October 29, 2018

The Concept and Theory of Power

Power is the ability to accomplish useful goals at affordable cost, especially against the determined will of others. More power can accomplish larger goals against more opposition.

We have to holistically account for ends: We generally have the power to commit crimes, but not the power to get away with it. Must look at entire goal state and all relevant effects of reachable outcomes. Must look at cost the same way. We roll all effects together into one notion:

Speaking precisely, the power of an actor is the set of outcome states available to that actor for planning choice. More power means more and better available states.

Sets of outcome states, and thus power, are partially ordered, not scalar. One power state may subsume and be superior to another, or they may overlap to varying degrees.

An important implication of this is that some things not traditionally discussed as power, because not very general-purpose, are in fact power. For example, let’s say you have some idea or technology which will catch on and change the world. Maybe aliens dropped it in your lap. Then you can choose to release or not release the tech. You have large power of a sort.

This sort of power is limited in that you have limited discrimination of optimization. You have effectively one bit of optimization power, in that you can choose between two possible worlds, whose contents are otherwise not controlled by you. Controlled effect can be large, but intuitive power is low.

Unless you do something to convert your large-effect, low optionality power into smaller-effect, large-optionality power. For example, you sell the alien tech to a large company, now you have lots of liquid capital and perhaps much else. Something like this.

Thus there is a way in which power is partially fungible and convertible, depending on the market. This is one dimension of how power is intuitively scalar, despite being fundamentally high-dimensional.

Another related thing is that if you control some large power, for example the power to create better technology, perhaps by asking the aliens for tips, you may have high discrimination capacity, in that you can design possible worlds with many kilobits of discrimination, but your power is still limited to one dimension. There are possible worlds not reachable by you, because you can’t touch those dimensions.

In a narrow-dimension power situation, you can ally with other holders of other types of power, to make trades. By combining power dimensions, you gain much more holistic power. Because of this “covering each other’s blind spots” alliance trade dynamic, power again looks more scalar than it actually is.

Another dimension of scalarization is that many components of power, like money and intelligence, are inherently highly flexible, and can be applied to most or all dimensions of influence. Higher intelligence in particular will tend to make the other mechanisms of scalarization, trading and allying, much stronger. If you are smarter, you can find trades and make alliances that a dumber agent could not.

Thus power tends to become scalarized, in that power varies mostly along one dimension, despite being fundamentally very high-dimensional.

Something important missed in the pure “high-dimensional reachable state set inclusion” formalism is that in planning, possible states must be compared on a scalar basis. Since power is very closely related to reachable states and difficulty of accomplishing goals, it will also be very closely related to this scalar planning hueristic. Roughly “how good is this power state for my goals or larger strategy?”.

The planning scalar is another way that power ends up scalarized, but this is a very different thing from the empirical scalarization. In particular, the planning scalar power dimension could in principle be quite orthogonal to the empirical scalarizaton.

That said, in practice, for sovereign agents, those which are not embedded and specialized within a larger power system that solves most of their goals for them, the planning heuristic scalar and the empirical power scalar will be inherently very closely related. That is, for agents playing the sovereignty game, power is very centrally useful, becoming a large component of the planning heuristic.

Further, the kind of power an agent or society of agents will build will tend to be that which they need to accomplish their goals. Thus the overall direction of the empirical power scalar will be close to the planning heuristic for those goal systems.

Thus we intuitively tend to treat power as a scalar, despite the high-dimensional reality: it tends to scalarize for a number of reasons.

Another thing missed is time. Power has a temporal dimension, and changes over time depending on strategy, in a way that isn’t accounted here. We’ll look into this later.

Another thing we have not accounted for is first person versus third person power. An agent may believe they have the skills and a plan that enables them to have a large, detailed, and wide-ranging effect, that is to become powerful, but this may not be apparent to other agents. It also may not be true; they may be mistaken. This means large differences in apparent power depending on perspective, and possibly some definitional difficulties.

Conceptually, it is useful to distinguish between extrinsic and intrinsic power. Extrinsic power, the set of reachable states, is reduced with the presence of opposition. Intrinsic power is not. Intuition generally follows the intrinsic meaning.

Let’s decompose intrinsic power into its components, and account for how they combine to produce total power:

  • Position: the current state of the game board, including fortified position, resources, tools, etc. The components of world-state that is different for your first-person perspective than from some other agent.

  • Knowledge: the breadth, depth, and accuracy of your map of the world, and what will happen under what conditions.

  • Active Skill: action sequences and known state-transition subpaths. The more and better skills you have, the better the individual steps in your plans.

  • Cognitive Skill: techniques that improve the planning and theorizing process to enable you to come to better plans with fewer cognitive resources.

  • Intellect: the ability to search over conceptualizations and action-sequences, in terms of raw speed and breadth of thought.

  • Will: how much you care about the problem, how focused and ordered your mind is in directing your attention to accomplishing this end.

At some point, we should define these with formal logic, code, math, or otherwise make them more conceptually crisp, such that we can prove that they account totally for power. That is, define them crisply enough that we can typecheck that the combination of these things works and produces a set of reachable states. For now this intuitive definition is fine.

This accounts for intrinsic power. Extrinsic power would also include the shared third-person world-state, other agents, and their intrinsic power. These things will also have to be rigorously accounted for at some point.

After a point, extrinsic power is zero-sum, and relative, between competing goal systems. It is always zero-sum and relative if you count the natural default as an agent that other agents can have more or less power against.

Intrinsic power is absolute, non-relative; you could imagine a world with agents of uniformly very large power, or very small. These are importantly distinct.

This gives us a working theory of power which is candidate for formalization into a very crisp calculus of power, as part of the larger project of a crisp calculus of statecraft.

Edited and curated by Wolf Tivy

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