We were accepted to the conference as a poster presentation. The poster displayed our model and our research results, as well as, our article. The article was written by Dr. Brian Castellani, Michael Ball (me) and Kenneth Carvalho. Click here to visit Dr. Castellani's Sociology and Complexity web site.
We will have some photos from the conference up shortly.
We have duplicated the functions from our original Summit-Sim Visual Basic program in NetLogo. But this time we have increased the grid space to 51 x 51, giving us a total of 2601 available agent spaces (a ten-fold increase from the 256 agent spaces in the original).
NetLogo also gives us the ability to post the model as an applet directly to the web.
Give the model a try! Directions for use are listed below the applet, as well as, a summary of the rational behind the program.
powered by NetLogo
view/download model file: pareto_schelling_mobility.nlogo
This model explores the relationship between Pareto's 80/20 rule and Schelling's segregation threshold. The model is a 51X51 lattice structure, upon which a randomly distributed set of upwardly-mobile rich, middle-class, and poor agents roam. Three rules govern the behavior of these agents: preference, preference-degree, and capacity.
PREFERENCE is a modification of Schelling’s segregation rules. Unlike the original Schelling model, wherein agents seek their own kind, preference concerns upwardly mobile agents seeking agents of a higher status. In our model, rich agents seek rich agents; middle-class agents seek rich agents; and poor agents seek middle-class agents.
PREFERENCE-DEGREE determines the number of higher status agents around which others prefer to live. In a 2-D lattice structure, “neighbors” is defined as the total number of spaces available around an individual agent, which range from 0 to 8.
CAPACITY (which ranges from 0 to 10) determines the number of random spaces an agent can move per iteration.
Two important principles governing upward social mobility are Pareto’s 80/20 rule and Schelling’s segregation threshold. Pareto shows that wealth follows a power law, where a few have the most. Schelling shows that neighborhood preference (beyond a certain threshold) leads to spatial segregation. The link between these two principles, however, remains undeveloped—particularly in relation to the current U.S. financial crisis (circa 2008). To explore this link, we created an agent-based, Pareto universe of rich, middle and poor agents. The rules for this universe follow Schelling, with a slight modification: while rich agents seek their own, middle and poor agents do not; instead (pursuing upward mobility), middle agents seek rich agents and poor agents seek middle agents. Congruent with the current U.S. financial crisis, our model finds that, in a log-normal wealth distribution with a power-tail, moderate upward social mobility produces spatial segregation, instability and, in particular, unhappiness on the part of middle-class and poor agents. We call this insight the upward social mobility rule (MR). Unexpectedly, the MR also provides a corrective: it appears that, at threshold, upward social mobility leads to integrated, stable neighborhoods with very high rates of happiness. The MR therefore suggests that the U.S. financial/housing crisis might be effectively addressed for the greater good of all if upward social mobility is controlled and regulated, even on the part of poor households.
In a Pareto universe, once preference (p) for upward social mobility passes a certain threshold (x), the spatial segregation of wealth (S) emerges. We can state this rule more generally: when (p < or = x), segregation approaches zero; however, once (p > x), segregation approaches near completion. Furthermore, as (p) moves past threshold, segregation increases—although the relationship between (S) and (p) is nonlinear, levelling off across time (t) at about (p = 3).
S --> 0 if p < or = x
S --> 1 if p > x
In this first formula, the MR defines upward social mobility as an agent’s preference and capacity to improve its economic status within a Pareto wealth distribution. Together, capacity and preference create a likelihood of happiness distribution (L). At any given moment, an agent’s likelihood for happiness—that is, the agent’s capacity to secure upward social mobility—is expressed as follows:
L(H) = (s / (t-h) ) (c/c')
Where H = happiness; s = neighborhood spaces available around the higher status agents being sought; t = total population of agents seeking a particular set of spaces; h = similar seeking agents that have already secured a position of happiness; c = an agent’s actual capacity to move randomly at any given point in time; and = the agent’s ideal capacity. Furthermore, in this second formula, s is determined, in part, by preference (p), which defines the type and number of empty spaces agents are seeking. For example, if rich agents seek spaces with p = 2 neighbors, only those empty spaces are sought by rich agents; s for each of the three agent types is also dependent upon the number of spaces already taken by other agents.
In our model, we simplify the likelihood of happiness into a basic prevalence rate of unhappiness—which we obtain by plotting the prevalence rate of unhappy rich, middle and poor agents at each moment in time, along with an overall unhappiness rating.
1. Determine the number of red, blue and green agents. RED are rich agents; BLUE are middle-class agents; and GREEN are poor agents.
2. PARETO DISTRIBUTION: Use the sliders to determine population estimates. In a Pareto universe, RED agents are few (e.g., 90 to 100); BLUE agents are perhaps double in size or more (e.g., 300 to 320) and GREEN agents are the largest group (e.g., 700 to 750). You can try any Pareto estimate you want or try other arrangements, perhaps based on a log-normal distribution or Guassian (bell shaped) distribution.
3. PREFERENCE DEGREE: Use the sliders to determine the number of higher status agents each color is seeking. In our model, A) RED seek other RED; B) BLUE seek other RED and C) GREEN seek other BLUE. The higher the preference-degree is for each agent type, the harder it will be for those agents to secure a position of upward mobility.
4. CAPACITY: Use the sliders to determine the capacity of RED, BLUE and GREEN agents. Capacity determines how many random spaces an agent can mover per iteration. In the real world, RED agents have the greatest capacity to move because of their wealth. Poor agents have the least capacity to move because of their lack of wealth. Try different CAPACITY combinations to see what impact it has on mobility.
5. SETUP: Once you have completed the above four steps, hit SETUP and you are ready to go. All you need to do next is hit GO. When you want the model to stop hit GO again.
