It's already well established. Lifecycle investing is common practice among pension funds.
"You would need to show it wasn't one of those factors"
Firstly, I'm not the one with the burden of proof that has to check whether this fits the theory.
Secondly, you're misunderstanding my objection. What I'm objecting to are the very conceptual foundations of the theory. Old people demonstrably accept a lower EV than young people because of a difference in expected utility over the distribution of near-term outcomes. To throw the concept of expected utility in the bin is therefore a departure from reality and as such the theory automatically fails on conceptual grounds.
Once again, you are misunderstanding my objection.
The math of EE is correct given the axioms from which it is deduced. Nobody anywhere is disputing that.
What I'm disputing is whether it is a theory that explains human financial decision making, in the same way that some physicists dispute that string theory explains physical reality (despite acknowledging that the math behind string theory is deductively correct).
"Saying Expected Utility is correct"
It is conceptually correct, as my old vs young example shows. The fact that EE fails to model this is a fatal counterexample.
Once again - the math IS deductively correct, but that same math fails as a theory of financial decision making since it doesn't explain the observed reality.
"I'm not talking about orthodox utility theory ("EUT"), and I'm not trying to say that it's currently a good theory, either."
The reply button is missing below so I'll reply here.
The issue is that the major results of economics in this sort of area are been effectively destroyed by EE. Prospect theory for example is completely gone.
There may be places where people's behaviour isn't rational but research into that needs to be effectively carried out again from scratch. The main "evo psych" results in economists have been effectively disproven.
So you might be right that people don't act rationally but all existing research into that area is currently dead in the water. It's start from square 1 again.
There's no need for explicit research to establish the fact that people differ in their subjective preferences (utility) pertaining to outcome distributions. The evidence is abundant.
I can go down to the casino and see this. Or I can see that family member A has insurance while family member B doesn't.
You talked earlier about wanting a theory to have stable foundations. A theory that doesn't even recognize the existence of subjective expected utility is not that.
I'm talking about the concept of expected utility. If EE does away with that concept, then it is a failed theory on conceptual grounds.
Without this concept, tell me how EE is supposed to grapple with:
(1) gamblers who take on negative EV bets
(2) old people who shift into fixed income
(3) low risk-tolerance young people who keep only cash
(4) high risk-tolerance young people who put everything into crypto
(5) why some people buy insurance and some don't, despite earning the same income
The fact is, you can't explain this heterogeneous behaviour without the concept of expected utility of outcomes.
Our brains are emotional, irrational vehicles designed by evo psych, and you can't grapple with that reality without some notion of subjective preference pertaining to expected outcome.
I think that the errors you are making are that EE does not do away with expected utility, and expected utility is not a strict requirement for the development of a theory to describe economic outcomes.
1) It seems to me that it is only utility, rather than its expectation, that is the concept you are treating as necessary. There are an infinity of ways to reduce a distribution of utility-weighted outcomes to a single summary, albeit not with the same simplicity (and perhaps value) as the expectation.
2) All of the phenomena you list could be described by some mechanism other than the agents involved computing expected utilities - whether or not this is a useful
or effective description is beside the point, it is possible. (Expected) Utility is not required to describe these phenomena.
3) The basic EE claim is that the ergodic hypothesis, roughly that the temporal and ensemble distributions are the same, is false in the context of these economic systems. This has nothing to do with whether or not you can associate utility values with states, nor whether it is possible to compute expected utilities, but instead is a claim about how, and from where, those utilities should be measured, in particular when considering problems like optimising long-term returns.
1) If the expectation is there it's because the expected value of the utilities for a probability distribution over outcomes allows for an ordering of the available choices which is consistent with the preferences over outcomes. Is that true for any other among that infinity of ways of producing a summary?
3) Ok. Some people seem to think that EE disproves EUT somehow, though. That's the context of the comment your reply to.
The comment I replied to was discussing the necessity of the concept of expected utility for the success of any economic theory. My points were with reference to that - I am only claiming that it is not a requirement for a reasonable economic theory, for the reason I stated. There are other syntheses that might better describe actual economic behaviour.
More generally, there are two aspects of the value of EUT being discussed:
1) Does expected utility theory describe observed economic behaviour. There is evidence that it does not, and my previous points concern that fact.
2) Can expected utility theory be used to design a system that will produce optimal outcomes. EE confronts this question, and claims that, in the usual formulation of EUT, it cannot (because the ergodic hypothesis does not apply).
