Labor history in the making

Oct 24 JDN 2459512

To say that these are not ordinary times would be a grave understatement. I don’t need to tell you all the ways that this interminable pandemic has changed the lives of people all around the world.

But one in particular is of notice to economists: Labor in the United States is fighting back.

Quit rates are at historic highs. Over 100,000 workers in a variety of industries are simultaneously on strike, ranging from farmworkers to nurses and freelance writers to university lecturers.

After decades of quiescence to ever-worsening working conditions, it seems that finally American workers are mad as hell and not gonna take it anymore.

It’s about time, frankly. The real question is why it took this long. Working conditions in the US have been systematically worse than the rest of the First World since at least the 1980s. It was substantially easier to get the leave I needed to attend my own wedding—in the US—after starting work in the UK than it would have been at the same kind of job in the US, because UK law requires employers to grant leave from the day they start work, while US federal law and the law in many states doesn’t require leave at all for anyone—not even people who are sick or recently gave birth.

So, why did it happen now? What changed? The pandemic threw our lives into turmoil, that much is true. But it didn’t fundamentally change the power imbalance between workers and employers. Why was that enough?

I think I know why. The shock from the pandemic didn’t have to be enough to actually change people’s minds about striking—it merely had to be enough to convince people that others would show up. It wasn’t the first-order intention “I want to strike” that changed; it was the second-order belief “Other people want to strike too”.

For a labor strike is a coordination game par excellence. If 1 person strikes, they get fired and replaced. If 2 or 3 or 10 strike, most likely the same thing. But if 10,000 strike? If 100,000 strike? Suddenly corporations have no choice but to give in.

The most important question on your mind when you are deciding whether or not to strike is not, “Do I hate my job?” but “Will my co-workers have my back?”.

Coordination games exhibit a very fascinating—and still not well-understood—phenomenon known as Schelling points. People will typically latch onto certain seemingly-arbitrary features of their choices, and do so well enough that simply having such a focal point can radically increase the level of successful coordination.

I believe that the pandemic shock was just such a Schelling point. It didn’t change most people’s working conditions all that much: though I can see why nurses in particular would be upset, it’s not clear to me that being a university lecturer is much worse now than it was a year ago. But what the pandemic did do was change everyone’s working conditions, all at once. It was a sudden shock toward work dissatisfaction that applied to almost the entire workforce.

Thus, many people who were previously on the fence about striking were driven over the edge—and then this in turn made others willing to take the leap as well, suddenly confident that they would not be acting alone.

Another important feature of the pandemic shock was that it took away a lot of what people had left to lose. Consider the two following games.

Game A: You and 100 other people each separately, without communicating, decide to choose X or Y. If you all choose X, you each get $20. But if even one of you chooses Y, then everyone who chooses Y gets $1 but everyone who chooses X gets nothing.

Game B: Same as the above, except that if anyone chooses Y, everyone who chooses Y also gets nothing.

Game A is tricky, isn’t it? You want to choose X, and you’d be best off if everyone did. But can you really trust 100 other people to all choose X? Maybe you should take the safe bet and choose Y—but then, they’re thinking the same way.


Game B, on the other hand, is painfully easy: Choose X. Obviously choose X. There’s no downside, and potentially a big upside.

In terms of game theory, both games have the same two Nash equilibria: All-X and All-Y. But in the second game, I made all-X also a weak dominant strategy equilibrium, and that made all the difference.

We could run these games in the lab, and I’m pretty sure I know what we’d find: In game A, most people choose X, but some people don’t, and if you repeat the game more and more people choose Y. But in game B, almost everyone chooses X and keeps on choosing X. Maybe they don’t get unanimity every time, but they probably do get it most of the time—because why wouldn’t you choose X? (These are testable hypotheses! I could in fact run this experiment! Maybe I should?)

It’s hard to say at this point how effective these strikes will be. Surely there will be some concessions won—there are far too many workers striking for them all to get absolutely nothing. But it remains uncertain whether the concessions will be small, token changes just to break up the strikes, or serious, substantive restructuring of how work is done in the United States.

