I do independent research on EA topics. I write about whatever seems important, tractable, and interesting (to me). Lately, I mainly write about EA investing strategy, but my attention span is too short to pick just one topic.
I have a website: https://mdickens.me/ Most of the content on my website gets cross-posted to the EA Forum.
My favorite things that I've written: https://mdickens.me/favorite-posts/
I used to work as a software developer at Affirm.
If we're talking about financial risk, I enjoyed Deep Risk, a short book by William Bernstein.
The use of quantitative impact estimates by EAs can mislead audiences into overestimating the quality of quantitative empirical evidence supporting these estimates.
In my experience, this is not a winnable battle. Regardless of how many times you repeat that your quantitative estimates are based on limited evidence / embed a lot of assumptions / have high margins of error / etc., people will say you're taking your estimates too seriously.
Do you have some estimate of the cost-effectiveness of helping slaughterhouse workers as compared to, say, cage-free campaigns?
I came up with a few problems that pose challenges for ergodicity economics (EE).
First I need to explicitly define what we're talking about. I will take the definition of the ergodic property as Peters defines it:
The expected value of the observable is a constant (independent of time), and the finite-time average of the observable converges to this constant with probability one as the averaging time tends to infinity.
More precisely, it must satisfy
where W(t) is wealth at time t, f(W) is a transformation function that produces the "observable", and the second integral is taking the expected value of wealth across all bet outcomes at a single point in time. (Peters specifically talked about wealth, but W(t) could be a function describing anything we care about.)
According to EE, a rational agent ought to maximize the expected value of some observable f(W) such that that observable satisfies the ergodic property.
According to EE, making decisions in a non-ergodic system requires applying a transformation function to make it ergodic. For example, if given a series of bets with multiplicative payout, those bets are non-ergodic, but you can transform them with , and the output of now satisfies the ergodic property.
(Peters seems confused here because in The ergodicity problem in economics he defines the transformation function f as a single-variable function, but in Evaluating gambles using dynamics, he uses a two-dimensional function of wealth at two adjacent time steps. I will continue to follow his second construction where f is a function of two variables, but it appears his definition of ergodicity is under-specified or possibly contradictory.)
The problem: There are infinitely many transformation functions that satisfy the ergodic property.
The function "f(x) = 0 for all x" is ergodic: its EV is constant wrt time (because the EV is 0), and the finite-time average converges to the EV (b/c the finite-time average is 0). There is nothing in EE that says f(x) = 0 is not a good function to optimize over, and EE has no way of saying that (eg) maximizing geometric growth rate is better than maximizing f(x) = 0.
Obviously there are infinitely many constant functions with the ergodic property. You can also always construct an ergodic piecewise function for any given bet ("if the bet outcome is X, the payoff is A; if the bet outcome is Y, the payoff is B; ...")
Peters does specifically claim that
These assumptions are not directly entailed by the foundations of EE, but I will take them as given. They're certainly more reasonable than f(x) = 0.
Consider two bets:
Bet A: 50% chance of winning $2, 50% chance of losing $1
Bet B: 99% chance of 100x'ing your money, 1% chance of losing 0.0001% of your money
EE cannot say which of these bets is better. It doesn't evaluate them using the same units: Bet A is evaluated in dollars, Bet B is evaluated in growth rate. I claim Bet B is clearly better.
There is no transformation function that satisfies Peters' requirement of maximizing geometric growth rate for multiplicative bets (Bet B) while also being ergodic for additive bets (bet A). Maximizing growth rate specifically requires using the exact function , which does not satisfy ergodicity for additive bets (expected value is not constant wrt t).
In fact, multiplicative bets cannot be compared to any other type of bet, because is only ergodic when W(t) grows at a constant long-run exponential rate.
More generally, I believe any two bets are incomparable if they require different transformation functions to produce ergodicity, although I haven't proven this.
This is relevant to Paul Samuelson's article that I linked earlier. EE presumes that all rational agents have identical appetite for risk. For example, in a multiplicative bet, EE says all agents must bet to maximize expected log wealth, regardless of their personal risk tolerance. This defies common sense—surely some people should take on more risk and others should take on less risk? Standard finance theory says that people should change their allocation to stocks vs. bonds based on their risk tolerance; EE says everyone in the world should have the same stock/bond allocation.
Consider a bet:
Bet A: 50% chance of doubling your money, 50% chance of losing $1
More generally, consider the class of bets:
50% chance of multiplying your money by
a
, 50% chance of losingb
dollars
Call these multiplicative-additive bets.
EE does not allow for the existence of any non-constant evaluation function for multiplicative-additive bets. In other words, EE has no way to evaluate these bets.
Proof.
Consider bet A above. By the first clause of the ergodic property, the transformation must satisfy (for some wealth value )
for some constant . This equation says must have a constant expected value.
Now consider what happens at x = -1. There we have and therefore .
That is, f(-1, -2) must equal the expected value of f for any x.
we can generalize this to all multiplicative-additive bets to show that the transformation function must be a constant function.
Consider the class of all multiplicative-additive bets. The transformation function must satisfy
for some constants a, b which define the bet (in Bet A, a = 2 and b = 1). (Note: It is not required that a and be be positive.)
The transformation function must equal when . To see this, observe that and , so .