As others have mentioned, in practice some people do account for non-ergodic behaviour. Others, however, do not, and being explicit about the limitations of any given model rarely hurts anything except people's egos.
I think he pointed to the need of having something similar to expected utility maximization in the context of a theory of rational decision making.
I guess it's true that one can also have economic theories which are not compatible with rational decision making as understood in EUT so they could be completely different.
> claims that, in the usual formulation of EUT, it cannot
EE claims that, but it's a baseless claim. The growth optimization arguments used by EE can be perfectly used (and have been used) in the usual formulation of EUT. If the agent has a preference for growth that can be described with a utility function.
(I agree that EUT doesn't explain all behaviour. EE even less, being even more restrictive.)
> EE claims that, but it's a baseless claim. The growth optimization arguments used by EE can be perfectly used (and have been used) in the usual formulation of EUT.
The disagreement seems to boil down to what is considered the "usual" formulation of EUT. My understanding of the basic formulation is in accordance with that in the paper, namely that one typically assumes single-period uncertainties either explicitly or in effect (e.g. assume they are IID), and time is treated by discounting - but I admit I am no expert.
That it is possible to extend that formulation is, I think, not in doubt, but we should be able to agree that what I have described above does, implicitly, make an ergodic assumption, and thus the EE critique would apply.
You may contest my description of what the basic formulation is, and, as I suggested, lack of clarity about that does seem to be driving a lot of the discussion.
These discussions are typically made more problematic by the fact that practitioners often use more advanced methods than the basic theory, to overcome such problems whilst remaining within the same broad intellectual frame. It seems to me that the claim of EE is that the basic theory itself should be replaced because it fails to account for many important real-world phenomena, so that even the "what is the basic formulation" question would become moot.
EUT is a theory of decision making under uncertainty. If an agent preferences are rational (as in they verify a number of properties) his preferences can be described assigning a number to each outcome. If the outcome is uncertain, the utility is the weighted average of the outcomes utilities.
For example, for outcomes A, B, C and D there will be four numbers U(A), U(B), U(C), U(D) such that
if U(A)>U(B) the agent prefers A to B
if the agent is indifferent between C and D
Say that A is "in the beach, it's sunny", B is "in the beach, it's raining", C is "at home, it's sunny" and D is "at home, it's raining".
With the equations above, if I'm in the beach I prefer that it's sunny. If I'm at home, I'm indifferent to rain.
Let's make a couple of additional assumptions U(A)>U(C) and U(B)<U(D). If it's sunny, I prefer to be at the beach. If it's raining, I prefer to be at home.
Let's say that my preferences are described by the following values: U(A)=10, U(B)=-20 and U(C)=U(D)=0.
If the probability of rain tomorrow is 50% do I prefer to go to the beach or to stay at home?
EUT allows me to calculate U(beach)=0.5 U(A)+0.5 U(B)=-5 and U(home)=0 (it doesn't depend on the weather). I prefer to stay at home.
What is the probability of rain that makes me I'm indifferent between going to the beach or staying at home?
U(beach)=(1-x) U(A)+x U(B)=10-30 x = U(home)=0 => x=1/3
__ Remarks __
The probability doesn't have to be "right" for the theory to work. It only has to be a faithful description of the expectations of the agent. If I believe that the chance of rain is higher than 1 in 3 is rational that I stay at home.
Would Ole Peters say that this use of probabilities to make decisions is incorrect because it assumes that I'm interacting with a copy of myself in parallel universe? I suspect so.
Would you say that there is a problem with EUT up to this point?
The problem you have described is a single-step problem, and the process you work through gives a satisfactory answer to the question you have asked. So my answer to
> Would you say that there is a problem with EUT up to this point?
Is no, not for this problem, and question.
However, consider figure 2 (and correspondingly equation 2) from the paper. It considers a problem very similar to the one you pose, but with a couple of important differences:
1. We maintain a stock of "utility", and are aiming to maximise this stock over multiple iterations of the bet.
2. The utility response is multiplicative rather than additive.
If we consider the expected utility of taking the bet at any point in time given some wealth W we obtain a positive utility (0.5 * 1.5W + 0.5 * 0.6W = 1.05W). However, multiplicative wealth is not an ergodic process, and so the expected change over time does not reflect that expected utility, and after T timesteps is something like (1.5^(0.5T) * 0.6^(0.5T)).
