City as a Human-Driven System

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City as a Human-Driven System Three basic dynamic regimes of the Schelling

and Human Environment, 2 Revson Environment Simulation Laboratory University

2005, University of Surrey, UK Visually random Segregation Always in move City

decision-makers Components of the modern urban GIS: Basically accepting this

fashion, namely: To model interactions between urban decision-makers as

vague assumptions and potentially unlimited number of parameters.

1 City as a Human-Driven System Three basic dynamic regimes of the Schelling model Itzhak Benenson 1,2, Erez Hatna 2, Ehud Or 2 1 Department of Geography and Human Environment, 2 Revson Environment Simulation Laboratory University Tel Aviv Presented at WORKSHOP ON MODELLING URBAN SOCIAL DYNAMICS 7-8 April 2005, University of Surrey, UK Visually random Segregation Always in move City is an artificial system, which development is determined by human decision-makers Components of the modern urban GIS: Basically accepting this view, we yet describe behavior of urban decision-makers in an over-physical fashion, namely: To model interactions between urban decision-makers as symmetric, short-range, isotropic, ignore ability of urban agents to adapt to the environmental changes, etc. Yes, we need serious endorsements to pass to human-based models, with their vague assumptions and potentially unlimited number of parameters. Recent crucial advances in data availability regarding both urban infrastructure and population, force us to try. Residential distributions is the best example to begin with Infrastructure 1

2 Components of modern urban GIS: The city of Ashdod (100,000): Russian- and Israeli-born population Geo-referenced data on individuals and families Members of each ethnic groups are segregated over the part of the area, but share the rest of the area with members of other groups. Tel-Aviv (pop. 350,000), mean gross family income in a building (1995) Yaffo Distribution of families according to the income: Heterogeneous with the patches of homogeneity. Jewish and Arab householders in the city of Ramle (population of 30000). Distribution of ethnic groups: Heterogeneous in some areas and homogeneous in the others. 2

$Tel-Aviv by income, with too high fraction of rich residing among poor The overall impression we ve gained is that Israeli cities are over-heterogeneous High-resolution view of the family income$

3 The simplest explanation of the phenomena: householders reaction to neighbors depends on more than one factor. Say, rich Arab and Jews (or Russians emigrants and Israeli-born Jews) don t care to live close to each other Or, in opposite, poor Arab and Jews cannot avoid living together For nine Israeli cities we ve constructed the maps of: level of education, number of children, age of house Well, skeptic would ask whether explanations of this kind remain valid for the distribution of Jewish families in Tel-Aviv by income, with too high fraction of rich residing among poor The overall impression we ve gained is that Israeli cities are over-heterogeneous High-resolution view of the family income spatial pattern in nine Israeli cities Kfar Saba We base on Log 2 (Income); its non-spatial distribution is close to normal We present the data at resolution of houses 3

Ramat Hasharon Ramla Bat Yam Rich in poor

Educated N Building age N Tel-Aviv 350,000 20.

581** 117 Kfar-Saba 70,000 44.2 0.177** 1435 0.

262** 517 0.140 30 Ashdod 130,000 22.8-0.

4 Ramat Hasharon Ramla Bat Yam Rich in poor areas are they attracted by the new constructions? STD > 1.25 Mean(3) < 12 Pop Area % % Children N % Educated N Building age N Tel-Aviv 350, ** ** ** 117 Kfar-Saba 70, ** ** ** 98 Ramat-Hasharon 40, ** ** Natanya 150, ** ** Ashdod 130, ** ** Lod 52, * ** Ramla 40, ** Rosh-Haayin 40, ** Bat-Yam 140,

Ok, we can partially explain the heterogeneity by infrastructure and family characteristics, with R 2

Skeptic: No way, the data-hungry researches ignore hundreds of studies, which reached a dead end long

passes the threshold of R 2 0.4 (Benenson, 2004).

Instead, we assumed that the reason of the observed mix of homogeneous and homogeneous areas is in

This assertion can be tested in field experiments Based on GIS maps at resolution of the houses, we

within relatively heterogeneous, according to the family income, areas.

