Power is conventionally thought of as a quantity. The more you have, the more you can do. While not inaccurate, it is a partial view that misses the essential dynamics of agency.

Strategic State Space

The way I conceptualize power has to do with this idea which I’m borrowing from the field of artificial intelligence. The “state space approach” is a strategy for solving complex problems. You encode the state of your game or problem and define vectors by which the state can change. Applying a change to the current state results in a new state. Doing this repeatedly results in a network of connected states also referred to as a state space. If you hypothetically explored all the possible permutations of vectors of change you would have spanned the entire space of possible states. Often this is computationally infeasible due to combinatorial explosion.

A common form of state space is a decision tree. This is the kind of structure used by chess engines to look at different possible future states of the game. A state space is more general in that the connections between states need not necessarily be decisions, players don’t necessarily take turns, and connections don’t even need to be deterministic. The state may change probabilisitically based on an environmental factor for instance.

The solution to your problem is a path from the current or initial state to a desired state which we call the goal. Finding that path is a matter of executing a search algorithm. This approach is not guaranteed to work as there may very well not be a solution or the search space may simply be too large. So you have to be clever. Finding constraints on the way things can change or a simpler encoding of the states can help keep the problem manageable.

In chess, the goal is checkmate against your opponent and a winning strategy comes from searching the decision tree with good heuristic board evaluations. A more sophisticated game involving multiple agents or environmental changes may involve tracking many such “action sequences” and hedging your bets.

In general we can think of an agent as having a goal which corresponds to a set of desirable states. This set of goal states in turn implies a set of viable paths through the state-space from any given state. This set may be empty if there are no viable paths. As a general observation, desirable states tend to cluster or be in proximity to each other in the state space. We can therefore think of the agent as having a corresponding bundle of viable paths toward its goal, each branching off of the current state and eventually terminating in a desirable state. A different agent, or the same agent in a different initial state will have a different path bundle toward its goal.

Conventional Power

The conventional understanding of power corresponds to an agent’s choices having a significant impact on the individual state space of many other agents. Either in a way that helps them along their way toward their goals or in a way that impedes them. Both are considered powerful. But this concept of power focuses too much on impact. What this view doesn’t consider is how narrowly constrained this sort of power really is. It may seem like certain offices or roles wield a lot of power, and that they therefore would be advantageous positions to be in. But more often than not such positions and roles are forced along tram lines by game theory and non-trivial forces. It’s like having the keys to a supercar. But you don’t get to steer or let off the gas.

Power in State Space

When we see that choices and events link states into an elaborate network, we get a richer picture of what power really means.

Goal Locked Power

In this conceptualization of power, the agent has a given goal and the degree of power is defined in relation to the given goal. The simplest measure of power in this category is proximity to the goal in state space. This idea can be augmented in a state space that isn’t entirely dependent on the agent’s choices or has probabilistic vectors of change. For instance we can think of states which have a higher likelihood of taking us to the goal successfully given the robustness of the path bundle. In this way robustness of a given state works as a measure of power. Evidently the robustness of a state will be a function of the robustness of the downstream states which are requisite to obtaining the goal. Note that this kind of power is entirely contingent on the a priori goal.

General Rules for Agents

This notion of robustness gives rise to some general rules for agents interested in attaining a goal no matter what it may be.

Consider the relative width of your bundle for instance. States with narrow downstream bundles are less secure because there are fewer contingencies in the event that you get knocked off your path. With a narrow bundle, the agent’s next moves are “forced”. In this condition the agent is also more predictable. A wide bundle gives you alternative routes to your goal.

It also makes sense to minimize the influence of external factors on your state. You should choose states where the outgoing vectors of change have more to do with your choices as an agent rather than the actions of other agents or environmental factors.

“Thus the expert in battle moves the enemy, and is not moved by him.”

— Sun Tzu, The Art of War

Convergence of Paths

One observation that can be made if we allow the goal of the agent to vary is that some states tend to be part of viable strategies for many different goals. These states can be thought of as convergent instrumental goals. These are goals which agents will tend to pursue as a stepping stone regardless of their terminal goal. For instance acquisition of money is a convergent instrumental goal for most people because regardless of what your terminal goal is, money is likely to help you get there. True knowledge of the world is also a convergent instrumental goal. As is self-preservation. Generally, you are more likely to achieve your goal if you’re alive rather than dead.

Topological Power

These converging paths give rise to another definition of power. The idea here is that something can be powerful because of the variety of different goals it can serve.

The simplest approach here might be to consider the local connectedness of a state. So basically the more options you have in a given state, the more powerful you are. This set of options is however agnostic to the particular goal of the agent. It is simply a function of capabilities. Again, the concept can be broadened. Just as how in goal-locked power we can construct a concept of robustness, in goal-agnostic power we can construct a concept of centrality in the state space.

The more central your state, the easier it is to move toward a broader set of goals. You would have to come up with estimator metrics as it’s unlikely you’ll be able to calculate the centrality of a particular node based on the topology of the entire state space. Nevertheless, the idea here is that the more central the node is with respect to arbitrary goals, which is to say arbitrary nodes, the more powerful it is. We can improve the metric by ignoring unworthy goals which is of course a metric bias, but it might be more efficient to calculate and even serve our purposes better.

Notice that a form of this topological power is already built into robustness. If you break your single goal down into a set of sub-goals you suddenly have a multi-goal scenario. States that score high in centrality with respect to sub-goals are also high in robustness. This is much like how topologically powerful states have centrality to arbitrary terminal goals. We can think of robustness as equivalent to topological power in a reformulated state space which only encodes bundle states.

