Uwe Matzat – Complexiteit: Schelling/Ising 1 A social science variation: Schelling’s segregation...

Uwe Matzat – Complexiteit: Schelling/Ising 1

A social science variation:

Schelling’s segregation models

http://www.gisagents.blogspot.com/


Thomas Schelling

Basics are from 70s Several fascinating “think out loud”

books (and much more)

http://nobelprize.org/nobel_prizes/economics/laureates/2005/schelling-lecture.html


FYI: book list

1. The Strategy of Conflict (Schelling, 1960). 2. Micromotives and Macrobehavior (Schelling, 1978). 3. Arms and Influence (Schelling, 1966). 4. ‘‘Dynamic Models of Segregation’’ (Schelling, 1971a). 5. ‘‘The Life You Save May Be Your Own’’ (Schelling, 1968, reprinted in

Choice andConsequence). 6. Choice and Consequence (Schelling, 1984a), subtitled on its cover

but not on its titlepage Perspectives of an Errant Economist. 7. ‘‘Self-command in Practice, in Policy, and in a Theory of Rational

Choice’’ (Schelling, 1984b). 8. ‘‘Some Economics of Global Warming’’ (Schelling, 1992). 9. ‘‘Hockey Helmets, Concealed Weapons, and Daylight Saving: A Study

of BinaryChoices with Externalities’’ (Schelling, 1973, reprinted in Micromotives andMacrobehavior).

10.‘‘An Essay on Bargaining’’ (Schelling, 1956, reprinted in The Strategy of Conflict).


Segregation: background

In many (American) cities, races segregate This has unwanted consequences Why does this happen, and what can we do about it?

Basic hypothesis: this is because people of different kinds don’t like each other

If that would be true, high-tolerance cities would have lower segregation than low-tolerance cities …

… but empirically this does not hold.


Just a rough idea…

New York

Los Angeles


Percentage niet-Westerseallochtonen per stad

Segregatie-index per stad


Algemene ontwikkeling ... wat bevolkingscijfers

Inw W.Allocht. NW.Allocht. T M S1996 15.5 1.3 1.2 0.27 0.23 0.282000 15.9 1.4 1.4 0.31 0.26 0.302005 16.3 1.4 1.7 0.36 0.32 0.332010 16.8 1.5 1.9 0.38 0.35 0.34

(bron: CBS)


Schelling’s segregation model Reds and greens live on a

checkerboard (torus) Each red and green has a

happiness function: happy if enough neighbors of same color, unhappy if not (same for all reds and greens)

At random, one agent is chosen. If agent is unhappy -> agent moves to another place on the board where he is happy

Process repeats until everybody happy, or no movements possible any more


Upcoming …

Main conclusion(s) of a simulation like this

For sure, this model is an abstraction of reality. How or in which direction can/should we extend the model?


Check this out in NetLogo

Netlogo allows uploads of changed models (see e.g. http://www.personal.kent.edu/~mdball/pareto_schelling_mobility.htm)

<check out NetLogo model now>

http://ccl.northwestern.edu/netlogo/

http://www.personal.kent.edu/~mdball/pareto_schelling_mobility.htm


Schelling’s conclusion

Harsh preferences are not necessary to create segregation. In other words: ever under ‘mild’ circumstances, segregation can occur

And the simulation shows that segregation also depends on for instance how full the checkerboard is (if crowded, moving is more difficult)


Schelling’s segregation model (repeat) Reds and greens live on a

checkerboard (torus) Each red and green has a

happiness function: happy if enough neighbors of same color, unhappy if not (same for all reds and greens)

At random, one agent is chosen. If agent is unhappy -> agent moves to another place on the board where he is happy

Process repeats until everybody happy, or no movements possible any more


Extending the model

How or in which direction can/should we extend the model?


Kinds of analyses on these models

Run the model for different parameters, save results in data set, do (statistical) analysis on data set. Then derive (testable) predictions

For the mathematically savvy: Markov chain models

Comparisons with empirical segregation data

…


However…

What does it mean if we can create simple local models that seem to mimic observed aggregate behavior?

At best, we can argue that preferences need not play a role. Let’s have a look at some empirical data …


This is a black vs other issue …

Three-quarters of African-Americans live in highly segregated neighborhoods today, whereas 90-100% of other groups experience only moderate levels of segregation.

Massey, Douglas S. and Mary J. Fischer. 2000. “How Segregation Concentrates Poverty.” Ethnic and Racial Studies 23(4): 670-691.

Black

White

Hispanic

Asian

…


1992 Detroit Survey on Neighborhood Preference

Als de buurt 20% zwart iswil een derde van de blanken daar liever niet leven

Als de buurt 33% zwart is, wil 60% van de blanken daar niet meer leven, 44% zou zich niet meer comfortabel voelen, and 29%

zou willlen gaan zoeken om te verhuizen

Als de buurt 50% zwart is: dit is niet acceptabel meer voor bijna alle blanken,

op een kleine minderheid


1992 Detroit Survey on Neighborhood Preference

For African-Americans: The most popular choice is a neighborhood that is half black

and half white. 87% willing to live in a neighborhood that is 20% black.


Gevolg: een kettingreactie

In een buurt met 20% zwarten, krijg je minder of geen instroom van blanken meer, en juist wel van zwarten.

Nu wordt het bijvoorbeeld 70% blank en 30% zwart. Een deel van de blanken begint hun huis te verkopen en verhuist

De buurt wordt 50-50 en zwarten gaan niet meer weg maar er komen er wel bij (voor hen is dit ideaal), terwijl blanken vertrekken

zwarte buurt (zie Amerika in de jaren 80 en 90)


Wisselwerking tussen empirie en simulatie


Eenvoudige aannames op micro-niveau leiden tot “verrassend” gedrag op macro-niveau

Bijv: milde preferenties over segregatie leiden toch tot segregatie

“complexity light”


There is plenty more where this came from …

“Wealth distribution” (Pareto’s law) Traffic simulation Crowd panic Flocking birds / fish Ant movements … and many others (including Ising)


This is Ising-like, but with …

agents moving instead of switching or flipping a binary operator for the state of the agent local interaction, but agents can see the aggregate …

As in Ising, the Schelling model shows that simple (quasi-)local interaction can lead to surprisingly complex aggregate behavior. The link between the models is not perfect though.


Same model (almost), different questions

“The goal of statistical physics is to not to predict all of these detailed motions but only to calculate certain average properties of these motions, for example, how many spins on average are pointing up, what is the mean energy etc.”

In social science also, or rather: process / speed of segregation (asymptotic results don’t count) what can be done to overcome segregation?

Uwe Matzat – Complexiteit: Schelling/Ising 1 A social science variation: Schelling’s segregation...

Documents

Transcript of Uwe Matzat – Complexiteit: Schelling/Ising 1 A social science variation: Schelling’s segregation...