The results were much more definite I used to see in human geography Is it important that the level

(1 unimportant, 5 very important) Rich in homogeneous areas Rich in heterogeneous areas Is it

5 Ok, we can partially explain the heterogeneity by infrastructure and family characteristics, with R Maybe more factors will work even better? Skeptic: No way, the data-hungry researches ignore hundreds of studies, which reached a dead end long ago. Whatever factors are investigated, the explanation of the residential distribution pattern never passes the threshold of R (Benenson, 2004). Feeling hopeless, we decided to cancel the hard work of building maps of factors. Instead, we assumed that the reason of the observed mix of homogeneous and homogeneous areas is in varying relations between the householders and their neighbors. This assertion can be tested in field experiments Based on GIS maps at resolution of the houses, we ve picked 40 rich householders according to their location 20 within relatively homogeneous and 20 within relatively heterogeneous, according to the family income, areas. We asked them about their attitude to the neighbors. The results were much more definite I used to see in human geography Is it important that the level of education of your neighbors be the same as yours? (1 unimportant, 5 very important) Rich in homogeneous areas Rich in heterogeneous areas Is it important that the socio-economic status of your neighbors be the same as yours? (1 unimportant, 5 very important) Rich in homogeneous areas Rich in heterogeneous areas Mean = 3.38 N = 13 Mean = 2.11 N = 18 Mean = 3.31 N = 13 Mean = 2.56 N = 18 Inside the building Inside the building Mean = 3.10 N = 20 Mean = 1.80 N = 20 Mean = 3.10 N = 20 Mean = 2.20 N = 20 Outside the building Outside the building 5

Is it important that the cultural level of your neighbors be the same as yours?

00 N = 13 Inside the building Mean = 2.72 N = 18 So individual relations in, infrastructure out?

distribution Mean = 3.75 N = 20 Mean = 2.

The model of residential dynamics in ethnically mixed Yaffo area of Tel-Aviv (Benenson, Omer, Hatna, EPB,

of householders, all concentrated in Adjami Arabs comprise 32% of Yaffo population, less concentrated

Omer Some results (all expected): Householders are well-informed about their immediate neighborhood and

of Yaffo as a whole and about all Yaffo neighborhoods Householders have definite preferences regarding

6 Is it important that the cultural level of your neighbors be the same as yours? (1 unimportant, 5 very important) Rich in homogeneous areas Rich in heterogeneous areas Mean = 4.00 N = 13 Inside the building Mean = 2.72 N = 18 So individual relations in, infrastructure out? Well, it is not hard to combine them We ve already did that for the simplest case of Yaffo residential distribution Mean = 3.75 N = 20 Mean = 2.35 N = 20 Outside the building Yaffo 1955 Jews and Arabs in Yaffo - the simplest case. The model of residential dynamics in ethnically mixed Yaffo area of Tel-Aviv (Benenson, Omer, Hatna, EPB, 2002) turned our theoretical view of modeling urban residential dynamics upside down Arabs comprise 10% of householders, all concentrated in Adjami Arabs comprise 32% of Yaffo population, less concentrated Yaffo 1995 Besides its conceptual simplicity, Yaffo case was well-studied in the field, mostly by Itzhak Omer Some results (all expected): Householders are well-informed about their immediate neighborhood and neighbors and react to this information Householders are well-informed about the population composition of Yaffo as a whole and about all Yaffo neighborhoods Householders have definite preferences regarding architectural type of the house Example of a field study: Individual home areas of Arabs (blue) and Jews (red) מעבדה להדמיה סביבתית וחוג לגיאוגרפיה וסביבת האדם Environment Simulation Laboratory and Dept of Geography and Human n Environment 6

The model loop was standard: Update data on vacant/occupied dwellings Set up in-migration flow We didn t have any

and have chosen the rough description - 6 grades of attitude: zero, very low, low, intermediate, high, very high (do

T T + 1 Simulate outmigration from the city Simulate residential search and resettling Update agents features We didn