--------------------Click GO to start the simulation.---------------------------------
To test the MR, we used the BehaviorSpace tool in Netlogo to run 27 different preference-degree combinations, starting with r1,m1,p1 (rich seek one rich agent; middle seek one rich agent and poor seek one middle agent) and ending with r3,m3,p3 (rich seek three rich, middle seek 3 rich; poor seek 3 middle). We tested each combination 100 times for a total of 2,700 runs.
1. We found that, in a Pareto universe, the spatial segregation of wealth is a function of some type of social mobility rule—which can be mapped, across time, as a series of unhappiness distributions.
2. More specifically, it appears that the (r1,m1,p1)combination has the best happiness ratings.
3. The degree of unhappiness in our Pareto universe is best explained in systems terms—that is, the 27 different combinations of micro-level behaviors we examined lead to unintended and, in some instances, unexpected macro-level patterns. Two systems issues are of particular importance.
The first has to do with the behavior of rich agents. We found that the upward mobility of rich agents at (p =2) negatively impacts the happiness of middle and poor agents. Rich agents close-out middle agents because of their increased mild preference (p = 2), which causes a rippling effect wherein the lack of spaces for middle agents causes instability, which makes it harder for poor agents to secure a stable place to live.
The second has to do with the behavior of middle and poor agents. The rippling effect of the rich is less dramatic when the upward mobility of middle and poor agents is kept at (p = 1). In other words (and unexpectedly so), middle and poor agents have a much better chance at happiness when they enact a mild level of upward mobility, especially when rich agents begin seeking higher rates of mobility.
4. It appears that (r1,m1,p1) is the most spatially integrated of all 27 models.
5. Spatial segregation in our Pareto universe is also best explained in systems terms. Again, two systems issues are of particular importance.
First, higher rates of mobility amongst rich, middle and poor agents lead to higher rates of spatial segregation—both within and between agent types. More specifically, once preference-degree becomes moderate, reaching p=3, almost everyone in a Pareto universe (from the rich to the poor) has high rates of unhappiness.
Second, if preference-degree is kept at threshold ), integrated, stable neighborhoods emerge and unhappiness is low. For example, because R1 (see note e, Figure 1) remains at threshold, spatial segregation amongst the three agent types is almost absent. (Note: here preference is expressed as , where p = preference-degree and n = total neighborhood spaces available, which in our model (n=8).
6. Finally, we found that, in an already segregated model, setting social mobility at (p = 1) functions as a corrective: it improves integration and happiness. For example, running our model at (r2,m2,p2) we found that, after 1000 iterations, unhappiness was at 61%. At this point we reset mobility at (r1,m1,p1). After another 1000 iterations, unhappiness dropped from 61% to 23% and segregation significantly decreased.
Congruent with the current U.S. financial crisis, our model suggests that, in a log-normal wealth distribution with a power-tail, moderate upward social mobility produces significant system-wide spatial segregation, instability and, in particular, unhappiness on the part of the middle-class and poor.
Unexpectedly, however, our model also suggests that, one way to address the current U.S. financial crisis is to slow down mobility to a mild, threshold level. The important byproduct of this more systemically aware mobility is integrated, stable neighborhoods that have very high rates of happiness. In other words, Pareto’s law seems more effectively addressed for the greater good of all if upward social mobility is controlled and regulated, even on the part of poor households. This is particularly true in terms of housing.
Over the last decade, many Americans and their lenders have used a variety of high-risk housing strategies (sub-prime lending, etc) to obtain higher levels of upward social mobility. The result has been the increased spatial segregation of wealth: the neighborhood distances from the rich to the poor have geographically increased as upwardly mobile families lost their homes, primarily through failed attempts to gain more than they could financially support. Within the confines of our model, the failure of this strategy seems evident. Past a certain threshold, upward social mobility threatens (rather than stabilizes) the system, creating unstable, chaotic mobility patterns amongst the poor and middle-class—which results in increased, rather than decreased, wealth segregation.
In such a chaotic system, the effects of neighborhood, in particular poverty traps, also make sense—albeit with an important (and unexpected) twist. As shown in R2, once mobility passes a certain threshold, poor agents (despite their individual efforts) remain stuck. They cannot improve their position no matter how aggressive their social mobility. In other words, poverty traps are not strictly a function of neighborhood effects. Instead, poverty traps and neighborhood effects are the product of something larger: the system, or more specifically, the mobility patterns of the rich, middle-class and poor.
This last finding is perhaps our most important. Individual micro-level social mobility is not self-regulating. Contra Adam Smith, our model suggest that there is no invisible hand guiding the role upward social mobility plays in the spatial distribution of wealth. As the recent U.S. financial/housing crisis shows, and our model seems to concur, in a Pareto Universe, without some type of threshold-based recognition, upward social mobility (even at relatively mild levels) does not promote the good of the community; instead, it supports Schelling-like segregation.
Our model is very basic. It would therefore be interesting to see what types of additional factors impact our findings. We welcome researchers to try other types of senarios.
Schelling, T. (1978). Micromotives and Macrobehavior. New York: Norton.
See also a recent Atlantic article: Rauch, J. (2002). Seeing Around Corners; The Atlantic Monthly; April 2002;Volume 289, No. 4; 35-48. http://www.theatlantic.com/issues/2002/04/rauch.htm
Wilensky, U. (1997). NetLogo Segregation model. http://ccl.northwestern.edu/netlogo/models/Segregation. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
Wilensky, U. (2005). NetLogo Wolf Sheep Predation (System Dynamics) model. http://ccl.northwestern.edu/netlogo/models/WolfSheepPredation(SystemDynamics). Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
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