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It's not. You can read the proofs to see that they aren't missing a step. If you don't want to do that, I can give some indirect evidence. The "conventional

It's not. You can read the proofs to see that they aren't missing a step. If you don't want to do that, I can give some indirect evidence. The "conventional economics literature" begins with a theorem of von Neumann and Morganstern, published in 1944. This is the John von Neumann of math and physics fame. In particular, von Neumann was one of the architects of ergodic theory. He proved the mean ergodic theorem all the way back in 1932. It would be pretty surprising indeed if it was von Neumann who missed the subtlety.

ReflectedImage 6y ago
It would be more correct to say economists misinterpreted what von Neumann said.
- QuesnayJr 6y ago
  They didn't, though. Look at von Neumann and Morganstern's "Theory of Games and Economic Behavior". There's nothing in there about time-series averages. It's a theory of games that you might play only once.
  - ReflectedImage 6y ago
    It's fairly obvious that in the real world time does play a role. This may shock you but theories advance over time. There isn't a holy paper which can never be improved on (at least not in sensible research fields).
    - dash2 6y ago
      You're suggesting that sometimes time matters. I agree. There's a whole subfield of economics studying the dynamics of decisions. However, As Wakker et al. point out: "Although it is true that our consumption of economic goods develops over time, time is not the most central aspect of all our decisions. For many of our decisions, other equally ubiquitous aspects such as risks, strategy and the balancing of pros and cons are more central. Just because something is ubiquitous, it should not be confused with being explanatory; for example, we can argue everything consists of molecules, but it is not a reason to think that all questions in economics, geography and throughout life should be answered by molecular dynamics.... Economists use static EU for static decisions, when dynamics are not central. Otherwise, a dynamic model is used."
    - QuesnayJr 6y ago
      Essentially all economic models of investment have a time dimension. I'm not sure where you're getting the idea that it's left out. Also, the field has gone far beyond von Neumann-Morganstern, so I'm not sure where you're getting that, either. I'm simply making the point that expected utility does not require ergodicity. If you read the proofs, it's clear. If you don't want to read the proofs, the best that I can do is provide indirect historical evidence.
      - ReflectedImage 6y ago
        "I'm simply making the point that expected utility does not require ergodicity." Okay well that point is wrong, as in very wrong. Ergodicity can be directly defined as it is valid to take the Expected Value. That's just what Ergodicity means. Expected Utility is defined on top of Expected Value. So Expected Utility assumes Ergodicity.
      - QuesnayJr 6y ago
        Weird, I can't reply directly. Peters (and you, I assume) are taking a strong philosophical stance on the meaning of probability. Lots of people would disagree with you. Essentially all Bayesians would disagree with you, for example.
        ReflectedImage 6y ago
        Yeah reply seems to be a bit buggy. "strong philosophical stance on the meaning of probability" ??? It's taken directly from thermodynamics: https://en.wikipedia.org/wiki/Ergodic_hypothesis https://en.wikipedia.org/wiki/Ergodic_hypothesis You would be arguing directly with the laws of thermodynamics.
        QuesnayJr 6y ago
        This is what I've always suspected was the subtext of this. "We're physicists, and what we learned while thinking about microcanonical ensemble is all you need to know about probability. No, we have nothing to learn from the hundreds of probabilists and statisticians on the subject of probability, or the hundred-year old debate on the meaning of probability." There are more things in heaven and earth than dreamt of in your philosophy, Horatio: https://plato.stanford.edu/entries/probability-interpret/ https://plato.stanford.edu/entries/probability-interpret/

ReflectedImage 6y ago

It would be more correct to say economists misinterpreted what von Neumann said.

QuesnayJr 6y ago
They didn't, though. Look at von Neumann and Morganstern's "Theory of Games and Economic Behavior". There's nothing in there about time-series averages. It's a theory of games that you might play only once.
- ReflectedImage 6y ago
  It's fairly obvious that in the real world time does play a role. This may shock you but theories advance over time. There isn't a holy paper which can never be improved on (at least not in sensible research fields).
  - dash2 6y ago
    You're suggesting that sometimes time matters. I agree. There's a whole subfield of economics studying the dynamics of decisions. However, As Wakker et al. point out: "Although it is true that our consumption of economic goods develops over time, time is not the most central aspect of all our decisions. For many of our decisions, other equally ubiquitous aspects such as risks, strategy and the balancing of pros and cons are more central. Just because something is ubiquitous, it should not be confused with being explanatory; for example, we can argue everything consists of molecules, but it is not a reason to think that all questions in economics, geography and throughout life should be answered by molecular dynamics.... Economists use static EU for static decisions, when dynamics are not central. Otherwise, a dynamic model is used."
  - QuesnayJr 6y ago
    Essentially all economic models of investment have a time dimension. I'm not sure where you're getting the idea that it's left out. Also, the field has gone far beyond von Neumann-Morganstern, so I'm not sure where you're getting that, either. I'm simply making the point that expected utility does not require ergodicity. If you read the proofs, it's clear. If you don't want to read the proofs, the best that I can do is provide indirect historical evidence.
    - ReflectedImage 6y ago
      "I'm simply making the point that expected utility does not require ergodicity." Okay well that point is wrong, as in very wrong. Ergodicity can be directly defined as it is valid to take the Expected Value. That's just what Ergodicity means. Expected Utility is defined on top of Expected Value. So Expected Utility assumes Ergodicity.
    - QuesnayJr 6y ago
      Weird, I can't reply directly. Peters (and you, I assume) are taking a strong philosophical stance on the meaning of probability. Lots of people would disagree with you. Essentially all Bayesians would disagree with you, for example.
      - ReflectedImage 6y ago
        Yeah reply seems to be a bit buggy. "strong philosophical stance on the meaning of probability" ??? It's taken directly from thermodynamics: https://en.wikipedia.org/wiki/Ergodic_hypothesis https://en.wikipedia.org/wiki/Ergodic_hypothesis You would be arguing directly with the laws of thermodynamics.
        QuesnayJr 6y ago
        This is what I've always suspected was the subtext of this. "We're physicists, and what we learned while thinking about microcanonical ensemble is all you need to know about probability. No, we have nothing to learn from the hundreds of probabilists and statisticians on the subject of probability, or the hundred-year old debate on the meaning of probability." There are more things in heaven and earth than dreamt of in your philosophy, Horatio: https://plato.stanford.edu/entries/probability-interpret/ https://plato.stanford.edu/entries/probability-interpret/