Chris Snijders – Complexiteit: Schelling/Ising

A social science variation:

Schelling’s segregation models

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

Chris Snijders – Complexiteit: Schelling/Ising

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

Chris Snijders – Complexiteit: Schelling/Ising

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).

Chris Snijders – Complexiteit: Schelling/Ising

Segregation: background

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

Main idea: this is because people 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.

Chris Snijders – Complexiteit: Schelling/Ising

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

Chris Snijders – Complexiteit: Schelling/Ising

Check this out in NetLogo (nb: was also used in networks lecture)

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

<check out NetLogo model now>

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

Chris Snijders – Complexiteit: Schelling/Ising

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)

Chris Snijders – Complexiteit: Schelling/Ising

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

Chris Snijders – Complexiteit: Schelling/Ising

Extending the model

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

Chris Snijders – Complexiteit: Schelling/Ising

Kinds of analyses on these models

Simulate for different parameters, save results in data set, statistical analysis on data set

Markov chain models

…

Chris Snijders – Complexiteit: Schelling/Ising

There is plenty more where that came from …

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

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

Chris Snijders – Complexiteit: Schelling/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.

Chris Snijders – Complexiteit: Schelling/Ising

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.”(Kees, am I missing something?)

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