Prisoner’s dilemma: Bernie Sanders rivals staying in the race prop him up and fall victim to game theory problem

If more centrist Democratic presidential candidates want to stop ideological rival Bernie Sanders from amassing a delegate lead on Super Tuesday, why are they all staying in the race and refusing to coalesce around a single alternative?

The campaigns of former New York Mayor Michael Bloomberg and former South Bend, Indiana, Mayor Pete Buttigieg have each warned that the socialist Vermont senator could gain an “insurmountable” lead that is “impossible to stop” unless centrist candidates, including former vice president Joe Biden and Minnesota Sen. Amy Klobuchar, drop out before March 3 Super Tuesday contests in 14 states and one U.S. territory.

“A vote for all of these candidates that are not polling high, in my view, is a vote for Bernie Sanders,” South Carolina state Sen. Marlon Kimpson, a supporter of Joe Biden, said on CNN Tuesday. “At some point, we’re going to have to consolidate the moderates in this race and really start talking about electability.”

But as Sanders becomes the clear front-runner following his decisive win in the Nevada caucuses and centrist rivals warn that his radical policies could keep Democrats from winning the White House and down-ballot races, the candidates show no sign of bowing out of the race, keeping the field unusually large.

One answer is that the candidates are stuck in a classic game theory problem. The situation is akin to the prisoner’s dilemma, a game theory principle that describes a situation in which individuals each acting in their own self-interest do not produce an ideal outcome.

“Each candidate is feeling some pressure to get out of the race to help consolidate the non-Sanders and even the non-Bloomberg vote,” said Barry Burden, a political science professor and director of the elections research center at the University of Wisconsin-Madison. “The trouble is that each candidate also has reasons to stay in the race. All are hoping for an unsettled party convention in which neither Sanders nor anyone else walks in with a majority of pledged delegates.”

The classic prisoner’s dilemma example is two co-conspirators who each face a year in prison. If one turns and blames the other, he will go free while the other serves two years — the seemingly best option for self-interested individuals. But if both defect, each will be sentenced to two years in prison, a worse situation.

Real-world variations of the prisoner’s dilemma manifest in business analysis — such as dropping prices in hopes of selling more than a main competitor, while risking that main competitor matching the price, resulting in lower profits for both companies. And in economic principles like the tragedy of the commons, in which individuals overuse a commonly available resource to the point of making it unavailable to anyone.

In the Democratic presidential race, if each centrist candidate works in their primary self-interest by staying in the race, it has the disastrous effect of boosting their ideological rival and preventing any of them from winning the Democratic presidential nomination. And it hurts their shared goal of defeating President Trump in November.

“It is not in any individual candidate’s self-interest to drop out,” Christian Grose, a political science professor at the University of Southern California. “Candidates are motivated by them winning first, and other motivations are secondary. A motivation to stop a particular candidate from winning is secondary to their motivation of wanting to be the nominee.”

A USC Price-Schwarzenegger California Issues Poll conducted in the first half of February found that Sanders was the top choice among likely Democratic primary voters at 29.2%, with Biden in second at 21.4%, Massachusetts Sen. Elizabeth Warren at 20.2%, Bloomberg at 7.7%, Buttigieg at 5.8%, and Klobuchar at 2.7%.

Based on that poll, it is plausible that “Sanders could beat the 15% delegate threshold while all these other candidates get just under 15% of the delegate total. If one’s goal is to stop Bernie Sanders, it makes sense for one candidate to emerge as the focal point of the stop Bernie group,” Grose said.

Middlebury College professor Bert Johnson said that the dynamic among centrist Democratic presidential candidates could be explained as another game theory concept: A game of chicken.

The classic game of chicken scenario is two drivers heading for each other on a road. If neither swerves, both crash and lose. If one swerves, the other keeps going and is the winner.

For centrists in the field, the game of chicken is whether any candidates will “swerve” and drop out to prevent a “crash” of Sanders winning.

“The way to win a game of chicken is you metaphorically tear the steering wheel out of your car and throw it out the window so that everybody else knows that you’re committed to not swerving,” Johnson said. “Bloomberg probably has the best argument for that, saying, ‘Well, you know, I’ve got so much money I can throw at this no matter what. Whatever my standing in the polls, I’m just going to stay in it.”

The situation poses a challenge for centrist voters who do not want Sanders to win the Democratic presidential nomination. To cast a consequential vote for a Sanders alternative, voters must figure out “who everyone else is going to vote for and vote for that person,” Johnson said. “But it’s impossible for them to figure that out at this point.”

The game theory applications assume, however, that the candidates do genuinely fear socialist Sanders as the Democratic presidential nominee. Other motivations for staying in the race include boosting a national profile or not wanting to give up after committing enormous time and money to their bids.

“As long as the campaigns have enough cash to pay for travel, staff, and advertising, they will be enticed to hang around at least long enough to see if Sanders or Bloomberg is on a path to a delegate majority,” said Burden, the University of Wisconsin-Madison professor. “Each is also further buoyed by the hope that another moderate will drop, giving them an even stronger claim as the alternative to Sanders or Bloomberg.”

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