If the latter sounds overly optimistic, consider that this is basically what happened in the New Deal. Those massive—and massively successful—reforms were not generated out of nowhere; they were the result of the economic crisis of the Great Depression and substantial pressure by organized labor. We may yet see a second New Deal (a Green New Deal?) in the 2020s if labor organizations can continue putting the pressure on.

The most important thing in making such a grand effort possible is believing that it’s possible—only if enough people believe it can happen will enough people take the risk and put in the effort to make it happen. Apathy and cynicism are the most powerful weapons of the status quo.


We are witnessing history in the making. Let’s make it in the right direction.

Stupid problems, stupid solutions

Oct 17 JDN 2459505

Krugman thinks we should Mint The Coin: Mint a $1 trillion platinum coin and then deposit it at the Federal Reserve, thus creating, by fiat, the money to pay for the current budget without increasing the national debt.

This sounds pretty stupid. Quite frankly, it is stupid. But sometimes stupid problems require stupid solutions. And the debt ceiling is an incredibly stupid problem.

Let’s be clear about this: Congress already passed the budget. They had a right to vote it down—that is indeed their Constitutional responsibility. But they passed it. And now that the budget is passed, including all its various changes to taxes and spending, it necessarily requires a certain amount of debt increase to make it work.

There’s really no reason to have a debt ceiling at all. This is an arbitrary self-imposed credit constraint on the US government, which is probably the single institution in the world that least needs to worry about credit constraints. The US is currently borrowing at extremely low interest rates, and has never defaulted in 200 years. There is no reason it should be worrying about taking on additional debt, especially when it is being used to pay for important long-term investments such as infrastructure and education.

But if we’re going to have a debt ceiling, it should be a simple formality. Congress does the calculation to see how much debt will be needed, and if it accepts that amount, passes the budget and raises the debt ceiling as necessary. If for whatever reason they don’t want to incur the additional debt, they should make changes to the budget accordingly—not pass the budget and then act shocked when they need to raise the debt ceiling.

In fact, there is a pretty good case to be made that the debt ceiling is a violation of the Fourteenth Amendment, which states in Section 4: “The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned.” This was originally intended to ensure the validity of Civil War debt, but it has been interpreted by the Supreme Court to mean that all US public debt legally incurred is valid and thus render the debt ceiling un-Constitutional.

Of course, actually sending it to the Supreme Court would take a long time—too long to avoid turmoil in financial markets if the debt ceiling is not raised. So perhaps Krugman is right: Perhaps it’s time to Mint The Coin and fight stupid with stupid.

Marriage and matching

Oct 10 JDN 2459498

When this post goes live, I will be married. We already had a long engagement, but it was made even longer by the pandemic: We originally planned to be married in October 2020, but then rescheduled for October 2021. Back then, we naively thought that the pandemic would be under control by now and we could have a wedding without COVID testing and masks. As it turns out, all we really accomplished was having a wedding where everyone is vaccinated—and the venue still required testing and masks. Still, it should at least be safer than it was last year, because everyone is vaccinated.

Since marriage is on my mind, I thought I would at least say a few things about the behavioral economics of marriage.

Now when I say the “economics of marriage” you likely have in mind things like tax laws that advantage (or disadvantage) marriage at different incomes, or the efficiency gains from living together that allow you to save money relative to each having your own place. That isn’t what I’m interested in.

What I want to talk about today is something a bit less economic, but more directly about marriage: the matching process by which one finds a spouse.

Economists would refer to marriage as a matching market. Unlike a conventional market where you can buy and sell arbitrary quantities, marriage is (usually; polygamy notwithstanding) a one-to-one arrangement. And unlike even the job market (which is also a one-to-one matching market), marriage usually doesn’t involve direct monetary payments (though in cultures with dowries it arguably does).

The usual model of a matching market has two separate pools: Employers and employees, for example. Typical heteronormative analyses of marriage have done likewise, separating men and women into different pools. But it turns out that sometimes men marry men and women marry women.

So what happens to our matching theory if we allow the pools to overlap?

I think the most sensible way to do it, actually, is to have only one pool: people who want to get married. Then, the way we capture the fact that most—but not all—men only want to marry women, and most—but not all—women only want to marry men is through the utililty function: Heterosexuals are simply those for whom a same-sex match would have very low utility. This would actually mean modeling marriage as a form of the stable roommates problem. (Oh my god, they were roommates!)

