An opportunity cost model of subjective effort and task performance (h/t lukeprog) is a very interesting paper on why we accumulate mental fatigue: Kurzban et al. suggest an opportunity cost model, where intense focus on a single task means that we become less capable of using our mental resources for anything else, and accumulating mental fatigue is part of a cost-benefit calculation that encourages us to shift our attention instead of monomaniacally concentrating on just one task which may not be the most rewarding possible. Correspondingly, the amount of boredom or mental fatigue we experience with a task should correspond with the perceived rewards from other tasks available at the moment. A task will feel more boring/effortful if there's something more rewarding that you could be doing instead (i.e. if the opportunity costs for pursuing your current task are higher), and if it requires exclusive use of cognitive resources that could also be used for something else.

This seems to make an amount of intuitive/introspective sense - I had a much easier time doing stuff without getting bored as a kid, when there simply wasn't much else that I could be doing instead. And it does roughly feel like I would get more quickly bored with things in situations where more engaging pursuits were available. I'm also reminded of the thing I noticed as a kid where, if I borrowed a single book from the library, I would likely get quickly engrossed in it, whereas if I had several alternatives it would be more likely that I'd end up looking at each for a bit but never really get around reading any of them.

An opportunity cost model also makes more sense than resource models of willpower which, as Kurzban quite persuasively argued in his earlier book, don't really fit together with the fact that the brain is an information-processing system. My computer doesn't need to use any more electricity in situations where it "decides" to do something as opposed to not doing something, but resource models of willpower have tried to postulate that we would need more of e.g. glucose in order to maintain willpower. (Rather, it makes more sense to presume that a low level of blood sugar would shift the cost-benefit calculations in a way that led to e.g. conservation of resources.)

This isn't just Kurzban et al's opinion - the paper was published in Behavioral and Brain Sciences, which invites diverse comments to all the papers that they publish. In this particular case, it was surprising how muted the defenses of the resource model were. As Kurzban et al point out in their response to responses:

As context for our expectations, consider the impact of one of the central ideas with which we were taking issue, the claim that “willpower” is a resource that is consumed when self-control is exerted. To give a sense of the reach of this idea, in the same month that our target article was accepted for publication Michael Lewis reported in Vanity Fair that no less a figure than President Barack Obama was aware of, endorsed, and based his decision- making process on the general idea that “the simple act of making decisions degrades one’s ability to make further decisions,” with Obama explaining: “I’m trying to pare down decisions. I don’t want to make decisions about what I’m eating or wearing. Because I have too many other decisions to make ” (Lewis 2012 ).

Add to this the fact that a book based on this idea became a New York Times bestseller (Baumeister & Tierney 2011 ), the fact that a central paper articulating the idea (Baumeister et al. 1998 ) has been cited more than 1,400 times, and, more broadly, the vast number of research programs using this idea as a foundation, and we can be forgiven for thinking that we would have kicked up something of a hornet’s nest in suggesting that the willpower-as-resource model was wrong. So we anticipated no small amount of stings from the large number of scholars involved in this research enterprise. These were our expectations before receiving the commentaries.

Our expectations were not met. Take, for example, the reaction to our claim that the glucose version of the resource argument is false (Kurzban 2010a ). Inzlicht & Schmeichel, scholars who have published widely in the willpower-as-resource literature, more or less casually bury the model with the remark in their commentary that the “mounting evidence points to the conclusion that blood glucose is not the proximate mechanism of depletion.” ( Malecek & Poldrack express a similar view.) Not a single voice has been raised to defend the glucose model, and, given the evidence that we advanced to support our view that this model is unlikely to be correct, we hope that researchers will take the fact that none of the impressive array of scholars submitting comments defended the view to be a good indication that perhaps the model is, in fact, indefensible. Even if the opportunity cost account of effort turns out not to be correct, we are pleased that the evidence from the commentaries – or the absence of evidence – will stand as an indication to audiences that it might be time to move to more profitable explanations of subjective effort.