Of course, as mentioned in the paper, some processes are ergodic - in particular changing the utility response to be additive rather than multiplicative. Overall, the point is that one must consider the nature of the problem carefully.
> Would Ole Peters say that this use of probabilities to make decisions is incorrect because it assumes that I'm interacting with a copy of myself in parallel universe?
I think the answer to this is no - not in the problem as you have framed it. However, if we extend it in the way I have outline above then we clearly need to be more careful.
Take a step back and look at his description of the bet and equation (2).
Is says “a simple gamble”. It doesn’t say anything about an infinite series of iterations of the bet. It’s a single step problem. Do you play once or do you pass?
(If the question is “do you want to play twice (or N times)” it’s also effectively a single-period problem. One just has to consider the distribution of outcomes after two (or N) rounds.)
The usual EUT resolution is what I just described, which you don’t find problematic. He does find it problematic, because for him calculating an expectation is interacting with a copy of yourself in a parallel universe or something.
The reason why he talks about infinite sequences of games is not because the problem is about an infinite sequence of games. To solve the simple problem he has to hypothesize that there is an infinite sequence of them.
edit: As noted in your other comment, the expectation with a standard utility function is actually negative, thus the premise for part of the below is incorrect, and therefore so are its conclusions. A more faithful reproduction of Peters' argument is that EE recovers the correct solution without requiring the addition of an arbitrary utility function, and corresponding appeals to irrationality.
original comment:
Yes, you are correct that in the initial framing it is just a single gamble, but of course the point is that an individual's life is made up of many gambles. Expected utility assures us that this bet has a positive expectation, and so naively we might think that iterating it also produces a positive expectation sequence, but it does not, as we saw.
We can recover a correct answer by considering the expected utility of the whole sequence, but there is nothing in the problem to suggest that we should do so, unless we acknowledge the cause of the issue, which is that the ergodic hypothesis does not hold.
The point of the whole "parallel universe" thing is that even though the expectation in a single step may be positive, an individual never realises that ensemble average - they only ever realise a time average. Thus, the time average is the more useful object of study.
> If we consider the expected utility of taking the bet at any point in time given some wealth W we obtain a positive utility (0.5 * 1.5W + 0.5 * 0.6W = 1.05W)
No. That is not the expected utility in the usual EUT solution.
In the usual EUT solution (with the usual logarithmic utility that would be used in a textbook problem like this one) the expected utility is 0.5 log(1.5) + 0.5 log(0.6) + log(W) which is lower than the expected utility of not playing log(W).
Ah yeah, fair point - I think it would actually be 0.5 log(1.5 W) + 0.5 log(0.6 W), without the additional log(W) term, because the reward is multiplicative, but it works out the same if we let W=1.
I read this paper when it was on here previously, and only skimmed choice parts again this time - rereading some more of it I can see that part of his point is that the introduction of utility, and its loose association with psychology and preference, was required to explain why you need to put a logarithm (or something similar) into the expectation in order to generate correct results, and not, as I was wrongly suggesting, that EUT generates incorrect results for problems like these. His claim is that you can recover identical behaviour, without needing to add arbitrary preference functions, by considering the time-average behaviour. Furthermore, as I suggested in another comment, this actually makes sense, because this is what an individual agent experiences.
You may not have to add arbitrary preference functions but you have to add the arbitrary assumption that people don’t care about anything else than the hypothetical asymptotic growth if the current “bet” was to be replayed endlessly. (I don’t think that’s what the agent experiences either.)
Using EUT with a logarithmic utility function is not more arbitrary than that. Assume that people look to maximize asymptotic growth under repeated bets and you know that the logarithmic utility function is what you need.
And as a bonus EUT can be applied in many cases where people don’t care just about the asymptotic growth rate!
The assumption that one's life will be composed of a series of risky choices doesn't seem to be a very strong one. The use of a single form of bet is just illustrative - the point applies equally well to any series of bets with similar overall properties (multiplicative rather than additive changes in wealth).
I think that the choice of a logarithmic utility function is more arbitrary - do you know what the explanation for it is, other than it fits with observed behaviour.
Another point is that the "(non-)ergodic theory" neatly explains why behaviour would change given different expectations about repetition. If you only had one bet left in your life then using logarithmic utility would produce what I would argue would be "incorrect" results for the equation 2 bet - I think that the rational choice would be to bet, because you don't really have anything to lose. It is only with iteration that losing starts to factor in. In EUT this would be explained with a change in preferences - but the point is that we don't need these additional mechanisms, it all falls out of the dynamics of the problem.
