This is a common question that has good arguments for both sides, but instead of trying to resolve it in this post, I'd like to speak about something a little bit more meta:
Your belief in how much willpower is possible can limit your effectiveness.
Whether you believe that you will run out of willpower from decision fatigue, or that you can build your willpower reserves by regularly exercising them - you are right. Even before we could objectively test the physiological basis of willpower, your perceptions and expectations will have a greater magnitude of effect on its outcome.
Beliefs are deeply held understandings about the world that we have created as a result of past experience, education, logic and reality testing. We only hold onto a belief as true if it is something that is consistently held up with the way that we experience things in the world. This is not to say it is absolutely true or immune to bias, but it is a coherent perspective that we continue to validate.
Beliefs are important because they shape how we perceive things. Our moment to moment experiences is filtered through our system of interconnected beliefs so that we can make sense of it faster without having to start fresh every time with no assumptions. Some beliefs are so deeply held that we don't even know that we are adhering to them, others are quite obvious.
Our beliefs will change how we react to what is happening around us. If you have a pet tiger with whom you've had a relationship with for many years, you believe that they will not eat your face without warning, and thus do not react in fear when they are expecting as normal. With a wild tiger, we do not have that belief, and are very much aware of their power.
Once filtered, beliefs and sensory experiences create rapid feelings and emotions. These come as physical reactions, intuitions or psychic impressions - gut feelings, hunches and suspicions. This happens before we are aware of why. They are an instinctive objective reaction that stems from our system of beliefs.
Our thoughts arise as ways to label these phenomena. We know that we are angry before we know why. Thoughts are a way to conceptualize, make meaning and 'sense'. Essentially they are constructing ideas that make a logical framework that supports our understanding of why they happened. Thoughts are incredibly useful, because they allow us to make predictions about the future to simulate outcomes.
Acting without thinking can often lead to ruin. The exception to this is in situations where our skills and intuitions are great enough that we do not need to dissect the happenings with logic any more, and our wisdom gives us the ability to react with flow.
Thinking allows us to plan, and then actions are implementing that plan.
Beliefs => Feelings => Thoughts => Actions
Thus we can see that our beliefs, both known and unknown, will shape our ability to take action.
So what could or should we believe about willpower?
However, we necessarily must create beliefs with incomplete information - it is impossible to know everything for every circumstance. If you are aware of your beliefs and why you hold them to be true, you can see where they are serving you or not.
The evidence for willpower being limited is conditional on it being provided by other things like energy level, concentration/focus, morale, and so on. The muscle analogy for building willpower strength is also dependent upon arguments that willpower is limited unless fortified.
Each belief is true for those who hold it, and they will act according to their world view, with the advantages and the limits that they bring.
Will you choose to adopt someone else's view of willpower? Or will you test it yourself to find if it's true? Authority is valuable in the sense that it is a mentorship shortcut to rapid learning. But it hinders you that you cannot learn beyond what you are told. Personal experimentation will give you wisdom that is more free to adapt, but it requires self-awareness and persistence of inquiry.
How can you test what is true for you?
What do you believe?
Are you aware of the limits of yours and others beliefs?
Having known and worked with many scientists who are experts in their respective fields, asking them directly "Is X true?" where X is a fundamental working assumption in the field, they will often say "Yes, but it is also not true" or "Yes, but only under conditions Y" or "Most of the time, enough to use it as a general rule, but there are exceptions which are very interesting..."
So, even those at the forefront of their specific field of knowledge live in ambiguity or uncertainty, but still need to make assumptions or generalizations in order to move forward - asking good questions and finding useful relationships of concepts.
If all knowledge is subject to shades of grey, then we must be careful when our beliefs are too rigid and would limit us. Strive to find the best explanations, but accept that there is always the exciting opportunity to be wrong.
Aaron Ball. Recovered Academic. Grieving Environmentalist. Evidence-Based Transformational Coach. Electronic musician. Transrationalist.