From anarchy to organized violence – a perfectly competitive market of protection

Many individuals learn to protect themselves. As the art of self-protection is acquired, a few individuals offer their protection services to others in exchange for other goods and services that generate utility. The incentive to trade is no different from that depicted by an Edgeworth-Bowley box, in which individuals with different levels of tolerance for violence will engage in mutually beneficial exchanges. We shall call this the 1st degree of organized violence, which is contingent only upon differences in preferences. The trading of violence can result in some specializations in violence, allowing the mechanics of violence to be practised more efficiently, and thus leading to organized violence.

The 1st degree of organized violence has an enforcement issue at the most fundamental level that is as difficult to resolve as the end period problem in game theory. ^[34] Yet, in contracts for protection (violence), a higher degree of organized violence need not resolve the end period problem in order to reach equilibrium. A specialist of violence may not be able to expropriate all his clients at the same time. What is more likely is that specialists will expropriate bit by bit rather than renege on all their clients at the same time. Although for cultural and whatever reasons, some primitive isolated society may want to uniformly expropriate the welfare benefits of all the clients who cannot make choices, the market for protection is contingent upon the assumption that individuals (and their assets) have some degree of mobility and choice. Without this assumption, the market for protection is a moot issue. In other words, a market for protection hypothetically assumes individuals can seek other competitive producers of violence, which would result when surviving victims vote with their feet. If buyers of protection can choose alternative suppliers of protection, this would impose a constraint on expropriation and equilibrium within a market of protection can exist.

Give the above setup of the problem, anarchy can evolve into a primitive form (1st order) of organized violence, which would then evolve into a spot market (perfect competitive market) for protection, which can then be considered the 2nd order of organized violence. Notice that the spot market structure implies nothing about the roving or stationary ability of the protectors. All it requires is that the customer is willing to pay, there are competitive suppliers willing to protect, and implicit contracts can be honoured.

Theoretically, the above notions can be conceptualized as conditions for which suppliers of protection offer it to individuals who want it in a competitive market. Without including the element of innovation, the model is similar to the demand-supply model in any market except for one thing: competing suppliers of protection can raise each other’s costs of protection by engaging in violent conflict. In this spot market of protection, entry will raise, rather than reduce, costs. The essential features of the equilibrium include:

1. Rising marginal costs of protection;

2. free entry in supplying protection; and

3. violent interactions among suppliers of protection.

We wish to first illustrate this spot market model as a benchmark for further consideration of (and including) the element of innovation. The benchmark case is similar to a standard demand and supply model found in economics textbooks:

Inclusion of innovation: formation of a centralized government

A society can transform a perfectly competitive market of protection, which is characterised by the rising cost of protection, into an alternate market structure of protection. To do so, societal interactions would have to go beyond the first and second degrees of organized violence. Higher degrees require protectors (and therefore their clients under protection) to give up their means of executing violence – a process of centralizing military resources under a centralized government. One can speculate the process through which this can occur, but the precise trajectory cannot be easily formulated. For one thing, oligopoly theory in this direction has not been well-developed, and many real world examples are still undergoing trials. Moreover, a centralized government has not been viewed as similar to the problem of democracy in the literature. Therefore, centralized democracy has not been the focus of attention. ^[37] Yet, in modern Chinese political thought, a centralized democracy is a very important philosophy even in today’s pro-market PRC government politics.

The framework here is not saying that a centralized democracy will necessarily be the evolutionary outcome of a market structure of protection. Indeed, the current situation for modern China is still a duopoly, but the framework here describes the possibility of a tendency for the market structure to move towards this equilibrium, while admitting that other market structures, including the dynastic equilibrium examined by Usher, could also be theoretical outcomes. The choice variables that will enable a centralized democracy to be the market structure outcome include a current committed price protection scheme, a future spot market price protection scheme, technological shift parameters of α_j and γ_j (and their associated costs), and a game theoretical choice of military competition in the manner described by eq. [4] versus a cooperative solution of getting out of a prisoner’s dilemma.

Granted that the decision variables of the choice problem are much broader and much more complicated than what is needed in a perfectly competitive (atomistic) model, they should not prevent us from conceptualizing the nature of the choice problem in this dynamic setting. Although to introduce them runs the risk of underspecifying a model, omitting them can turn a model into one that addresses an empty issue, at least in the case of Modern China.