To your latter point, about the broader applicability of EUT - whilst I agree it is very convenient, fundamentally it doesn't seem that insightful that by choosing different scoring functions, and taking expectations over distributions of scores, we can recover all kinds of behaviours that might be of interest.
More explicitly, EUT doesn't really seem to tell us much - we can find a function that gives us any desired behaviour, sure, but it doesn't tell us why that behaviour is expected. As far as I know this is indeed where the theory stops, and the behaviours get effectively "written off" as preferences. A theory that explains the same behaviours without requiring these additional choices is surely preferable?
> fundamentally it doesn't seem that insightful that by choosing different scoring functions, and taking expectations over distributions of scores, we can recover all kinds of behaviours that might be of interest
Well, expected utility theory has been a great success and it’s used all the time to produce useful results in many fields. And the idea of optimizing growth is not new, it has been used within the expected utility framework since the fifties.
If you find the EE derivations interesting it’s fine. But don’t think it proves that EUT is wrong. And be aware that people use the same kind of analysis of the details of problems to select utility functions within the EUT framework.
EUT can be used for many things. It can be used to study empirically the behavior of people (who are not really “rational”).It can also be used to optimize industrial processes (according to a “rational” model). It can be used anywhere that there are decisions about uncertain outcomes which are more or less desirable.
The logarithmic utility doesn’t fit observed behavior particularly well. But it does lead to growth optimization. If you think the problem call for the maximization of asymptotic growth use logarithmic utility. If you don’t, don’t. Again, it’s exactly the same assumption. Not more arbitrary.
EE tells you that using the logarithmic utility is equivalent. The article mentions “the correspondences between linear utility and additive dynamics; and between logarithmic utility and multiplicative dynamics”.
I realise I am not explaining my self particularly well, but I don't think it is fair to call it the same assumption.
Assuming that we want to maximise growth over whatever our horizon is (be it one period, multiple periods, or an infinity of periods) is not much of an assumption - what other realistic goal would there be?
Your earlier point that EUT can be applied in other situations still holds, but I think that is a consequence of the fact that it is so flexible that it can be fit to all manner of situations.
With EE you recover different behaviours depending on the structure of the problem, both the reward structure and the temporal structure (e.g. number of periods), whereas with EUT you have to inject different utility functions to recover the desired behaviours for any given problem - they don't just fall out of the structure.
What is the EUT answer to the problem I posed in the previous comment - consider the same equation 2 bet we have been discussing, but in both the iterated case and the single-period case. Is there a utility function that correctly solves both cases?
> Is there a utility function that correctly solves both cases?
If the problems are different a different utility function may be appropriate. (Nobody says “don’t look at the structure of the problem”.)
> With EE you recover different behaviours depending on the structure of the problem, both the reward structure and the temporal structure (e.g. number of periods)
How so? EE works only with an infinite number of periods.
> If the problems are different a different utility function may be appropriate.
The claim of the paper is that you can derive an appropriate rational solution for each problem using a single technique.
> How so? EE works only with an infinite number of periods.
Afaik this is not correct - EE does not require the problem to have an infinite number of periods, rather it is saying that you cannot assume that the temporal integral is equal to the ensemble integral, and that you must act accordingly. You have to (in principle) integrate the whole time series of interest - this can be done over your uncertainty, but requires no utility function, a simple expectation will do.
In the problems that EE has actually solved the solution is known and is derived using similar arguments.
Note that EUT has two main uses, descriptive (how do people behave?) and normative (what should you do in this situation?). Descriptive: you try to find empirically a utility function that describes people's preferences when facing decisions.
Normative: you look at the problem (whether it's portfolio selection or deciding where to construct a dam), make assumptions about the probabilities of outcomes and their desirability and calculate what is the prefer solution that you should take.
Optimizing long-term growth because it's the defining property of a multiplicative process is not a new idea. The logarithmic utility function is derived for this problem using those arguments even in undergraduate textbooks. It's discussed for example in pages 232-234 of
http://dl.rasabourse.com/Books/Finance%20and%20Financial%20M... (I don't necessarily agree with everything said there, it's just an example.)
Empricically, though, people don't quite behave as growth-optimizers. They would be leveraged to be invested 200% in equities to have the optimal portfolio.