Truth and Goals

As you might have inferred from the analogy above, topological power is never really goal-agnostic. A particular state space will only ever allow for goals which are captured by its state encoding. Other goals may exist which are not accounted for in the formulation of the state space.

Choosing how to encode states is generally done in such a way that the a priori goal of the agent can be captured. If it couldn’t be captured, there wouldn’t be much point in setting up the state space in the first place. The state space formulation is a critical step in any goal oriented game. Some formulations will be perfectly contained within others. For example the state space of the soccer game is entirely contained within the soccer tournament. Other formulations will have states that partially overlap. Other ones still will miss each other completely as they seek to tackle entirely unrelated problems. In other cases states encoded by one method will have an ambiguous mapping to states encoded by a second formulation.

As a meta-strategy for tackling the current problem it might make sense to simplify the state space to form a heuristic. Or perhaps if you run out of options, you might try adding detail or complexity to the state space formulation to see if there’s a hidden path you may have missed with the previous encoding.

This all seams awfully topsy-turvy. It’s almost like truth is entirely subjective. The astoundingly good news however is that for any two agents, if we assume they exist in the same physical reality, there is a state space encoding which will capture both their machinations and objectives. However that shared state space is not guaranteed to be something either of the agents can act on. It may not include any vectors of change that correspond to actions by the agents. And that’s to say nothing of computability. If I’m calculating real time quantum states to fight off a viral infection in my body, I might be stuck strategizing at the wrong level to be effective. Alternatively, there may very well be some fluke butterfly-effect-type causal chain that removes the virus and cures me. But since I have to rely on pure luck with infinitesimal odds, it’s not really a viable strategy for me as an agent.

I believe this intricate dance of epistemology and meta-strategy is characteristic of the existential human condition. There is likely much to be said about how epistemology relates to values, action, power, and transformation.

Multiplayer State Space

There are perhaps two ways of considering multiplayer scenarios. If the agents are highly symmetric. This is to say that they effectively see the same state space from their respective points of view, we can use a single state space and see how the agents move within it individually. For the non-symmetric cases, we must consider a state space that uses both agent’s move sets as vectors for change. In many cases it likely makes sense to consider a combination of the two. Wherever possible we should use symmetry to reduce the complexity of the state space.

Let’s consider a non-simplified multiplayer state space.

In collaborative scenarios, the agent’s bundles run together and attain improved robustness, either because of better connections or wider bundles. Antagonism occurs when one agent improves their bundle robustness at the expense of another agent’s robustness. You either narrow your enemy’s course of action or otherwise decrease their chances of success to gain an advantage. Note that these are soft concepts. An agent may judge the risk associated with temporary narrowing to be worth it for the robustness they’ll gain later on. Antagonism and collaboration are therefore not always simple to distinguish.

Bottlenecks

A bottleneck is a mechanism which an agent can use to cause significant bundle narrowing for a large number of other agents. This increased predictability can be leveraged to secure the wielder’s bundle. The most advantageous bottlenecks allow the wielder to even decide between more than one direction of narrowing. This allows the wielder to piggy-back on the agency of the affected parties. They become instruments of the wielder’s purposes. This is the sort of thing that aligns with much of what is conventionally understood to be powerful.

“Who controls the food supply controls the people; who controls the energy can control whole continents; who controls money can control the world.”

— Henry A. Kissinger

Notice that bottlenecks have nothing to do with the narrowness or width of the wielder’s bundle. Again, bottlenecks may have a large impact as vectors of change in state space, but they are often heavily constrained by the game theory of self-preservation. They may provide determinism and robustness for certain kinds of goals, but they’re basically always low in topological power in them of themselves. Knowing what bottlenecks will do ahead of time is of course an advantage and perhaps the true power wielded by the high and mighty. You gain initiative, save on hedges, and can maximize payoffs for whatever your ends may be.

On Politics

Dictatorship and its relation to economy is bad for the same reason monopoly and its influence on politics is bad and also why fascism is essentially indistinguishable from both. Private versus public power is not the critical distinction. It’s whether or not a bottleneck is impeding people’s bundles toward what they see as ultimate value.

I think the state space approach also captures the concept of “systemic oppression” because it doesn’t require bad actors or motivated parties for someone’s bundle to be incidentally impeded.

The principle of secularity holds that church and state should be separate. Regardless of your views on religion, the general principle is worth incorporating here. (See my article on secularity.) That which mediates ultimate purpose must not be impinged upon by sovereign power. In terms of the strategic state space, respecting this principle is about valuing path bundles wherever they may lead. Political action ought not be justified in terms of particular ends, but rather only in terms of minimizing cohersion and maximizing collaboration to strengthen and broaden path bundles. In this way we may seek to maximize the synergy of society accounting for the variety of terminal goals among its constituents.

Of course determining which path bundles are affected how by what policy can be difficult in practice. How many people even really know where their personal convictions lie? And that’s to say nothing of cases where you have to prioritize or otherwise weigh changes to people’s robustness against eachother. Nevertheless, the shape of power is why I see secularity as the central principle of liberal politics and the justification for all rights and freedoms. Liberty is not for doing what we want, but to empower us to do what we must.

“Edward Moran 1886, Unveiling the Statue of Liberty”

Edward Moran 1886, Unveiling the Statue of Liberty

Inspiration for this Article

P.S.

I found an article from 2019 that features a similar intuition about linking state-space to power. It’s more AI-oriented whereas my article takes a more philosophical angle.