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.
I feel your pain. I hope the amount of upvotes and hearts you're getting helps you feel better, but I know brains don't always work that way (mine doesn't).
I believe this sort of thing doesn't get much attention from EAs because there's not really a strong case for it being a global priority in the same way that existential risk from AI is.
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
it seems important for my own decision making and for standing on solid ground while talking with others about animal suffering.
To this point, I think the most important things are
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.
I disagree-voted to indicate that I did not donate my mana because of this post (I use Manifold sometimes but I have only a trivial amount of mana)