We begin with three stories about three people.

First, Zhu Di, emperor of China from 1402 to 1424. In that period, it was traditional for foreign envoys to present gifts to the emperor and make a show of submission, reinforcing the emperor’s authority and China’s image as the center of civilization. Yet the emperor would send the envoys off with gifts in return, often worth more than the gifts the envoy had given - suggesting that the emperor’s authority and dominance did not actually translate into much bargaining power.

Second, Kevin Systrom, one of the founders of Instagram. When Instagram was bought by Facebook for $1B in 2012, it had only 13 employees. Systrom presumably found himself with a great deal of money, the most direct form of bargaining power amongst humans. Yet with only 13 employees, he commanded little of the obedience or authority displayed by an emperor.

Third, Benjamin Jesty. In 1774, a wave of smallpox raged through England, and dairy farmer Jesty was concerned for his wife and children. He knew that milkmaids sometimes contracted cowpox from cows, and that the (much milder) disease would immunize them for life against smallpox. So, he intentionally infected his wife and children with cowpox, 20 years before Edward Jenner popularized the same technique as the first vaccine. That same year, Louis XV, king of France, died of smallpox. Despite both great authority and great wealth, Louis XV had no power to stop smallpox.

These people demonstrate three quite different kinds of “power”.

Emperor of China: Dominance

The emperor of China has power in the form of dominance. In any competition of dominance within the vast Chinese empire, the emperor was the presumed winner. In some sense, the central function of an “emperor” is to create one giant dominance hierarchy over all the people in some territory, and then sit at the top of that dominance hierarchy.

(Much the same could be said of a “king” or “president”.)

Humans have a strong built-in instinct for dominance, as do many other animals. The ontology of a “dominance ranking” is justified experimentally, by the observation that various animals (including humans) form a consistent order of aggression/backing down - i.e. if Bob backs down in the face of Alice’s aggression, and Carol backs down in the face of Bob’s aggression, then empirically Carol will also back down in the face of Alice’s aggression. A > B and B > C (with “>” indicating dominance) empirically implies A > C.

I would guess that most humans intuitively see dominance as the main form of power, because of that built-in instinct. And humans seem to want dominance/submission as roughly-terminal goals. However, though dominance is hard-coded, it seems like something of a simple evolved hack to avoid costly fights among relatively low-cognitive-capability agents; it does not seem like the sort of thing which more capable agents (like e.g. future AI, or even future more-intelligent humans) would rely on very heavily.

One place where this comes up: ask someone to imagine AI “seizing power” or “taking over the world”, and I would guess that most people imagine some kind of display of dominance or creation of a dominance hierarchy. But I would guess that, to such an AI, “power” looks more like the other two categories below.

Instagram Founder: Bargaining Power

The instagram founders have power in the form of bargaining power, i.e. the ability to get others to give you things in trade. In practice, bargaining power mostly means money… and there’s good reason for that.

Bargaining problems are one of those domains where, as the problem gets bigger and has more degrees of freedom, things usually get simpler. With enough players and enough things up for trade, there’s usually some way to net-transfer a little bit of value from any player to any other. And if that’s the case, then (roughly speaking) the whole problem reduces to one dimension: everybody has a one-dimensional budget of bargaining power (which can be thought of in dollars), all the stuff up for trade has a price in bargaining power (which, again, can be thought of in dollars) coming from econ-101-style supply and demand, and players buy stuff with their bargaining power. That’s the ontological justification for a 1-dimensional notion of “bargaining power”, i.e. money.

This kind of “power” seems very natural in any system where many agents trade with each other.

Insofar as the generalized efficient markets hypothesis holds, bargaining power is basically synonymous with one’s ability to obtain any particular thing one wants - after all, under efficient markets, there’s no advantage to doing something oneself rather than outsourcing it, therefore one should be at-worst indifferent between obtaining X oneself vs doing something else to earn money and then spending that money to obtain X from someone else.

Of course, in reality the generalized efficient markets hypothesis is false, so bargaining power is importantly different from the ability to obtain what one wants - which brings us to our last concept of “power”.

Benjamin Jesty: Getting What You Want

Benjamin Jesty had power in the form of actually getting what he wanted - keeping his wife and kids safe from smallpox.

There are two main things to note about this form of power. First, it is distinct from the previous two. Second, unlike the previous two, it is not even approximately a single one-dimensional notion of power.

When and why is the ability to actually get what you want distinct from dominance or bargaining power? Well, in Benjamin Jesty’s case, there was no market for immunization against smallpox because nobody knew how to do it. Or rather, insofar as anyone did know how to do it, most people couldn’t distinguish the real thing from the many fakes, and the real thing was kinda icky and triggered lots of pushback even after Jenner’s famous public demonstration of vaccination. The hard part was to figure out what needed to be done to immunize against smallpox, and that step could not be outsourced because there were too many charlatans and naysayers; Jesty had to have the right knowledge and put together the pieces himself.

In short: not everything can be outsourced. Insofar as the things you want are bottlenecked by non-outsourceable steps, neither dominance nor bargaining power will solve that bottleneck.

That said, insofar as things can be outsourced, bargaining power has a big advantage over raw ability-to-get-what-you-want: bargaining power is fungible. Money can buy all sorts of different things. But ability-to-immunize-against-smallpox cannot easily be turned into e.g. ability-to-reverse-human-aging or ability-to-prove-the-Riemann-Hypothesis or ability-to-solve-AI-alignment. Those are all different difficult-to-outsource problems, the ability to solve one does not turn into ability to solve the others. Those abilities are all different dimensions of “power”; there isn’t a single underlying one-dimensional notion of “power” here.

… though looking at the apparent bottlenecks to these problems, there are some common themes; one could in-principle specialize in problems we don’t understand and thereby gain a generalizable skillset targeted at basically the sorts of problems which are hard to outsource. So arguably, skill-in-problems-we-don't-understand could be a single one-dimensional notion of “power”. And if so, it’s a particularly useful type of power to acquire, since it naturally complements bargaining power.