I think willpower and akrasia are both kind of fake concepts. Here's a different model: you have a bunch of parts, approximately in the IFS sense. Those parts want different things, and sometimes they come into conflict. Different parts are in control of what you actually do at different times. Some of your parts are verbal and some are not. (I don't think "verbal = S2, nonverbal = S1" is necessarily a helpful frame here; for example, focusing seems to be related to nonverbal parts, but it sort of breaks the S1/S2 dichotomy by being nonverbal but slow.)
"Akrasia" is when a nonverbal part is in control (and wants to, say, watch TV) and a verbal part wants to do something else, and says so. "Willpower" is when a verbal part attempts to forcibly override a nonverbal part. The skill to try to build is understanding what your nonverbal parts actually want, facilitating communication between parts, and either making compromises between your parts or getting your parts to agree on what to do (I'm genuinely uncertain which is better).
Edit: Also, my impression is that this is essentially the model currently being taught at modern CFAR workshops, although people who have been to a CFAR workshop more recently than me should chime in about whether they agree or not.
(for example, focusing seems to be related to nonverbal parts, but it sort of breaks the S1/S2 dichotomy by being nonverbal but slow.)
Noncentral nitpick that is meant to be helpful: Focusing is a counterexample to the lay dual process theory that people sometimes use around here, but not the up-to-date, cognitive-scientific one.
Briefly, the key distinction (and it seems, the distinction that implies the fewest assumptions) is the amount of demand that a given process places on working memory.
nonverbal
Although language is often involved in Type 2 processing, this is likely a mere correlate of the processes by which we store and manipulate information in working memory, and not the defining characteristic per se. To elaborate, we are widely believed to store and manipulate auditory information in working memory by means of a 'phonological store' and an 'articulatory loop', and to store and manipulate visual information by means of a 'visuospatial sketchpad', so we may also consider the storage and processing in working memory of non-linguistic information in auditory or visuospatial form, such as musical tones, or mathematical symbols, or the possible transformations of a Rubik's cube, for example. The linguistic quality of much of the information that we store and manipulate in working memory is probably noncentral to a general account of the nature of Type 2 processes. Conversely, the production and comprehension of language must often be an associative or procedural process, rather than a deliberative one; otherwise you might still be parsing the first sentence of this comment. That's all technically original research and I Am Not A Cognitive Scientist, but I think it should be pretty obvious even from a layperson's perspective.
slow
There's nothing stopping Type 2 from being relatively fast, either; it's just another correlate that doesn't always hold. Trivial example: Have you ever awoken and not been able to make mental sense of what you're seeing for a few seconds? It might take you longer to do that than to perform one transformation of a Rubik's cube while fully awake, even though the former is automatic and the latter deliberate. In general, people sometimes seem to act as if there has never been a judgment that was simultaneously deliberate and fast, because they have come to describe all fast judgments as automatic. Such judgments are plausible in my experience.
See also: Evans (2013).
The skill to try to build is understanding what your nonverbal parts actually want
Isn't that the easy part? Just look at what it's doing: if I'm eating a bag of chips instead of working out than it means that my non-verbal part wants to eat a bag of chips. Or there's something else?
The things your nonverbal parts are doing are often bad strategies for achieving reasonable goals, and so there's an inference problem to solve in figuring out what the underlying reasonable goal is. A lot of the things your nonverbal parts do are pica in a metaphorical sense (pica in a literal sense is e.g. eating ice cubes because of an iron deficiency). Your desire to eat a bag of chips, for example, might reflect an underlying goal of getting more salt or fat in your diet, because in the ancestral environment those things were rarer, but if you already have too much salt and fat in your diet then that's not super helpful.
A more pica-like example: suppose you catch yourself watching a lot of TV. Depending on the content of the TV, this might reflect an underlying goal of having more social connection (say if you catch yourself watching a lot of How I Met Your Mother, where the main characters form a tightly-knit group of friends). TV's not social connection, but it sort of vaguely resembles it closely enough to be kind of satisfying but not really. I think this is more what "akrasia" looks like a lot of the time.
