doing so, they’ve moved into the realm of pure strategy, where the goal is not the election of Cruz but the defeat of Donald Trump, and by extension, Hillary Clinton.

You could argue that every endorsement is strategic. Very few are proffered without the expectation of something in return, be it as tangible as a position in a future administration (in the case of former opponents, or sitting senators), fundraising with the candidate (coveted by local legislators), or just the reflected glow of a successful election (county commissioners, party officials). Even so, you’re still expected to like the candidate you’re endorsing, or at least think they’re the best pick for the job. But that was before the 2016 race turned into a game theory experiment, where true feelings are set aside for the purpose of a single mathematical result.

When it comes to strategy, my comprehension ends at the old Prisoner’s Dilemma trick. So I called Kevin Zollman, an associate professor at Carnegie Mellon University, who studies game theory and the philosophical underpinnings of strategy. He and I talked through the rules of the games being played on the national stage, and how they theoretically could be won.

The push and pull of being first

By now, it’s no longer surprising to see Chris Christie tagging along behind Donald Trump like a younger brother. But at the time of his endorsement, no one could believe it. Why would Christie, still tan from his time in the spotlight, tie himself so quickly to such a divisive candidate?

Zollman notes being among the first to endorse a candidate who is best positioned to win has its advantages. “You get more credibility,” he said. “I want to endorse early so I can say, ‘I was there first’ — the political version of being a hipster.”

But it comes with risks. “You might endorse a loser, or you might waste an endorsement,” he continued. “Think of those people who rushed out and endorsed Bush. They can come back and change their endorsement… but in a certain sense, they’ve lost the gain they got. They’re not going to get the same influence now.”

This might not be a problem for Christie. While he’s maintained a friendship with Trump for years, Zollman told me he and his colleagues suspect the New Jersey governor is actually aiming to attach himself to Trump’s movement—a groundswell of discontent that could reshape the Republican Party. That way, even if Trump loses, Christie still wins.

Collective ignorance

At the other end of the game is the #NeverTrump movement. Mitt Romney, the one-man army, has to tread carefully while arguing to voters that Trump is the wrong pick—because after all, many of them voted for him.

But the parable of “The Emperor’s New Clothes” could shed light on his approach. As written by Hans Christen Anderson, the tale relates the plight of a king hoodwinked by a charlatan, who claims to have crafted a robe so fine that only the most discerning eye can see it. The king, too embarrassed to admit he can’t see his new suit, parades around in the buff to the ooh’s and ah’s of his court; it’s left to a child to point out that the monarch is actually naked.

In this framing, the American public is the king’s courtiers, certain that Trump will win and too embarrassed to admit they’d rather vote for someone else. Romney’s best hope is to play the child, the voice of reason that breaks the spell.

But in order for this to work, Zollman argues, that voice must be both impartial and credible. The kid grabbed attention because he had nothing to gain by pointing out the emperor’s nudity; Romney might not have that kind of trust.

“It might be that endorsements could be a way to overcome that collective ignorance,” Zollman said. “The problem Mitt Romney faces is that he might been seen as sufficiently out of touch … that people say, ‘Well, he doesn’t really know.’”

Costly signaling

Male peacocks are prized for their tails, but nature didn’t make them to be just pretty; they’re indirectly an indicator of the bird’s survival skills. If a peacock is adept at finding food and avoiding predators, it can afford the caloric cost of growing a magnificent plumage, which is irresistible to the opposite sex. Otherwise, they’re a tail-less loser.

That’s what game theorists call “costly signaling,” a concession an individual makes to indicate greater strength. Academics have theorized that the sharing of food in hunter-gatherer societies might not be primarily altruistic, but rather a chance for the best hunters to show off their skills, and thereby move up in the reproductive pecking order.

Washington has come a long way from hunting large game with spears. But Zollman suggests costly signaling is what actually gives endorsements their power. By showing you’re willing to stake your own political capital behind someone, you strengthen both of your reputations—if it goes well, of course.

“By endorsing a candidate, you are running the risk of losing your political reputation,” he said. “It has to be the case that there's some risk to the person that's saying it. Otherwise it's just cheap talk.”

This may matter even more as candidates consider running mates. In this frame, the prospective vice president becomes the peacock’s tail, a signal to the electorate that you’re willing to play ball.

“You're kind of saying to a particular constituency, ‘I'm guaranteeing that I'm going to pay attention to your interests,’ because the running mate comes with pluses and minuses,” Zollman said. “A moderate Republican choosing a far-right Republican as a running is saying to the far right, ‘Look, I’m taking on liability … I must be planning to represent your interests.’”

Bush, of course, is no longer in the position to make that play. But his endorsement on Wednesday was another turn of the cards in a game that refuses to conform to old rules. The winner will be the candidate who figures out the new ones.