Well, the first thing I would do is try to come up with a large number of safety precautions. Then I would try to determine exactly what infinite willpower meant. This seems like good advice in almost any preference system when you discover you have almost any super power. Find out "What EXACTLY can I do with this?"
For instance, right now, I doubt I could pull two consecutive all nighters.If I wake up this morning and simply have infinite willpower (and am aware of that fact), the first thing I would probably test is my sleep cycle from my house. What does pulling two all nighters do to me? What does pulling three all nighters feel like? Obviously I'd want to be careful with this. I don't want to say "Well, clearly, with my Infinite Willpower I never need to sleep again!" and then kill myself through sleep deprivation. Start off slow.
This brings up the next related question: Tranquilizers! Let's assuming we've determined that I can stay awake for a month with no ill effects and no apparent microsleeps, find out "Well, is it just natural sleep?" If I take a sedative, do I simply fail to lose consciousness if I don't want to? Am I simply utterly immune to sedatives? Or do I simply stay conscious right up until I overdose and my heart stops beating?
Again, this is why I'd have to be careful with this. By default, your bodies distress systems generally are trying to keep you healthy. They might be inaccurate, but they try. A large number of them can be disregarded by using willpower.
For instance, it would be very bad if, as an act of will, I consciously held my breath because I was trying to hear something and then simply forget to breathe, ignoring my increasing pain/fatigue because I am still trying to concentrate on some faint noise and then oops! I appear to have asphyxiated myself.
Once I've determined how to make sure I don't kill myself, I'd probably attempt to determine if the source of my willpower was paranormal by attempting to win The One Million Dollar Paranormal Challenge. This means I'd need to be in the news (Should be relatively easy, SOME safe feat of Infinite willpower should be newsworthy enough for that.) and the backing of an academic (Possibly a doctor. In the first phases when I was making sure I didn't kill myself, it would be handy to have a doctor's professional help nearby.)
This would likely fork:
1: It's paranormal! I now have not only Infinite Willpower, but Infinite Willpower and 1 million dollars! Score!
2: It's biologically explainable! Well, what's the biological explanation? Is it mass producible? Can I get a lawyer and get a share of the profits if it is?
If you were going to boil it down, I suppose this would boil down to
1:Caution
2:Testing
3:Wealth (If it's a good enough power to allow me to do this.)
4:???
I leave four blank because It's hard to plan out that far ahead without knowing the results from 2. I mean to me infinite willpower could translate into anything from:
A: It's like chronic insensitivity to pain, except with an on off switch but you still need to be careful or you'll kill youself.
B: I can do some cool things, but nothing much beyond parlor tricks like 'I bet I can hold more drinks than you.' My life is more or less functionally identical.
C: I can keep moving and be healthy after 100 simultaneous taser shocks by simply refusing to let myself be stopped!
To all sorts of things in between. I won't know what the next step is until I better know myself.
What I meant was ability to delay gratification, to actually live by a utility function that does not hyperbolically discount, which is more or less A.
I'm not on this level yet, but I think I can get there through prolonged effort. Unfortunately, I think it's mostly genetics and practice (which is exactly what everyone's trying to avoid, lol).
For the past few years my willpower has been steadily increasing. If it lasts and I use it to accomplish something noteworthy, I might write a post about it.
Anyway, what should a rational preference utilitarian with infinite willpower do? Assume that there are no negative effects (unhappiness, stress) with using this willpower, and that they can control their emotions at will.
Clearly they should work a lot more, not spend time on recreation (movies, TV, games), stand instead of sitting, etc..
What else? Should they listen to music? Should they keep their muscles flexed 24/7 ? What should they learn, where would they have the most relative advantage? How much time would be worth spending on social interaction?
I can figure out these things on my own, but those questions are important and good ideas are very valuable.