6 ms·

> 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

by mrow84 6y ago

> 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.

kgwgk 6y ago
__ The basic formulation of EUT __ 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?
- kgwgk 6y ago
  __ A simple investment decision application __ 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. (To be continued, maybe.)

by mrow84 6y ago

kgwgk 6y ago

__ The basic formulation of EUT __ 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?

kgwgk 6y ago
__ A simple investment decision application __ 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. (To be continued, maybe.)