> EE does not require the problem to have an infinite number of periods
Ok. But then the infinite repetion where the time-average is justified by the ability of the agent to experience every possible outcome infinite times is just a mental construct without any relation to physical reality. Which is fine for me, mind you.
Still, that doesn't explain how this is correct:
"With EE you recover different behaviours depending on the structure of the problem, both the reward structure and the temporal structure (e.g. number of periods)"
In the question of whether you take that bet, you get the same answer whether you play once, or ten times, or one million. (Or course the same is true when you analyse the problem using logarithmic utility, because it's mathematically equivalent to growth optimization in a multiplicative process).
EUT can be used descriptively because you can just pick any utility function to fit whatever behaviour you are trying to explain, but that doesn't offer any insight. If the theory was good you could find a utility function that fit a range of behaviours, but without it being overfit. Again, the EE claim, and one which is demonstrated for at least some simple cases, is that you can recover a range of behaviours without adding in parameters by considering time explicitly.
> In the question of whether you take that bet, you get the same answer whether you play once, or ten times, or one million.
If you are only playing one round, you should take the bet, if you are playing more than one round, you shouldn't. EUT requires you to change utility function to recover those two different answers, EE gives you the correct answer however many rounds you choose to play (one, or more) without requiring any additional modification.
I do, and no, not precisely, but I would prefer to have more wealth than less at any time step - that is a preference that is invariant. However, what may change is the structure of the problem in front of me - the nature of the bets, or my time horizon (as I age). Realistic spending vastly complicates the situation for any analysis, but some basic spending pattern does not, and is effectively just an exogenous event that doesn't affect the analysis.
In EUT some of the response to changes in situation is modelled as a change of preferences, and encoded in the utility function - for example, older people may have different preferences to younger people, and those who have a lot of "good fortune" (perhaps through a good network) may have different preferences to those with few good opportunities.
This is fine, and it produces good results, but a more satisfying theory would be able to derive the behaviours from the problem itself. One claim is that this is not possible - that preferences are a fundamental primitive, but it isn't obvious to me that this is necessarily true.
To be clear, I would distinguish between irrational behaviours caused by lack of information, poor estimation or analysis, etc. and differences in rational behaviour caused by problem structure - here I am only considering the latter.
> a more satisfying theory would be able to derive the behaviours from the problem itself
See my other comment about prescriptive vs. descriptive. You can postulate some utility and derive the theoretical behaviour. You can observe some behaviour and try to infer the utility that would be consistent with it (assuming that the behaviour is rational, for some definition of rationality).
EE can only do the former. Facing the same problem, people is not allowed to have different preferences. EE prescribes what rational behaviour is.
EUT and EE are not incompatible. When solving an optimization problem EUT can use the same arguments that EE does to find the utility function to use. I don't think these results are new, but even if they were they wouldn't invalidate EUT.
The point is that in the "prescriptive" setting the EUT framework can be used with whatever utility function makes sense for the problem. The basic theory doesn't tell you either what's the utility of inundating a valley to build a dam, or the utility of a floods if you don't. When you use EUT to find a solution to a problem you have to think about the problem.
Imagine that the outcomes are different levels of your wealth at the end of the year. For example A is $500k, B is $50k, C is $200k. What is the utility function that describes your preferences? (There should be one if you're rational in the sense of the EUT axioms.)
Surely we agree that you prefer A to C and C to B.
But would you prefer to have $500k or $50k with 50%/50% probability or to be certain of having $200k at the end of the year?
EUT doesn't give you an answer. Of course it's easy to calculate the expected value of the first alternative ($275k) but nobody says that you should prefer the "risky" $275k to the certain $200k. That's the point of introducing utility functions in the analysis, that preferences may be non-linear.
What EUT says is that if you're rational (etc) there are three numbers U($500k), U($50k) and U($275k). The expected utility of the first option is 0.5 U($500k) + 0.5 U($50k) and the expected utility of the second option is U($200k).
These expected utilities can be compared to see if you which option do you prefer. If you prefer one, you could also be indifferent.
EUT says that the rational decision is to chose the option with higher expected utility.
__ Remarks __
EUT doesn't fix the form of the utility function. Usually it's assumed that instead of linear it's concave. This means that a certain dollar is better than a dollar in expectation and you would never take fair bets.
(The fact that people plays in the casino where bets are not even fair could be explained with convex utility. One could explain it as well saying that there is utility obtained from the entertainment that offsets the monetary loss.)
