Land Use Regulation as an NK/CS System

Complexity in the Field
By J.B. Ruhl
Post 3
September 4, 2006

Here in Tallahassee we are in the throes of a debate over the merits of an “inclusionary zoning” ordinance that requires housing subdivision developers to set aside and intersperse 10 percent of new units as “affordable” to median income families, which here means a price tag of $160,000 (the median home price is closer to $200,000, beyond reach of the median family income, though probably a fantasy for people in many parts of the nation). The idea is that this will increase the stock of affordable housing and distribute it among higher-priced units rather than concentrated in some corner of the city. The building industry argues that this will backfire because (1) the reduced yield associated with the below market pricing of the affordable homes will be made up by higher prices for the unregulated units, which will (2) make demand, and thus prices, for existing homes at all above-median price levels rise, which will (3) reduce the total stock of affordable housing in the city. Also, they argue, development will leapfrog to areas outside of the city’s jurisdiction to avoid these rules, thus contributing to regional sprawl.

Even assuming the builders’ claims are overblown, there is some logic to them, and it would not be the first time a local land use regulation worked at cross-purposes within the jurisdiction and sent negative spillover effects into another jurisdiction. Indeed, land use is an area of law riddled with the properties of “NK/CS” systems.
Let’s say we were evaluating the long-term performance of cities in the realm of sustainable land use management. We’ve come up with a list of attributes, each of which, if implemented effectively, can contribute to the “fitness” of a city’s performance (e.g, traffic control, stormwater management, affordability of housing, public utility infrastructure, etc.). The problem is that each of those attributes could have an impact on how one or more other attributes perform. And as there are many cities in an particular state, it may be the case that a city managing its attributes effectively intra-jurisdictionally in fact causes problems for other cities in their management of their attributes. We could describe this as an NK/CS system, a model Stuart Kauffman introduced in Origins of Order and At Home in the Universe, in the following terms:

N = The number of attributes. (In our case, the collection of land use attributes cities are trying to optimize)

K = For each attribute, the number of other attributes that influence it depending on how they are managed. The maximum K therefore is N-1.

C = For each NK system (in our case, each city), the number of attributes of other co-evolving NK systems that influence its attributes.

S = The number of co-evolving NK systems (number of cities in our case) exhibiting C.

This model captures the complexity of the balancing act each city has to perform among its attributes intra-jurisdictionally, as well as the co-evolutionary forces of inter-jurisdictional influence. NK/CS systems can exhibit a range of adaptive states. Sometimes the system is configured to reach a relatively high level of stability. When K is high, for example, there are so many conflicting constraints between attributes that the system can get “stuck” in highly ordered but sub-critical states. Or if C is low, then co-evolving NK systems do not deform one another’s fitness landscapes, so they can all settle in for the long haul without worrying about each other. Although these conditions may produce a high fitness level, the systems may have little resilience to external perturbations that significantly alter how the N attributes perform in their environment. On the other hand, if C is very high, each co-evolving NK system has to constantly respond to other NK systems’ moves in a Red Queen arms race of super-critical behavior. The result is likely to be mediocre fitness levels that nonetheless roll with the punches of external perturbation until something really big comes along. In between the sub- and super-critical ranges—in the transition regime between order and chaos—is where complexity theory posits that adaptive behavior can lead to both sustained levels of relatively high fitness and strong adaptive resilience to external perturbations.

Complexity theory models suggest that one way of manipulating NK/CS systems to find that sweet spot is to adjust the “patch size” of the co-evolving NK systems. In the land use context, for example, what is the best size for jurisdictions? The list of problems that appear to be too large in scope for the traditional city and county units of land use authority is growing: traffic, habitat loss, dwindling affordable housing, urban runoff, and the other of sprawl. Environmental issues such as watershed and ecosystem service management also don’t fit very well onto the city and county mosaic. Do we need larger patches? Many states have experimented with regional or state-wide management of certain land use issues, and while there has been some success, it has proven politically difficult to break out of the conventional approach. The land use system, after all, is just one of many within the complex array of state and local politics.

I’ll be referring back to the NK/CS system model in future posts exploring how disasters (thin tail events on the power law curve) and cumulative effects (lots of thick tail events adding up) can wreak havoc on legal systems.