While the silence on the glucose model is perhaps most obvious, we are similarly surprised by the remarkably light defense of the resource view more generally. As Kool & Botvinick put it, quite correctly in our perception: “Research on the dynamics of cognitive effort have been dominated, over recent decades, by accounts centering on the notion of a limited and depletable ‘resource’” (italics ours). It would seem to be quite surprising, then, that in the context of our critique of the dominant view, arguably the strongest pertinent remarks come from Carter & McCullough, who imply that the strength of the key phenomenon that underlies the resource model – two-task “ego-depletion” studies – might be considerably less than previously thought or perhaps even nonexistent. Despite the confidence voiced by Inzlicht & Schmeichel about the two-task findings, the strongest voices surrounding the model, then, are raised against it, rather than for it. (See also Monterosso & Luo , who are similarly skeptical of the resource account.)

Indeed, what defenses there are of the resource account are not nearly as adamant as we had expected. Hagger wonders if there is “still room for a ‘resource’ account,” given the evidence that cuts against it, conceding that “[t]he ego-depletion literature is problematic.” Further, he relies largely on the argument that the opportunity cost model we offer might be incomplete, thus “leaving room” for other ideas.

(I'm leaving out discussion of some commentaries which do attempt to defend resource models.)

Though the model still seems to be missing pieces - as one of the commentaries points out, it doesn't really address the fact that some tasks are more inherently boring than others. Some of it might be explained by the argument given in Shouts, Whispers, and the Myth of Willpower: A Recursive Guide to Efficacy (I quote the most relevant bit here), where the author suggests that "self-discipline" in some domain is really about sensitivity for feedback in that domain: a novice in some task doesn't really manage to notice the small nuances that have become so significant for an expert, so they receive little feedback for their actions and it ends up being a boring vigilance task. Whereas an expert will instantly notice the effects that their actions have on the system and get feedback of their progress, which in the opportunity cost model could be interpreted as raising the worthwhileness of the task they're working on. If we go with Kurzban et al.'s notion of us acquiring further information about the expected utility of the task we're working on as we continue working on it, then getting feedback from the task could possibly be read as a sign of the task being one in which we can expect to succeed in.

Another missing piece with the model is that it doesn't really seem to explain the way that one can come home after a long day at work and then feel too exhausted to do anything at all - it can't really be about opportunity costs if you end up so tired that you can't come up with ~any activity that you'd want to do.

A surprisingly good New York Times essay on willpower / ego depletion:
Do You Suffer From Decision Fatigue?

As it turns out, the essay is based on an upcoming Roy F. Baumeister book, "Willpower: Rediscovering the Greatest Human Strength", which will be available from Amazon in a couple of weeks (September 1, 2011) both as a hardcover and a Kindle edition.

Some quotes from the essay (italics and headings mine):

You spend the most willpower when you have to make AND implement your decisions:

which phase of the decision-making process was most fatiguing? To find out, Kathleen Vohs, a former colleague of Baumeister’s now at the University of Minnesota, performed an experiment using the self-service Web site of Dell Computers. One group in the experiment carefully studied the advantages and disadvantages of various features available for a computer — the type of screen, the size of the hard drive, etc. — without actually making a final decision on which ones to choose. A second group was given a list of predetermined specifications and told to configure a computer by going through the laborious, step-by-step process of locating the specified features among the arrays of options and then clicking on the right ones. The purpose of this was to duplicate everything that happens in the postdecisional phase, when the choice is implemented. The third group had to figure out for themselves which features they wanted on their computers and go through the process of choosing them; they didn’t simply ponder options (like the first group) or implement others’ choices (like the second group). They had to cast the die, and that turned out to be the most fatiguing task of all. When self-control was measured, they were the one who were most depleted, by far.

Willpower depletion makes you reluctant to make trade-offs:

Once you’re mentally depleted, you become reluctant to make trade-offs, which involve a particularly advanced and taxing form of decision making. In the rest of the animal kingdom, there aren’t a lot of protracted negotiations between predators and prey. To compromise is a complex human ability and therefore one of the first to decline when willpower is depleted. You become what researchers call a cognitive miser, hoarding your energy. If you’re shopping, you’re liable to look at only one dimension, like price: just give me the cheapest. Or you indulge yourself by looking at quality: I want the very best (an especially easy strategy if someone else is paying). Decision fatigue leaves you vulnerable to marketers who know how to time their sales, as Jonathan Levav, the Stanford professor, demonstrated in experiments involving tailored suits and new cars.