For any pair defining a particular additive-multiplicative bet, it must be the case that is a constant (and, specifically, it equals the expected value of the transformation function with parameters ).
Next I will show that, for (almost) any pair in , there exists some pair that forces to be a constant.
Solving for in terms of , we get . This is well-defined for all pairs of real numbers except where . For any pair of values we care to choose, there is some bet parameterized by such that is a constant.
Therefore, if there is a function that is ergodic for all additive-multiplicative bets, then that function must be constant everywhere (except on the line , i.e., where your starting wealth is 0, which isn't relevant to this model anyway). A constant-everywhere function says that every multiplicative-additive bet is equally good.
EDIT: I thought about this some more and I think there's a way to define a reasonable ergodic function over a subset of multiplicative-additive bets, namely where a > 1 and b > 0. Let
This gives which is the average value, and I think it's also the long-run expected value but I'm not sure about the math, this function is impossible to define using the single-variable definition of the ergodic property so I'm not sure what to do with that.
(Sorry this comment is kind of rambly)
I looked through the first two pages of Google Scholar for economics papers that cite Peters' work on ergodicity. There were a lot of citations but almost none of the papers were about economics. The top relevant(ish) papers on Google Scholar (excluding other papers by Peters himself) were:
Peters makes a similar mistake to Davidson by making ergodicity the centre of his work, rather than a supporting concept where relevant. The metaphysical baggage accompanying EE [ergodicity economics] is supposed to clarify the problem. In practice it has obscured the observation that EE is essentially no more than a mechanical claim that stochastic processes, when iterated many times, are very likely to give certain outcomes. One does not have to accept [expected utility theory] as a good model of decision making to see that it is nonetheless more reasonable than EE.
So basically, I found a few favorable articles but they were shallow, and all the other articles were critiques. Some of the critiques were harsh (calling ergodicity pseudoscience or confused) but AFAIK the harshness is justified. From what I can tell, ergodicity economics doesn't have anything to contribute.
For example, consider playing a game where you flip a coin, and if it's heads, you increase your wealth by 50%, but if it's tails, you lose 40%. Mathematically, the average outcome looks positive. But, if you play this game repeatedly, because of the multiplicative nature of wealth (losing 40% can't just be "averaged out" by gaining 50% later), you're likely to end up with less money over time. This game is non-ergodic - the long-term outcome for an individual doesn't match the seemingly positive average outcome.
The long-term outcome in this game is only the correct thing to optimize for under specific circumstances (namely, the circumstances where you have a logarithmic utility function). Paul Samuelson discussed this in Why we should not make mean log of wealth big though years to act are long. For a more modern explanation, see Kelly is (just) about logarithmic utility on LessWrong.
Taking ergodicity seriously can strengthen the EA longtermist movement both from a theoretical and a practical perspective.
Are you saying that it immediately produces solutions? Or that it hasn't produced solutions yet, but it might with more research? For example, what does an ergodicity framework say is the correct amount to bet in the St. Petersburg game? Or the correct decision in Cowen's game where you have a 90% chance to double the world's happiness and a 10% chance to end it?
(I should say that my questions are motivated by the fact that I'm pretty skeptical of ergodicity as a useful framework, but I don't understand it very well so I could be missing something. I skimmed the Peters & Gell-Mann paper and I see it makes some relevant claims like "expectation values are only meaningful in the presence of [...] systems with ergodic properties" and "Maximizing expectation values of observables that do not have the ergodic property [...] cannot be considered rational" but I don't see where it justifies them, and they're both false as far as I can tell.)
I was originally going to write an essay based on this prompt but I don't think I actually understand the Epicurean view well enough to do it justice. So instead, here's a quick list of what seem to me to be the implications. I don't exactly agree with the Epicurean view but I do tend to believe that death in itself isn't bad, it's only bad in that it prevents you from having future good experiences.
RE #2, I helped develop CCM as a contract worker (I'm not contracted with RP currently) and I had the same thought while we were working on it. The reason we didn't do it is that implementing good numeric integration is non-trivial and we didn't have the capacity for it.
I ended up implementing analytic and numeric methods in my spare time after CCM launched. (Nobody can tell me I'm wasting my time if they're not paying me!) Doing analytic simplifications was pretty easy, numeric methods were much harder. I put the code in a fork of Squigglepy here: https://github.com/michaeldickens/squigglepy/tree/analytic-numeric
Numeric methods are difficult because if you want to support arbitrary distributions, you need to handle a lot of edge cases. I wrote a bunch of comments in the code (mainly in this file) about why it's hard.
I did get the code to work on a wide variety of unit tests and a couple of integration tests but I haven't tried getting CCM to run on top of it. Refactoring CCM would take a long time because a ton of CCM code relies on the assumption that distributions are represented as Monte Carlo samples.
It's really hard to judge whether a life is net positive. I'm not even sure when my own life is net positive—sometimes if I'm going through a difficult moment, as a mental exercise I ask myself, "if the rest of my life felt exactly like this, would I want to keep living?" And it's genuinely pretty hard to tell. Sometimes it's obvious, like right at this moment my life is definitely net positive, but when I'm feeling bad, it's hard to say where the threshold is. If I can't even identify the threshold for myself, I doubt I can identify it in farm animals.
If I had to guess, I'd say the threshold is something like
To this point, I think the most important things are