There Is No Good Way to Measure “Power”

The Tragedy of Political Science revisited.

Long before Married with Children and the Boomerific “hate my wife” humor of post-Vietnam America, there was Henny Youngman. Best known for his one-liners — “Take my wife… please!” — Youngman is also the inspiration for a cult-famous joke about economists.¹ It goes like this:

Q: “How’s your wife?”

A: “Compared to what?”

The joke gets at the concept of opportunity cost. It subverts expectations because the economist answering the question interprets it as referring to the net value he derives from having a wife, rather than the wife’s subjective affect. To answer the question, he needs to know what he’s giving up by having a wife (or at least, what he’s giving up by having that specific wife).

I feel a bit like the economist in the joke whenever I hear somebody say country X is more powerful than country Y, or make a sweeping claim about the relationship between X and Y based on their relative military budgets or the size of their economies. “The United States is more powerful than China.” Really? Power to do what?

Power as a concept is only useful if you know what it’s supposed to indicate. The most intuitive sense in which a state has power over another is that it’s able to coerce or induce the lesser state into doing things it otherwise wouldn’t. But coercion and inducement are multifaceted. There are many things the United States can get China to do that it otherwise wouldn’t want to do, and there are many things China can get the United States to do as well. If there was a single neat variable that described the distribution of power between the United States and China that applied across every domain of the relationship, you’d expect one country to be strictly dominant over the other. But that’s obviously not the case!

So we know that power in the real world is domain specific. The United States and China are not just powerful — they’re powerful relative to each other in specific capacities and situations, and power in these capacities and situations has different proxies. If the United States attacked China with nuclear weapons tomorrow, there’s a 38% chance China would be able to launch a second strike. China has 274 diplomatic posts around the world and the United States has 271. The United States has a virtual monopoly on many advanced military technologies. Chinese researchers publish more top 1% cited papers than American researchers in many fields. And so on.

You can see how sifting through all this information would be impractical if you had to make a judgment about the relationship between the United States and China that cut across multiple issue domains. You probably wouldn’t have time to weigh countless quantitative and qualitative variables against each other or read a 1,000-page study by the RAND Corporation. What you’d ideally want is a way to measure how much a state can coerce and induce another state — let’s call this “preference fulfillment” — and a single observable variable that predicts how well the state’s preferences are going to be fulfilled. But that’s not the type of thing that can be easily quantified and aggregated across issue domains.

Even if you found a way to express a state’s material — economic and military — power in a single cogent variable, there would still be lots of different types of power that operate more subtly. Joseph Nye conceives of soft power, which functions on culture and values. John Ikenberry and Charles Kupchan suggest that states often exercise power by socializing other states into adopting their values and interests. More critical theorists have conceptualized power as “the production, in and through social relations, of effects on actors that shape their capacity to control their fate,” meaning that power can be exercised either directly or indirectly through formal or informal institutions, and can even structure the way states conceive of themselves and their interests.

(Again, not something that can be easily quantified or aggregated.)

Barnett and Duvall, “Power in International Politics.”

So you have to decide: What level of precision is best? Pick two: concision, accuracy, and explanatory breadth.

• You can have a concise measure of power that’s really accurate, but it’s only going to explain preference fulfillment in some very specific domain.

• You can have a measure of power that applies across a lot of domains and is concise, but it’s going to commit a lot of errors.

• You can have a measure of power that explains a lot of things and gets most of them right, but it’s just going to be a description of the world and won’t teach us much that we can’t learn through (very time-consuming) direct observation.

Thus goes The Tragedy of Political Science!

The most common proxies for power in the political science literature are all concise. Some are less accurate and more broad than others, or more accurate and less broad, or even less accurate and less broad if you’re dealing with a strictly inferior proxy. GDP measures a state’s economic output and is used to estimate both economic and military power. CINC, the Composite Index of National Capability, takes into account a state’s population, level of urbanization, industrial capacity, and military might and turns it into a single data point per country-year to estimate the country’s ability to wage war. Michael Beckley’s “net resources” measure multiplies a state’s GDP by its GDP per capita to factor out resources that don’t get invested in warfighting because they’re used to provide for people’s basic needs.

Beckley finds that out of 54 wars and 276 militarized interstate disputes (MIDs) between 1816 and 2010, GDP accurately predicts the winner 68% and 64% of the time, respectively. CINC has an accuracy of 70% and 64%, and GDP times GDP per capita has an accuracy of 78% and 70%. In other words, the measures that seek to explain a smaller range of outcomes explain those outcomes better — especially Beckley’s measure, which was designed specifically to explain war and MID outcomes.

Beckley, “The Power of Nations: Measuring What Matters.”

Still, you might think it’s possible this Beckley fellow has stumbled across a way to have it all. If you want to exercise power, you need to survive. And if you want to survive, you need to win wars. So all power in the international system must be downstream of military power, which is downstream of net resources. The trilemma isn’t a problem because reality actually isn’t more complicated than theory!

But even if you just have military power in mind, Beckley’s numbers ought to strike you as highly suspect. Below is a spreadsheet calculating each country’s share of world power since 1990 according to Beckley’s measure, based on World Bank data.

Beckley Scores All States Since 1990

414KB ∙ XLSX file

Download

Download

And here it is in graph form:

The headline conclusion: The United States is just as militarily powerful today as it was at the end of the Cold War, both relative to the world and relative to its next most powerful competitor.

You don’t have to think the sky is falling on the Pax Americana (a view I’ve written against before) to know that this is false.² Even Marco Rubio is admitting the United States doesn’t have the coercive capacity it did 35 years ago.

So net resources doesn’t tell you how much more powerful a state’s military is compared to another, much less how much more powerful a state is in the aggregate compared to other states. It might tell you who’s going to win a war — at least, it has a good chance of telling you who’s going to win a war under analogous conditions to the wars it predicted between 1816 and 2010 — but that’s not the only input to state power. There are diminishing returns to warfighting, and even relatively weak states like South Korea can have outsized influence in other domains that aren’t easily accommodated into a single measure of national power. In 2024, according to the International Monetary Fund’s Global Soft Power Index, South Korea actually exerted more cultural influence around the world than any other country, even though Beckley says it’s just one-fourteenth as powerful as the United States and less than one-fifth as powerful as China.

Or, to put it in other terms:

Q: “How’s your army?”

A: “Compared to what?”

1. The “cult” here is libertarian economist Walter Block, who’s used the joke in almost any context you can imagine.

2. Actually, I do fear the Pax Americana is coming to an end, but that’s the result of policy choices made by the United States, not changes in the international environment.