We can use additional mathematical symbols to represent each of the parameters listed above and organize a set of modified equations that describes this broader dynamic choice problem corresponding to Equations (1) to (5). However, this process would not provide additional analytical insights in that we cannot predict, at this stage of our analysis, under what situation will one type of evolution trajectory necessarily dominate another. We are thus compelled to discuss the outcome conceptually. Basically, the evolutionary process could come about through choices made by the individual actions of both the suppliers and demanders of the market of protection.

On the supply side: a protector offers a prior contract for a committed price, which will reduce the demand for protective services to his competitors, with the future spot market (uncommitted) size shrinking. His competitor, upon seeing a possible shrinking future market, will compare a spot pricing tactic with the strategy of following suit to also offer a committed price, which is very much like a Bertrand competition. The twist here is that the average and variable costs of protection are also lowered (or anticipated to lower). The incentive of offering lower committed prices to customers would be much higher if the costs are expected to go down by an amount larger than the price cut. On the other hand, if a protector continues to operate in a spot market context only, he will be alienated (or marginalized) when individuals under his protection switch to an alternative protector perceived to have a lower cost through α_j and a higher military means of protection, γ_j

On the demand side: an individual shopping for protection will compare offered committed prices, the level of security, and the amount of public goods offered by j (and the expected spot price if uncommitted) and choose whether or not he wants to commit to a prior contract, and if so, from whom. The larger the spot price one has to pay for identical security and public goods, the larger is one’s incentive to accept a lowered committed price. In order to choose a particular protector, an individual will pick the one who presents the highest chance of reducing the average and marginal costs of protection (i. e., delivering what he promises to deliver).

It may be useful to think of this evolution as a contract for innovation and an institutional choice problem. ^[38] In other words, the evolution can be achieved through a contract between protected individuals and a protector who promises to improve his/her protection ability so that the marginal cost of protection becomes a decreasing cost function in return for the taxes paid by the protected individuals. This contract can be considered a social contract and a form of “quid pro quo taxation”. ^[39]

We noted that an important precondition of a centralized democracy is a decreasing marginal cost of protection. Without that, a protector cannot handle a large population under protection, just as a mom-and-pop street corner restaurant will not be able to handle a large patronage. α_j is important not only for shifting the variable cost components of protection, but for making them decline (i. e., recruiting additional individuals under the same system of protection lowers the marginal cost of protection).

A decreasing cost of protection, however, is only one precondition for a centralized democracy. If “consumers” of protection have not made prior arrangements with a centralized government, and if the latter evolves purely from the supply side as weapons and/or administrative technology improve, the protector can turn into a single despot who charges a monopoly price for the protection of MR=MC. Conceptually, a government with a declining average cost of protection may emerge dictatorially by might or under a democratic social contract, in which buyers of protection are directly (or indirectly) involved in government policies. Figure 2 in the text compares the various equilibria in this technological cost-decreasing environment.

Note in the diagram in the text that a dictator would charge a monopoly rent (AR–AC)N_o by equating MC with MR. How this monopoly rent is divided determines the outcome of the ideal of centralized democracy vs. a despot. S/he may be a benevolent or enlightened dictator if part of this rent is redistributed to his/her subjects, but a despot or tyrant if s/he grabs all the rent for him/herself. Olson “did not” consider this problem, which went from Point O to Point M in the diagram. Point M denotes a democratic government that aims to charge at the average cost (i. e., adopt a uniform head tax with balanced budget in the long run) and earn normal returns with AR=AC. This is one notion of democracy that is consistent with the notion of constitutional economics.

The mechanism by which equilibrium, M, emerges over equilibrium, O, is tricky and not easily engineered. The history of the world suggests that it does not always happen, although there is a great efficiency gain for a society as a whole to choose M over O, even if it is achieved for only a short period of time. The condition of M as a stable equilibrium is a theoretical possibility, but it can also act as an ideal that many governments in the world try to achieve. The choice problem entails the involvement of individuals: a person can do nothing and wait to be forced to pay a monopoly protection fee of Po, or commit to the offer of a lower price of protection, Pm, of an emerging central government.

This appendix basically outlines all political institutional equilibria within a framework of market of protection without predicting which will necessarily be the outcome. The framework does imply that transaction costs aside, and from pure economic efficiency perspective, equilibrium M is clearly the long run solution. Unfortunately, Feng Yu-Hsiang has not been successful in reaching that equilibrium. Although he managed γj (technology in affecting fixed costs) well, he had little to offer in αj (principles affecting the variable costs). Perhaps that was what contributed to his political failure. Nevertheless, his existence served being a transitional step, in a very important process on how other “protectors” in China have tried to reach the equilibrium of a centralized democracy.