The stable roommates problem actually turns out to be harder than the conventional (heteronormative) stable marriage problem; in fact, while the hetero marriage problem (as I’ll henceforth call it) guarantees at least one stable matching for any preference ordering, the queer marriage problem can fail to have any stable solutions. While the hetero marriage problem ensures that everyone will eventually be matched to someone (if the number of men is equal to the number of women), sadly, the queer marriage problem can result in some people being forever rejected and forever alone. (There. Now you can blame the gays for ruining something: We ruined marriage matching.)

The queer marriage problem is actually more general than the hetero marriage problem: The hetero marriage problem is just the queer marriage problem with a particular utility function that assigns everyone strictly gendered preferences.

The best known algorithm for the queer marriage problem is an extension of the standard Gale-Shapley algorithm for the hetero marriage problem, with the same O(n^2) complexity in theory but a considerably more complicated implementation in practice. Honestly, while I can clearly grok the standard algorithm well enough to explain it to someone, I’m not sure I completely follow this one.

Then again, maybe preference orderings aren’t such a great approach after all. There has been a movement in economics toward what is called ordinal utility, where we speak only of preference orderings: You can like A more than B, but there’s no way to say how much more. But I for one am much more inclined toward cardinal utility, where differences have magnitudes: I like Coke more than Pepsi, and I like getting massaged more than being stabbed—and the difference between Coke and Pepsi is a lot smaller than the difference between getting massaged and being stabbed. (Many economists make much of the notion that even cardinal utility is “equivalent up to an affine transformation”, but I’ve got some news for you: So are temperature and time. All you are really doing by making an “affine transformation” is assigning a starting point and a unit of measurement. Temperature has a sensible absolute zero to use as a starting point, you say? Well, so does utility—not existing. )

With cardinal utility, I can offer you a very simple naive algorithm for finding an optimal match: Just try out every possible set of matchings and pick the one that has the highest total utility.

There are up to n!/((n/2)! 2^n) possible matchings to check, so this could take a long time—but it should work. I’m sure there’s a more efficient algorithm out there, but I don’t have the mental energy to figure it out at the moment. It might still be NP-hard, but I doubt it’s that hard.

Moreover, even once we find a utility-maximizing matching, that doesn’t guarantee a stable matching: Some people might still prefer to change even if it would end up reducing total utility.

Here’s a simple set of preferences for which that becomes an issue. In this table, the row is the person making the evaluation, and the columns are how much utility they assign to a match with each person. The total utility of a match is just the sum of utility from the two partners. The utility of “matching with yourself” is the utility of not being matched at all.


ABCD
A0321
B2031
C3201
D3210

Since everyone prefers every other person to not being matched at all (likely not true in real life!), the optimal matchings will always match everyone with someone. Thus, there are actually only 3 matchings to compare:

AB, CD: (3+2)+(1+1) = 7

AC, BD: (2+3)+(1+2) = 8

AD, BC: (1+3)+(3+2) = 9

The optimal matching, in utilitarian terms, is to match A with D and B with C. This yields total utility of 9.

But that’s not stable, because A prefers C over D, and C prefers A over B. So A and C would choose to pair up instead.

In fact, this set of preferences yields no stable matching at all. For anyone who is partnered with D, another member will rate them highest, and D’s partner will prefer that person over D (because D is everyone’s last choice).

There is always a nonempty set of utility-maximizing matchings. (There must be at least one, and could in principle have as many as there are possible matchings.) This actually just follows from the well-ordering property of the real numbers: Any finite set of reals has a maximum.

As this counterexample shows, there isn’t always a stable matching.

So here are a couple of interesting theoretical questions that this gives rise to:
1. If there is a stable matching, must it be in the set of utility-maximizing matchings?

2. If there is a stable matching, must all utility-maximizing matchings be stable?

Question 1 asks whether being stable implies being utility-maximizing.
Question 2 asks whether being utility-maximizing implies being stable—conditional on there being at least one stable possibility.

So, what is the answer to these questions? I don’t know! I’m actually not sure anyone does! We may have stumbled onto cutting-edge research!