This appears to be a useful way to think about internal desires in a non-combative way. You're not focused on trying to override parts of yourself, but just listen and try to be an arbiter in the conflict.
In my conversations with people from CFAR, I believe this is the view they espouse. They mention this during their discussion of motivation. Elo, Nate Soares, and Andrew Critch have also written about this at some point. (I can dig up links if you want to see how others tackle this.)
As a result, this looks to be a sorta stable fixed point for motivation-related thoughts. Despite knowing this, I often still miss opportunities to debug my internal motivations and source some more sustainable motivation. In general, I'd like to see more people outlining perhaps a mental transcript or a steps that they go through to get the S1/S2 cooperation to actually happen. Easier said than done, as they say.
Yeah, this is pretty much my conclusion, too. If I had read this article a couple of years ago, it'd have helped me a lot.
I'd add that you should still overrule system 1 in some really important and rare cases, it's just not practical for recurring things.
Rationality is designed to make you win, to help you attain your objectives. One of the most prominent phenomena getting in the way is akrasia, the lack of willpower preventing us to perform whatever action we want to do.
So, wait, do we want to act or not? There are two facets of willpower, which I'll describe using Kahneman's System 1 and System 2, the two working modes of the mind (bear in mind it's a simplification to get the point across).
What we call System 1 willpower is what gets you up in the morning, out of a good shower, what makes you start things, the grit, the sudden confidence, the "just do it" part. It's the short-term impulse of "I can go one step further and my body shall obey. It's the thing many productivity methods want to trigger. For example, the 2-minute rule ("if it takes less than 2 minutes to perform, do it now") is based on the intuition that you won't need a lot of effort to get something done, akin to going briefly out of your way to help a friend. Of course you can do it. No planning needed. It's very appealing to your brain.
What we call System 2 willpower is the high-level justification, the reason behind the actions, the thought-out plan, the will to make good decisions, to make things right, to keep akrasia in check in order to achieve long-term goals, the thing that sees problems as obstacles to be overcome instead of monsters to avoid. It's the background buzzing of "I want to go there and I shall find a path". It's the thing many productivity methods want to manage. The Getting Things Done methods starts with a list of tasks, which you can process in orderly manner, setting long and short-term goals and stay in control at all times. It's also very appealing to your brain.
However, what makes you actually do things is S1 willpower, not S2. S1 is more low-level, and has no knowledge of plans. Your willpower can be misguided. You want to throw paper planes, scribbling randomly, following click-bait headlines, when your plan is to work, or train, or be otherwise productive. S2 willpower is supposed to keep S1 in check, to make you perform counter-intuitive actions for your own good.
The willpower tricks work, but they're costly. They require a part of your attention, a conscious effort to keep yourself focused. It's just much less costly to have S1 willpower run everything, with S2 staying where it should belong: abstract thought, not micromanagement of S1. This is flow, where S1 willpower remains high and has no reason to go down because everything goes smoothly (and it's a fragile state, any disruption can get you out of it).
Conversely, ignoring completely S1 willpower and forcing yourself to do things isn't safe nor productive. If you ignore the natural drive that comes from pleasant activity, you may coerce your will into whatever "optimal" process you designed, working yourself ragged. You're not a machine. Your body is part of you, not a weak container, nor a lazy-by-default entity you should negotiate with.
My model of effective anti-akrasia isn't to poke System 1 repeatedly but to engineer situations where S1 agrees with S2 on what is best for you; where you don't encounter contradicting signals of "I don't really want to do that, is that necessary?" all the time. The goal is to make productivity the default state, to make it more attractive than doing nothing. How we can do this will be covered in later posts.
Special thanks to regex, who sparked the discussion leading to this post. I borrowed his "more attractive than doing nothing". It's a fascinating concept.