Willpower depletion makes you more likely to take the path of least resistance:

As they started picking features, customers would carefully weigh the choices, but as decision fatigue set in, they would start settling for whatever the default option was. And the more tough choices they encountered early in the process — like going through those 56 colors to choose the precise shade of gray or brown — the quicker people became fatigued and settled for the path of least resistance by taking the default option. By manipulating the order of the car buyers’ choices, the researchers found that the customers would end up settling for different kinds of options, and the average difference totaled more than 1,500 euros per car (about $2,000 at the time).

Testing willpower depletion in rural Indian villages:

Most of us in America won’t spend a lot of time agonizing over whether we can afford to buy soap, but it can be a depleting choice in rural India. Dean Spears, an economist at Princeton, offered people in 20 villages in Rajasthan in northwestern India the chance to buy a couple of bars of brand-name soap for the equivalent of less than 20 cents. It was a steep discount off the regular price, yet even that sum was a strain for the people in the 10 poorest villages. Whether or not they bought the soap, the act of making the decision left them with less willpower, as measured afterward in a test of how long they could squeeze a hand grip. In the slightly more affluent villages, people’s willpower wasn’t affected significantly.

Decision fatigue can be a factor in trapping people in poverty:

Spears and other researchers argue that this sort of decision fatigue is a major — and hitherto ignored — factor in trapping people in poverty. Because their financial situation forces them to make so many trade-offs, they have less willpower to devote to school, work and other activities that might get them into the middle class.

Glucose restores willpower in humans and dogs:

To establish cause and effect, researchers at Baumeister’s lab tried refueling the brain in a series of experiments involving lemonade mixed either with sugar or with a diet sweetener. The sugary lemonade provided a burst of glucose, the effects of which could be observed right away in the lab; the sugarless variety tasted quite similar without providing the same burst of glucose. Again and again, the sugar restored willpower, but the artificial sweetener had no effect. The glucose would at least mitigate the ego depletion and sometimes completely reverse it. The restored willpower improved people’s self-control as well as the quality of their decisions: they resisted irrational bias when making choices, and when asked to make financial decisions, they were more likely to choose the better long-term strategy instead of going for a quick payoff. The ego-depletion effect was even demonstrated with dogs in two studies by Holly Miller and Nathan DeWall at the University of Kentucky. After obeying sit and stay commands for 10 minutes, the dogs performed worse on self-control tests and were also more likely to make the dangerous decision to challenge another dog’s turf. But a dose of glucose restored their willpower.

Ego depletion causes activity to rise in some parts of the brain and to decline in others:

The results of the experiment were announced in January, during Heatherton’s speech accepting the leadership of the Society for Personality and Social Psychology, the world’s largest group of social psychologists. In his presidential address at the annual meeting in San Antonio, Heatherton reported that administering glucose completely reversed the brain changes wrought by depletion — a finding, he said, that thoroughly surprised him. Heatherton’s results did much more than provide additional confirmation that glucose is a vital part of willpower; they helped solve the puzzle over how glucose could work without global changes in the brain’s total energy use. Apparently ego depletion causes activity to rise in some parts of the brain and to decline in others. Your brain does not stop working when glucose is low. It stops doing some things and starts doing others. It responds more strongly to immediate rewards and pays less attention to long-term prospects.

Good decision makers structure their lives so as to conserve willpower:

“Good decision making is not a trait of the person, in the sense that it’s always there,” Baumeister says. “It’s a state that fluctuates.” His studies show that people with the best self-control are the ones who structure their lives so as to conserve willpower. They don’t schedule endless back-to-back meetings. They avoid temptations like all-you-can-eat buffets, and they establish habits that eliminate the mental effort of making choices. Instead of deciding every morning whether or not to force themselves to exercise, they set up regular appointments to work out with a friend. Instead of counting on willpower to remain robust all day, they conserve it so that it’s available for emergencies and important decisions.

“Even the wisest people won’t make good choices when they’re not rested and their glucose is low,” Baumeister points out. That’s why the truly wise don’t restructure the company at 4 p.m. They don’t make major commitments during the cocktail hour. And if a decision must be made late in the day, they know not to do it on an empty stomach. “The best decision makers,” Baumeister says, “are the ones who know when not to trust themselves.”