I found a paper showing that these properties do not hold when you are doing the hetero marriage problem and you use multiplicative utility for matchings, but this is the queer marriage problem, and moreover I think multiplicative utility is the wrong approach. It doesn’t make sense to me to say that a marriage where one person is extremely happy and the other is indifferent to leaving is equivalent to a marriage where both partners are indifferent to leaving, but that’s what you’d get if you multiply 1*0 = 0. And if you allow negative utility from matchings (i.e. some people would prefer to remain single than to be in a particular match—which seems sensible enough, right?), since -1*-1 = 1, multiplicative utility yields the incredibly perverse result that two people who despise each other constitute a great match. Additive utility solves both problems: 1+0 = 1 and -1+-1 = -2, so, as we would hope, like + indifferent = like, and hate + hate = even more hate.

There is something to be said for the idea that two people who kind of like each other is better than one person ecstatic and the other miserable, but (1) that’s actually debatable, isn’t it? And (2) I think that would be better captured by somehow penalizing inequality in matches, not by using multiplicative utility.

Of course, I haven’t done a really thorough literature search, so other papers may exist. Nor have I spent a lot of time just trying to puzzle through this problem myself. Perhaps I should; this is sort of my job, after all. But even if I had the spare energy to invest heavily in research at the moment (which I sadly do not), I’ve been warned many times that pure theory papers are hard to publish, and I have enough trouble getting published as it is… so perhaps not.

My intuition is telling me that 2 is probably true but 1 is probably false. That is, I would guess that the set of stable matchings, when it’s not empty, is actually larger than the set of utility-maximizing matchings.

I think where I’m getting that intuition is from the properties of Pareto-efficient allocations: Any utility-maximizing allocation is necessarily Pareto-efficient, but many Pareto-efficient allocations are not utility-maximizing. A stable matching is sort of a strengthening of the notion of a Pareto-efficient allocation (though the problem of finding a Pareto-efficient matching for the general queer marriage problem has been solved).

But it is interesting to note that while a Pareto-efficient allocation must exist (typically there are many, but there must be at least one, because it’s impossible to have a cycle of Pareto improvements as long as preferences are transitive), it’s entirely possible to have no stable matchings at all.

Against “doing your best”

Oct 3 JDN 2459491

It’s an appealing sentiment: Since we all have different skill levels, rather than be held to some constant standard which may be easy for some but hard for others, we should each do our best. This will ensure that we achieve the best possible outcome.

Yet it turns out that this advice is not so easy to follow: What is “your best”?

Is your best the theoretical ideal of what your performance could be if all obstacles were removed and you worked at your greatest possible potential? Then no one in history has ever done their best, and when people get close, they usually end up winning Nobel Prizes.

Is your best the performance you could attain if you pushed yourself to your limit, ignored all pain and fatigue, and forced yourself to work at maximum effort until you literally can’t anymore? Then doing your best doesn’t sound like such a great thing anymore—and you’re certainly not going to be able to do it all the time.

Is your best the performance you would attain by continuing to work at your usual level of effort? Then how is that “your best”? Is it the best you could attain if you work at a level of effort that is considered standard or normative? Is it the best you could do under some constraint limiting the amount of pain or fatigue you are willing to bear? If so, what constraint?

How does “your best” change under different circumstances? Does it become less demanding when you are sick, or when you have a migraine? What if you’re depressed? What if you’re simply not feeling motivated? What if you can’t tell whether this demotivation is a special circumstance, a depression system, a random fluctuation, or a failure to motivate yourself?

There’s another problem: Sometimes you really aren’t good at something.

A certain fraction of performance in most tasks is attributable to something we might call “innate talent”; be it truly genetic or fixed by your early environment, it nevertheless is something that as an adult you are basically powerless to change. Yes, you could always train and practice more, and your performance would thereby improve. But it can only improve so much; you are constrained by your innate talent or lack thereof. No amount of training effort will ever allow me to reach the basketball performance of Michael Jordan, the painting skill of Leonardo Da Vinci, or the mathematical insight of Leonhard Euler. (Of the three, only the third is even visible from my current horizon. As someone with considerable talent and training in mathematics, I can at least imagine what it would be like to be as good as Euler—though I surely never will be. I can do most of the mathematical methods that Euler was famous for; but could I have invented them?)

