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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

by mrow84 6y ago

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?

kgwgk 6y ago
> what other realistic goal would there be? Don’t you ever spend any money? Is your only goal really to maximize the growth rate of your wealth in the infinite-time limit?
- mrow84 6y ago
  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.
  - kgwgk 6y ago
    > 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.
kgwgk 6y ago
> 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.
- mrow84 6y ago
  > 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.
  - kgwgk 6y ago
    > The claim of the paper is that you can derive an appropriate rational solution for each problem using a single technique. Can you derive a rational solution for this problem using that technique? "An investor must choose how much to consume and must allocate his wealth between stocks and a risk-free asset" https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem 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%20Markets/%5BEdwin_J._Elton%2C_Martin_J._Gruber%2C_Stephen_J._Brow_Modern%20Portfolio%20Theory%20and%20Investment%28rasabourse.com%29.pdf 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).

by mrow84 6y ago

kgwgk 6y ago

> what other realistic goal would there be? Don’t you ever spend any money? Is your only goal really to maximize the growth rate of your wealth in the infinite-time limit?

mrow84 6y ago
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.
- kgwgk 6y ago
  > 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.

kgwgk 6y ago

> 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.

mrow84 6y ago
> 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.
- kgwgk 6y ago
  > The claim of the paper is that you can derive an appropriate rational solution for each problem using a single technique. Can you derive a rational solution for this problem using that technique? "An investor must choose how much to consume and must allocate his wealth between stocks and a risk-free asset" https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem 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%20Markets/%5BEdwin_J._Elton%2C_Martin_J._Gruber%2C_Stephen_J._Brow_Modern%20Portfolio%20Theory%20and%20Investment%28rasabourse.com%29.pdf 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).