The utility function describing someone's preferences could be very complex. Simple models are used for many reasons including tractability or theoretical properties. For example power functions (logarithmic utility is a special case).
There are some reasons to like logarithmic utility (including growth-optimality arguments) but it doesn't work too well empirically. This is why, at least in some settings, it may be better to use the more general power utilities that have a parameter that can be adjusted.
Using logarithmic utility, the $200k option is preferable to the $500k/$50k bet. The certainty equivalent is $158k.
Logarithmic utility (like the rest of the power utilities) is scale invariant. The amounts could by 100 times larger or 100 times smaller and the answer would be the same.
Does Ole Peters claim that the use of EUT here is wrong? I guess so. Parallel universes again, probably.
Would you say that there is a problem with EUT up to this point?
What are the problematic assumptions made by EUT? In my opinion it's EE who cannot really solve this problem without making "unphysical" assumptions. The solution corresponds to using the logarithmic utility above, EE declares any other preference the agent may have wrong.
"There's no such thing as a "correct result" because people's preferences (utility) varies by individual."
But there are incorrect results and setting U to anything other than log (Wealth) results in an incorrect result.
"It can also happen in other cases that EE cannot be used to explain the preferences of the agent while EUT is still applicable because a utility function (maybe logarithmic, maybe not) can be found which describes them adequately."
I just told you that you can not use an utility function other than log (Wealth). Any other utility function you use will give you a mathematically incorrect result. The log (Wealth) term covers up the maths error, so it can't be changed to another term.
If you want to do something like that then you need to use the maths from EE.
The role of the utility function in EUT is to represent the agents preferences.
Preferences can be rational (i.e. consistent) and not be represented by the logarithm of wealth.
If Mr. X has some amount to invest now to pay for his child’s college in five years it’s not “irrational” to opt for something less risky than taking a loan to get a leveraged equity investment.
Mr. X may not care that his portfolio wouldn’t growth at the optimal highest possible rate if left untouched forever, if that’s what you mean by “mathematically incorrect result”.
Mr. X doesn’t care about your idea of “correct result”, he cares about being reasonably certain to have enough money available in five years.
Now, you tell me to use the maths from EE to find the “correct” utility functions.
How can I use the maths from EE to select a portfolio if I want to take out a certain amount of money in five years?
EE shows that EUT only gives correct results when U = log (Wealth), that means as soon as you set U to anything other than log (Wealth), it is no longer giving correct results.
So it would be fair to say EUT also has no concept of utility.
You misunderstand the concept of subjective utility.
There's no such thing as a "correct result" because people's preferences (utility) varies by individual.
What's "correct" for a risk-seeking gambler is very different to what's "correct" for an investor who's trying to build generational wealth.
That's why we have a U(x) to begin with. Without addressing this concept, you're no longer attempting to describe reality, you're making a prescriptive normative assertion that everyone should follow a specific strategy of your choosing.
> EE shows that EUT only gives correct results when U = log (Wealth)
You seem to think that this invalidates EUT.
On the contrary, it's a vindication of EUT.
In that particular case, EUT works and the preferences of the agent would be correctly described by that particular utility function. Otherwise you wouldn't say that EE and U=log(w) give "correct results".
It can also happen in other cases that EE cannot be used to explain the preferences of the agent while EUT is still applicable because a utility function (maybe logarithmic, maybe not) can be found which describes them adequately.
Talking about portfolio selection, for example, the EE - a.k.a. U=log(wealth) - solution may be the "correct solution" to the "we never spend a dollar problem and we have an infinite horizon" problem.
But EE cannot get any results, correct or otherwise, for many other problems that are much more interesting where EUT can be applied.
Like investment decisions when your horizon is not infinite and you intend to use the money at some point.
EE stats that in EUT the U term must equal log (Wealth) otherwise EUT produces wrong results.
EE uses a completely different formula. It has an open space for a (slightly restricted) function (similar to U). An example of EE with this open space filled is Kelly's criterion, which of course looks nothing like EUT.
“The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate.”
Secondly, you're misunderstanding my objection. What I'm objecting to are the very conceptual foundations of the theory. Old people demonstrably accept a lower EV than young people because of a difference in expected utility over the distribution of near-term outcomes. To throw the concept of expected utility in the bin is therefore a departure from reality and as such the theory automatically fails on conceptual grounds.