经济与社会科学2019nature.com
经济学中的遍历性问题
The Ergodicity Problem in Economics
进阶 · 约 90 分钟读完前置知识：概率论与随机过程、期望效用理论、对数增长/Kelly 公式
导读
物理学家 Ole Peters 在《Nature Physics》上撰文指出经济学中的遍历性问题：传统期望效用理论把时间平均与集合平均混为一谈，相当于假设个体能同时体验平行宇宙的所有结果，而现实中个体只经历单一时间路径。作者主张放弃这一隐含假设、以时间平均（如对数增长最优）为基础重构决策理论，认为这能自然解释风险厌恶等现象。
HN 关注点：该文挑战了期望效用理论这一经济学基石，且由物理学家跨界发起，引发经济学界对模型假设是否成立、是否被夸大为'革命'的激烈争论。
HN 评论精选
这几条评论里：支持 1 质疑 3
质疑批评该文夸大其词，认为遍历性是已知话题，不太可能引发经济学革命
这是'手里拿锤子看什么都是钉子'的典型例子。作者忽视了经济学是横跨应用经济学到纯数学的广阔领域，他没在恰当的层面展开讨论：对理论数学家而言所有模型都只是假设的推论，对应用经济学家而言模型能解释现象即是对的。遍历性并非冷门话题，随机过程中级课程就会讲。放宽随机过程的假设或许能带来更好的模型，但不太可能引发经济学理论的革命。奇怪这样的文章能通过同行评审。可参见后续的批评性回应与作者的答复。
Pyramus查看英文原文
This is a fascinating example of 'if you have a hammer, all you see is nails'. It seems odd that this has been published at all - but then again, it is most likely to be published in journal that is not domain-specific. The author seems to miss that "economics" is a vast field spanning the whole spectrum from applied economics, over theoretical economics, mathematical finance, financial mathematics, to pure mathematics (with physicists working along the whole spectrum, so this is not a consequence of the author's background per se). He fails to engage at the right level. From a theoretical mathematician's point of view all models are wrong - they are just deductions from assumptions. From an applied economist's point of view are models are right - they explain some observed phenomena. Ergodicity is not a niche topic, most intermediate courses on stochastic processes will cover it. Will loosening an assumption about the properties of stochastic processes yield different, potentially better models? Maybe. Will it lead to a revolution in economic theory? Unlikely. Again, odd that this has been peer-reviewed. See also the reply here, which is rather damning [1] And the author's reply to the reply. [2] [1] https://www.nature.com/articles/s41567-020-01106-x [2] https://www.nature.com/articles/s41567-020-01108-9
质疑指出该文观点不新颖，且期望效用理论本身并不依赖遍历性假设
三点质疑：(1) 其洞见并不新颖，相当于独立重新发明了始于 Kelly 公式的思想；(2) 期望效用理论并未假设遍历性，在跨期设定下最大化期望效用的组合选择会得到与时间平均相近的结果，还能给出投资与消费划分的洞见；(3) 跨期分析中贴现率至关重要，经济学家和哲学家已对此有大量讨论——若不做重度贴现，未来相对现在的重要性会远超多数人和政府的实际行为。
oli5679查看英文原文
(1) their insight is not novel, they have independently reinvented Something that started with the Kelly Criterion https://en.m.wikipedia.org/wiki/Kelly_criterion (2) Expected utility theory makes no assumptions about ergodicity. In intertemporal setting, portfolio allocations maximising expected utility will chose something close to their metric as well as giving some insight into the split between investment and consumption. https://en.m.wikipedia.org/wiki/Intertemporal_choice (3) with intertemporal analysis, the rate of discounting is important. This has been heavily discussed by economists and philosophers already. If you don't have heavy discounting, the future becomes much more important relative to the present than would be consistent with many people and government's actions.
质疑认为文章低估了期望效用理论的公理化基础，但承认若预测更好则有价值
我觉得这篇文章过度弱化了期望效用理论的正当性。文中说把人建模为最大化期望效用，就像假设人在与平行宇宙的自己互动——但作者不可能不知道冯·诺依曼-摩根斯坦效用定理。文章抱怨当人们不按理论行事时被贴上'非理性'标签而不修正理论；虽然理论确实需要解释实际行为，但在我看来，人们违背 vNM 公理确实是没有达到理性主体的正确理想。也许应该形式化一个'算力受限的 vNM 公理近似'。如果这套方法能更好预测人的行为，那是有价值的，但会引出'为什么'的问题。
drdeca查看英文原文
I feel that this downplays the justification for theories of expected utility too much? But I still want to keep reading to see where they're going with this. Ok, like, it says that modeling people as trying to maximize expected utility, is like assuming something as if one is interacting with paralell universe copies of onseself. But, surely the author must be familiar with the Von Neumann–Morgenstern utility theorem? It complains that when people fail to act according to the theories, that the people are considered to be irrational, rather than amending the theories. While it is of course true that theories need to be made to account for how people actually behave, it seems to me that people failing to satisfy the vNM axioms, really is a way in which people fail to live up to the correct ideal of a rational agent. Well, maybe for it to make sense, instead there should be a formalization of like, a compute-limited approximation of following the vNM axioms, maybe throw in a dash of sub-agent stuff, and a few things along those lines. Hmm. Ok, well, if this makes better predictions of how people behave, that is valuable. Though, it would raise the question of "why?".
支持支持作者观点，并补充圣塔菲介绍文章和完整讲义等资料
我关注作者一段时间了，很认同这些想法——经济学中不似任何真人的'理性人'从来让我觉得不对劲。圣塔菲研究所同日发布的文章用具体例子解释：抛硬币游戏看似值得玩，因为 50% 收益与 40% 损失等概率，等价于稳赚 5%。人们拒绝玩这个游戏，传统上被心理学地解释为'风险厌恶'，但 Peters 认为这没触及根源：经典解法缺乏对个体独特时间轨迹的基本理解。他的完整讲义可在 ergodicityeconomics.com 获取。
photojosh查看英文原文
I've been following the author for a while now (no personal connection), and I'm taken with the ideas. Mainly because it's never seemed right to me that economics' "rational person" doesn't resemble anyone in the real world. [0] also out today explains it starting from a concrete example: > the coin toss game seems worth playing because equal probability of a 50% gain and a 40% loss are no different from a 5% gain.* > Why people don't choose to play the game, seemingly ignoring the opportunity to gain a steady 5%, has been explained psychologically-- people, in the parlance of the field, are "risk averse". But according to Peters, these explanations don't really get to the root of the problem, which is that the classical "solution" lacks a fundamental understanding of the individual's unique trajectory over time. You can also get his full lecture notes at [1]. [0] https://www.santafe.edu/news-center/news/fix-economic-theory-changes-everything-gambles-inequality-ponzi-schemes [1] https://ergodicityeconomics.com/lecture-notes/
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