So it turns out that the presidential debates are a noncooperative game. There are advantages to a strategy of cooperating with others, but if you see a way to improve your position by defecting, nobody can force you back in.
Maybe Donald Trump's decision to pull out of the Republicans' final televised debate before next week's Iowa caucuses will even improve his standing in the polls. After all, it's not like the news media will be talking about some other Republican candidate over the next few days. And if, as the months go by, other candidates follow Trump's lead, we'll likely see the end of the cattle-call-style debates that so depressingly saturate the electoral landscape.
A debate can be modeled as part of the larger game in which candidates vie for a prize, election victory, which only one can win. It is rational to cooperate with others by joining the debate when the payoff for participating is greater than the payoff for not participating. In making the calculation, the candidate must take into account the likely strategies of the other candidates. So the real question is whether the payoff for participating is greater than the payoff for not participating, assuming that everyone else participates.
That last proviso matters. If refusing to join the debate were a common strategy, Trump's payoff would be much smaller. But the payoff is likely to be large. His gains can be measured by the fact that he continues to be the focus of the news cycle.
On the other side of the scale, the payoff from showing up to debate would likely be small -- and not just for Trump. The gains to any presidential aspirant from cooperating (that is, attending the debate) are difficult to specify. The debates are really just joint press conferences.
Voters who crave information have sources aplenty. Voters who don't probably aren't watching anyway.
As a matter of fact, there's a good chance that even voters who claim to have seen the debates are lying. A 2012 study in Public Opinion Quarterly found that "the self-reported audience is about double the Nielsen estimate for most debates." Why would people lie to pollsters? My best guess is they think it sounds more civic-minded to say "I watched" than to say "I skipped it."
It's often suggested that the performance of a marginal candidate in the intra-party debates can provide a jump in the polls, but as the experiences of Carly Fiorina and Ben Carson remind us, such jumps tend to be short-lived. The effect of the inter-party debates in the fall is open to question. Academic work has been contradictory and inconclusive.
The political scientist James Stimson writes: "There is no case where we can trace a substantial shift to the debates. But in elections that were close at debate times, there are cases (1960, 1980, 2000) where the debates might have been the final nudge. As to why they are so often featured as the central story line of a presidential election campaign, I lean to the idea that they are conveniently available TV footage."
But Trump produces video footage aplenty wherever he goes.
The political scientist John Sides summarizes the academic research thus: "In the average election year, you can accurately predict where the race will stand after the debates by knowing the state of the race before the debates." What the evidence teaches is that the candidate who leads in the polls before the debate will almost certainly be leading after.
Then why do people watch? Because they have a rooting interest. And, like sports fans, they tend to see and hear with their hearts not their heads. As Sides reminds us, "In a CNN poll after one of the 2008 debates, 85 percent of Democrats thought that Obama had won, but only 16 percent of Republicans agreed."
If this analysis is correct, then the payoff from debating is small. Up until now, however, a candidate would have worried about the costs of not showing up. But Trump is likely to pay no penalty, and will likely see a gain. Should that happen, other candidates will begin to see the virtue of skipping the debates. A tipping point will be reached, and the current system of debates will collapse.
Sounds good to me.