A Mathematical Model for the Human Will – Outlook Zen

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June 23, 2026June 23, 2026

What is the human will?<br>How does the will interact with reason?<br>Does the will follow reason’s lead, or is the will the ultimate decider?<br>If the will is indeed the ultimate decider, how does it go about deciding, given that reason is responsible for all analysis?

These are questions that many famous historical philosophers have dedicated years of their lives to debating. Today, we shall discuss a mathematically rigorous model for the human will. One that offers an answer to the above, explains seemingly paradoxical behaviors, and offers some useful insights that can help us with our lives.

Delayed Gratification

Consider the following graph:

The X-axis in the above graph is time, relative to the present moment.

And the Y-axis is how much you currently value “one unit of well-being" at a future time, relative to how much you value it in the present. Or to give a grossly simplified example: if I promised you a delicious meal next year, how appealing is that compared to a delicious meal right now?

Almost everyone has a curve with the same shape as the above, illustrating the following common behaviors:

For any time range that is “close” to the present time, people’s valuation barely changes. Ie, if I promised you a delicious meal, it doesn’t matter much to you whether you eat that delicious meal 1 minute from now, or 2 minutes from now, or 5 minutes from now. All three possibilities seem almost equally desirable.

At a certain time-range however, things start to feel too abstract and unrelatable. And hence, its present value drops off rapidly. For example, if I promise you a delicious meal 10 years from now, that doesn’t seem nearly as valuable as a delicious meal today. Even if it were sealed in an ironclad contract, with all the money safely locked away in an escrow. 10 years from now simply feels too far away, too unrelatable, too abstract. This causes the curve to fall rapidly.

And finally, once you have crossed this inflection point, everything feels “equally abstract” no matter how much further you go in the future. Hence, the curve levels off again. For example, if I promised you a delicious meal 20 years from now, that seems just as valuable as a delicious meal 10 years from now. We see a massive drop-off in value when we go from today to 10 years later – but we only see a slight drop-off in value when we go even further to 20 years later.

Our ability to “reason” allows us to estimate how our actions will impact our well-being both in the present, and in the future. For example, your reasoning may tell you that you have enough money to eat one delicious meal today. But if you instead invested that money, you would have enough money for two delicious meals after 10 years. Which would give you twice as much future-well-being as one delicious meal.

The above analysis may be filled with unreliable assumptions, and may eventually prove to be false. But hey, we all need to make decisions somehow. And our reasoning abilities give us the best possible estimate of the consequences of each decision.

Does the above mean that you will forego eating that delicious meal today, and save the money instead? Two delicious meals are better than one delicious meal, so clearly you would always choose to save your money, right?

Wrong. Under the above model, we do not optimize for aggregate well-being. Rather, we all subconsciously optimize for our present perception of present/future well-being .

In essence, our decision really comes down to this: how much do we value “2 units of well-being” 10 years later, compared to “1 unit of well-being” today? Looking at the above curve, each unit of well-being in the distant future will definitely be discounted by some amount, relative to present well-being. But by how much do you discount it? If you discount it by less than 50%, you will definitely choose to save your money for 2 delicious meals next decade. Whereas if you discount it by more than 50%, you will definitely choose to buy that delicious meal today.

A Difference In Willpower

We had earlier discussed everyone’s curve following the same general “shape”. Despite this similarity however, each person’s curve has completely different parameters. Most notably, the point in time where the curve steeply falls off – everyone hits the "cliff" at a different point. Hence why everyone will assign a unique present valuation for 2 units of 2036 well-being.

Most crucially, when we talk about someone’s will, what we are really talking about are the parameters of the above curve for that individual . Two people with the exact same reasoning abilities, may still make different decisions, because their will-curve has different parameters, causing them to differently prefer immediate vs delayed gratification.

Someone with an iron will has a cliff that is infinitely far into the future. Ie, they will tolerate...