In fact it’s worse than this; there are levels of performance that would be theoretically possible for someone of your level of talent, yet would be so costly to obtain as to be clearly not worth it. Maybe, after all, there is some way I could become as good a mathematician as Euler—but if it would require me to work 16-hour days doing nothing but studying mathematics for the rest of my life, I am quite unwilling to do so.

With this in mind, what would it mean for me to “do my best” in mathematics? To commit those 16-hour days for the next 30 years and win my Fields Medal—if it doesn’t kill me first? If that’s not what we mean by “my best”, then what do we mean, after all?

Perhaps we should simply abandon the concept, and ask instead what successful people actually do.

This will of course depend on what they were successful at; the behavior of basketball superstars is considerably different from the behavior of Nobel Laureate physicists, which is in turn considerably different from the behavior of billionaire CEOs. But in theory we could each decide for ourselves which kind of success we actually would desire to emulate.

Another pitfall to avoid is looking only at superstars and not comparing them with a suitable control group. Every Nobel Laureate physicist eats food and breathes oxygen, but eating food and breathing oxygen will not automatically give you good odds of winning a Nobel (though I guess your odds are in fact a lot better relative to not doing them!). It is likely that many of the things we observe successful people doing—even less trivial things, like working hard and taking big risks—are in fact the sort of thing that a great many people do with far less success.

Upon making such a comparison, one of the first things that we would notice is that the vast majority of highly-successful people were born with a great deal of privilege. Most of them were born rich or at least upper-middle-class; nearly all of them were born healthy without major disabilities. Yes, there are exceptions to any particular form of privilege, and even particularly exceptional individuals who attained superstar status with more headwinds than tailwinds; but the overwhelming pattern is that people who get home runs in life tend to be people who started the game on third base.

But setting that aside, or recalibrating one’s expectations to try to attain a level of success often achieved by people with roughly the same level of privilege as oneself, we must ask: How often? Should you aspire to the median? The top 20%? The top 10%? The top 1%? And what is your proper comparison group? Should I be comparing against Americans, White male Americans, economists, queer economists, people with depression and chronic migraines, or White/Native American male queer economists with depression and chronic migraines who are American expatriates in Scotland? Make the criteria too narrow, and there won’t be many left in your sample. Make them instead too broad, and you’ll include people with very different circumstances who may not be a fair comparison. Perhaps some sort of weighted average of different groups could work—but with what weighting?

Or maybe it’s right to compare against a very broad group, since this is what ultimately decides our life prospects. What it would take to write the best novel you (or someone “like you” in whatever sense that means) can write may not be the relevant question: What you really needed to know was how likely it is that you could make a living as a novelist.


The depressing truth in such a broad comparison is that you may in fact find yourself faced with so many obstacles that there is no realistic path toward the level of success you were hoping for. If you are reading this, I doubt matters are so dire for you that you’re at serious risk of being homeless and starving—but there definitely are people in this world, millions of people, for whom that is not simply a risk but very likely the best they can hope for.

The question I think we are really trying to ask is this: What is the right standard to hold ourselves against?

Unfortunately, I don’t have a clear answer to this question. I have always been an extremely ambitious individual, and I have inclined toward comparisons with the whole world, or with the superstars of my own fields. It is perhaps not surprising, then, that I have consistently failed to live up to my own expectations for my own achievement—even as I surpass what many others expected for me, and have long-since left behind what most people expect for themselves and each other.

I would thus not exactly recommend my own standards. Yet I also can’t quite bear to abandon them, out of a deep-seated fear that it is only by holding myself to the patently unreasonable standard of trying to be the next Einstein or Schrodinger or Keynes or Nash that I have even managed what meager achievements I have made thus far.

Of course this could be entirely wrong: Perhaps I’d have achieved just as much if I held myself to a lower standard—or I could even have achieved more, by avoiding the pain and stress of continually failing to achieve such unattainable heights. But I also can’t rule out the possibility that it is true. I have no control group.

In general, what I think I want to say is this: Don’t try to do your best. You have no idea what your best is. Instead, try to find the highest standard you can consistently meet.