There are five fundamental definitions that serve as the foundation of quantitative realism.
An agent is an individual actor or a collection of individuals presumed to be acting in concert, in other words, a political unit. An agent can represent any number of real world political entities that are able to amass and utilize power. It could be a country, an institution, a group of people, or an individual person. It could even be a planet, should intergalactic warfare become a concern. China, the Persian Empire, the Egyptian Pharaoh, the British Labour party, a high school principal, a oil company lobbyist, a terrorist cell, and Singapore could all be agents in a power structure. That the definition of agent can be used at so many levels of social magnification goes a long way towards explaining the wide applicability of quantitative realism. Because this wiki focuses on world order, an agent in the models here is likely to be an empire, a nation, or some other large-scale political entity. Sometimes we use the term player as a synonym for agent, particularly when referring to the model as if it were a formal game.
We can expect that the more an agent reflects an aggregation of smaller entities, the more likely it will be to follow the assumptions soon to be delineated below. Conversely, the smaller the agent - at an extreme, a single individual - the more likely it is that other variables external to the model will intervene, causing the agent's behavior to deviate from the simplistic assumptions below. One could analogize this to statistical mechanics, which describes the behavior of gases in the aggregate, ignoring the contribution of individual molecules. Such physical laws are assumed to hold in the limit, meaning that they are more accurate when there are more individual particles in the system being analyzed. We take a similar approach here: the larger the agent, the more likely it is to be described by quantitative realism, such that we would expect the theory to reasonably model empires and countries, but perform worse when describing the behavior of individual people.
We sometimes use the term focal agent to refer to a particular agent who is the focus of our attention in a given situation.
Power is a quantity reflecting an agent's ability to affect the power of other agents. This is a deliberately recursive definition that strikes at the heart of what is obvious about power: those who have it can render others powerless, or conversely, empower them. Power is essentially the capacity to administer rewards and punishments, carrots and sticks. It could be loosely thought of as well-being or capital. It's a broad, deliberately abstract definition, not meant to correspond at all times to a single real-world quantity. In some contexts, it may not necessarily be measurable at all, such as where its means of use are unquantifiable or where there are many of them. Whatever specific form it may take, power must allow for a fungibility between wealth and violence.
One might object to this definition as being circular or reductive, or even meaningless. Before leaping to such a conclusion, it's important to understand the definition in the context of the wider theory. On its own, this definition doesn't give much indication of how power works. Without saying how it works, we can't say what it is. The definition only makes sense as part of the larger axiomatic structure. This is typical of mathematical objects: their meaning is often determined by virtue of their relationships to other objects.
Another objection is that this definition of power is not in line with how power is conceptualized in the social sciences. While the concept is indeed slippery, there is a fairly strong consensus in political science, international relations, sociology, anthropology, and psychology that power essentially has to do with the ability of one agent to compel another to do something it would not otherwise do [CITE]. Glossing over a host of nuances and semantic squabbles, there is not necessarily a conflict between this traditional definition and the one proposed here. The definition here is simply more abstract, encompassing both the means of compulsion, be it carrots or sticks, and the act being compelled. This more abstract definition will allow us to better understand power relations within a network of agents.
An action is an allocation or transfer of power from one agent to another. Actions are what cause other agents' power levels to change. They are essentially the relationships that agents form with each other, and they can be either friendly or antagonistic, to varying degrees.
One agent's action toward the other agents in the system is called a tactic. A tactic is essentially an agent's foreign policy, expressed numerically. A tactic is a list of numbers indicating the agent's actions with respect to the other agents.
The final definition is that of a power structure. This is our primary object of concern. In everyday life, this term refers to a system of relationships in which power and authority are distributed among people or organizations. We use it in exactly the same way, but as an abstraction that can be applied to a variety of real world situations.
Power structures are readily comprehended visually, as graphs. A power structure is composed of agents and their interrelationships. Each agent is represented by one of the nodes in the graph. The larger the node, the more powerful the agent is; conversely, smaller nodes have less power. For this reason, we use the term size synonymously with power. Friendly relationships are indicated by solid lines connecting two agents. Hostile relationships are denoted by dashed lines. When two agents have the same attitude toward each other, the relationship is displayed as an undirected edge (one without arrows). Asymmetrical relationships are displayed as directed edges. Vertex placement is not based on spatial or geographical distances, unless so indicated. Node colors represent how happy each agent is with its place in the network.
Power structures pull together the first four definitions: agents, power, actions, and tactics. Power structures are composed of agents, each of whom has some level of power, who take actions toward other agents by allocating their power in a tactic. If someone were to look at a power structure diagram like the one above, without knowing any other historical or political details about a situation, they would have a decent first approximation of the power struggle at hand.
A power structure exists at a point in time. What we want to know, and what the axioms describe, is how a given power structure will evolve as time unfolds.