Yesterday, CNN and YouTube hosted yet another Democratic presidential debate. This go-round elicited stories from the newspapers about debate "fatigue." In particular, there were indications that the candidates might be a little fatigued.

Why would they be fatigued by these debates? I think the answer is reducible to a simple calculation of costs versus benefits.

First, some basic principles. I assume candidates are rational utility maximizers - just like financial actors. However, they are not looking to maximize profit. Rather, they are looking to maximize electoral support. They are willing to deploy their resources to win this support. And, so it follows, they wish to deploy those resources as efficiently as possible.

The debates are quite inefficient. This is why they are getting fatigued.

The nice thing about these debates is that it is relatively easy to "do well" in them. I'd say that for the top-tier candidates, there is at least a 95% chance that they will not damage their prospects. Accordingly, there is no more than a 5% chance that they will damage their prospects. So, that is good.

However, consider the costs that the candidates must invest for the debate. They must study up. This costs time. They must take their campaign organizations to the debate. This costs time and money. They cannot conduct other activities they might otherwise have conducted. These are opportunity costs.

And what are their payoffs if they do well? In point of fact, they are slight. They get a declaration of victory-of-a-kind on the bottom half of the fold of the newspaper (so to speak) saying, at best, that they "won" the debate, or more likely they "did everything they had to do." This is not worth much to them - at least not to the top-tier candidates. They do not get any noticeable bump in the polls - most people are not watching. Those who are do not see enough of the top-tier candidates during the debate to begin supporting them; with 10 or so candidates, nobody gets to speak very long. Furthermore, I am sure that no candidate has enjoyed a bump in contributions based upon debate performance. In reality, all they get is the temporary estimation of the political elites. This is not worth all that much.

Meanwhile, what happens if they "lose" the debate and damage their electoral prospects? Well - we all know the answer to that. Electoral prospects that are damaged by a debate are usually damaged in a dramatic way. Recall:

Zing!

The chance of this happening in any given debate to any given candidate is, of course, really small. I indicated 5%. It is probably smaller than that. However, consider the costs inherent to such loses. They are incalculably large. There is no way to recover from a gaffe like this.

Thus, we might say that the payoffs from the debate are asymmetric. A win is a high-probability event that carries little benefit. A loss is a low-probability event that carries a great cost.

Now, of course, the benefits calculus changes greatly after Labor Day in the general election campaign. At that point, voters are paying attention. So, the potential rewards from doing well increase. Now, however, the potential rewards are low. And, while I imagine the damage done by such gaffes would not be as bad now as they would be in mid-October of the actual year of the election - they can still be quite significant. After all, gaffes can be replayed again and again on, ironically enough, YouTube. And what you say now is potential ammunition against you when you face the opposing party in the general campaign. Michael Dukakis probably would not have been punished as badly if he had flubbed that death penalty question in July, 1987 - but he still could have been quite damaged.

So, all in all, there is probably no net benefit from these debates, at least for the top-tier candidates. "Winning" the debate carries with it no net benefit - the meager benefits are probably outweighed by the costs in time, money, and opportunity. Meanwhile, the chance of defeat - and the major costs it entails - further diminishes a candidate's expected net benefit.

Why, then, are the top-tier candidates doing all of these debates?

The answer, I believe, is that there is no coordination between them. What the top-tier candidates have on their hands is a collective action problem. If all of the top-tier candidates coordinated their actions, and collectively reduced the number of debates, all of them would be well off. However, there are no formal institutions in place to facilitate this kind of coordination. Thus, each candidate must choose on his own to debate or not to debate. This changes their strategic calculations dramatically. They are placed within an interaction that can be modeled by the classic prisoners' dilemma game.

Assume two candidates who must choose, on their own, whether to debate or not to debate:

What happens to a candidate if he does not debate and the other candidate does not debate? They both do well (i.e. their payoffs are "good"). They do not do very well, (i.e. their payoffs are not "great"); but they probably do not do badly, either (i.e. their payofs are not "bad"). There is some scorn placed upon them by the press - but it is diffuse and short-lasting. Meanwhile, they save all the costs they must pay to debate - and they avoid the risk. So, all in all, we'd say their payoffs are good.

What happens if both candidates debate? They do OK. The chances are they will not embarass themselves, but they do not really get anywhere electorally, they have to pay a lot to get nowhere, and they run the risk of a major setback.

What happens to a candidate if he debates and the other does not debate? He does really well and the other guy does badly. After all, he can go to the debate and be a hero of "participatory democracy" (or whatever plaudits the press will offer). His opponent looks like the jerk who "refuses to face the people's questions!"

If he does not debate and the other guy does - the payoffs are reversed.

Without any coordination, each candidate is left making his own choice. And look carefully at the choices - even though the collective benefit is greatest with both candidates not debating, both candidates always are individually better off by debating. In other words, the choice to debate "dominates" the choice not to debate.

What is the way around this? One way is, as I said, coordination. If the candidates set up some kind of (formal or informal) contract with one another so that they agree to limit the numbers of debates, and the contract includes penalties for breaking it - they might be able to avoid this collective action dilemma.

Hmmm...an informal contract? Well:

This is not a conversation about cutting the number of debates, but it is a conversation about altering the payoff structure. With fewer candidates, the top-tier candidates will have more time, and thus, if they do a good job, their participation will be of more value to them.

So, why did the Democrats individually decide to bail on the Fox News debate? Well, hey - they're Democrats and its Fox News. They could bail on it without looking bad. Heck, bailing on it made them look good. In other words, the fact that it is FNC alters the payoff structure. A given Democratic candidate can individually choose to avoid Fox without reaping the penalties that would accrue to he if he avoids CNN/YouTube and the rest of the candidates participated.

We'll see if the Democratic candidates do something about these debates. The best way for them to do this would be through the Democratic National Committee - which could be the organization that can bring about some coordination among the candidates. It might also take the heat that the party would feel for cutting back.

Incidentally - who is best off because of these debates? It's not the candidates (at least the top-tier ones). It's not the voters (who are not really watching). It's...the media! It's a perfect setup for the media. Having 10 or so debaters means that each candidate only gets 30 seconds or so to respond to any given question, which is perfect for the media's sound byte methodology. They can also put it on their cable networks, where the average viewership for these summer debates is a boost for their ratings. It's perfect for the media.