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Comment by tylerhou | Hacker News Reader

Expected utility is positive implies that people have discontinuous utility functions wrt. money. That is, utility will jump significantly after reaching a certain net worth.

Another explanation that is consistent with gambling behavior is that people have inaccurate risk functions; that they overestimate positive upside and underestimate downside.

I am not familiar with the economic literature. But I believe that there is more evidence to support the second hypothesis. Behavioral economics has showed that humans are notoriously unable to estimate risk accurately. I have not seen as much evidence that humans have discontinuous utility functions.

Behavioral economics also tells us that humans are also terrible at estimating their actual utility functions. So I also don’t trust the original poster who claims that they have a discontinuous utility function. The only way to test that is to observe actual human behavior.

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The obvious discontinuity is "never have to work". People talk about this all the time when they talk about this stuff.

> The obvious discontinuity is "never have to work".

First, wanting to achieve "financial independence" does not imply a discontinuous utility function.

Suppose it takes $X to reach financial independence. Let's say that when I achieve $X, I have utility Y. It is possible that as I approach $X from the left, my utility continuously approaches Y.

In fact, I argue that's what happens for most people who have a FIRE goal — they get happier and happier until they reach their goal. (It's true that once they reach their goal and experience retired life, they decide that retirement's not all that it's cracked up to be, but I argue that's because their utility has dropped because of another variable has changed: they have stopped working.)

In other words, "wanting to not have to work again" and "having a continuous utility function" do not contradict each other. And the people who are dedicated to saving enough money to not have to work (FIRE) almost always have utility functions that are continuous wrt. money!

> when they talk about this stuff.

Again, people might say that they have a discontinuous utility function, but talk is cheap. Real economists (TM) measure utilities through examining a consumer's revealed preferences because what people say doesn't always reflect what people do.

It really depends on an individuals displeasure at work though right? To take a ludicrous example my utility function for eating a sandwich is has a sharp discontinuity as a function of how much Polonium is in the sandwich. So too with some people for money and work, especially when it is far away from your current state. I don't think this is an experiment that a real economist (TM) has ever performed on an individual to discover what the true utility function is (happy to be wrong though).

> To take a ludicrous example my utility function for eating a sandwich is has a sharp discontinuity as a function of how much Polonium is in the sandwich.

Well, in the real world, every sandwich likely has a little bit of polonium in it; maybe an atom or two. If that increased to three or four, you would be slightly unhappier, but not sharply so. Every little increase in polonium slightly decreases your utility until you reach a point where you do not derive any utility from your polonium-laced sandwich, and so you would not eat it. Therefore, I argue that your utility function is still continuous wrt. polonium in your sandwich.

(In economics this isn't really how you'd model utility because the assumption is that you always have the option to throw away the sandwich; therefore, having the polonium sandwich gives you more utility than not having it.)

Same with money. Imagine you had a "life changing amount of money," whatever number that means to you. Call that number $X. Now imagine that you instead had $X - $1. And then $X - $2. Even $X - $1000. How much less happy do you feel in those imagined scenarios? A lot less happy? I bet you feel marginally less happy and not sharply. Which implies a "smooth" utility function.

I believe that non-continuous utility functions can exist -- suppose someone says that they will kill you unless you give them $50,000 -- but for most people that's not a real scenario.

> I don't think this is an experiment that a real economist (TM) has ever performed on an individual to discover what the true utility function is (happy to be wrong though).

I don't think ever with polonium, but here's a short video about revealed preference theory. https://www.youtube.com/watch?v=kPXov3D1tfA. In practice, applications of revealed preference theory happen all the time.

But your example did make me think more about "continuity" and "sharpness" and I now think that continuity is not strong enough to support my original claim. Continuous does not mean "smooth" [1]. To define "smooth," I would instead say that most people have utility functions that have positive first derivatives and negative second derivatives; that is, their marginal increase in utility for a good is positive but diminishing.

[1] https://en.wikipedia.org/wiki/Weierstrass_function

> Imagine you had a "life changing amount of money," whatever number that means to you. Call that number $X. Now imagine that you instead had $X - $1. And then $X - $2. Even $X - $1000. How much less happy do you feel in those imagined scenarios? A lot less happy? I bet you feel marginally less happy and not sharply.

Talking only about myself and not claiming anything about humanity at large:

There is a particular number of USD that, if I have in my account, I feel calmer and non-chalant about losing a job. Let's call it $20000. If I have $19900, it's the same. But if I have $15000 then I'd start feeling uneasy and would revert to trying hard to refill that minimum leisure savings amount.

So IMO it's not a gradual linear function. It's more like, for values between X1-X2, Y remains relatively constant. Then for values X2 to X3, Y is a higher value compared to the previous bracket of X values but also stays relatively constant for the current range of X.

Again, just what I observed about myself.

Maybe I am missing something obvious but isn't watching stocks, analyzing news and predicting stock prices so you can multiply your money, an actual work?

You do spend time and energy chasing an income, no?

You can get a net positive utility gain from a net zero money gain with a continuous function, if it were say, logarithmic. A has 1X$ and B has 10X$, then an exchange occurs where 1X$ moves from B to A, now it's 2X$ and 9X$, but the change in happiness for A could be log(2/1)~=.30 while B log(9/10) ~=-.04

This is just one utility vs wealth model that would argue wealth transfers improve net utility in some contexts.

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