We employed agents of three kinds: Jews, Arabs Muslims Arab Christians and based on the explicit GIS map of Yaffo

Distribution of houses by architectural style, 1995 Type of agents Jewish Arab Muslim Arab Christian Intolerance to

7 The model loop was standard: Update data on vacant/occupied dwellings Set up in-migration flow We didn t have any definite idea regarding parameterization of the relationships (between agents of different kinds and their neighbors) and have chosen the rough description - 6 grades of attitude: zero, very low, low, intermediate, high, very high (do not tolerate at all). T T + 1 Simulate outmigration from the city Simulate residential search and resettling Update agents features We didn t have any quantitative idea how members of various Yaffo population groups tolerate each other, and simply tried different combinations. Shortly, Yaffo model didn t worked well until we assumed that the relationships between Jews and Arabs are asymmetric: We employed agents of three kinds: Jews, Arabs Muslims Arab Christians and based on the explicit GIS map of Yaffo houses. Distribution of houses by architectural style, 1995 Type of agents Jewish Arab Muslim Arab Christian Intolerance to the (homogeneous) neighborhood Jewish Muslim Christian Zero Very High High Intermediate Zero Very Low Low Low Zero Yaffo dynamics Yaffo model - goodness of fit Model 1995 Yaffo 1995 Overall % of Arabs agents in Yaffo Moran index I for Arab agents % of Jew agents in houses of oriental style % of Arab agents in houses of block style Model results were robust to the quantification of grades 7

8 Asymmetric relationships made the Yaffo model work Ok, it is quite common in ecological models. But where robustness came from? Bounded rationality of model agents residential choice made model robust Bonded rationality is a vague notion, what did it mean in Yaffo model? Rather anthropomorphically, I introduced an algorithm of the residential choice that imitates my own behavior as a householder. The algorithm was different from those described in the books on choice modeling People choice behavior in one sentence Optimization: Homo economicus scan over all existing opportunities and on the basis of complete information, chooses the opportunity, which utility provides maximum of some shared criteria Bounded rationality: Homo psychologicus makes decisions on the basis of a limited number of opportunities, partial information regarding their utility and does not necessarily choose the best one. General approach does not dictate formalization of the choice heuristic Fully rational (optimal) behavior Proportional choice The utility u i of each opportunity i is known before making a choice, all opportunities are considered in parallel, and the probability p i to choose opportunity i is a function of utility p i = p(u i ), given Σ i p i = 1. Standard example: p i = exp(αu i )/Σ k exp(αu k ), α parameter (logit) Bounded rationality No common models The most popular: satisficing behavior - opportunities are approached sequentially. The order is a parameter of model. The utility u i of the opportunity i is compared to a threshold value u Threshold and the opportunity is accepted if u i > u Threshold. The decision-maker then quits. The most popular Take the best behavioral heuristic assumes that humans first collect available information regarding the opportunities, and then choose the best between those they can compare, ignoring those they cannot compare (Gigerenzer, Goldstein, 1996). Take the best heuristic is problematic when several agents apply for the same opportunities. It is formally incomplete, thus. In Yaffo model we introduced Try the better heuristic, which generalizes Take the best. 8

9 Try the better Given a set of opportunities, the human agent will: 1. Estimate the utility of each opportunity 2. Order opportunities by their estimated value 3. Approach opportunities according to an established order of utility values. 4. If an opportunity is still available, try to accept it with a probability proportional to utility. 5. Quit when making a choice. Let us consider implications of Try the better view of householder s behavior. Try the better versus Proportional choice TB is non-parametric [PC (logit) depends on unknown parameter α] TB resolves conflicts between agents [PC ignores conflicts] TB amplifies the possibility that the better opportunities will be chosen and the worst ones will be ignored [PC: close values of utilities always lead to close probabilities of choice] To illustrate, let us consider choices A and B, when A is slightly better than B : Utilities of A and B are α = 0.9 and β = 0.8 Probability to choose A (B) when it is the only possible choice equals to utility Unconditional probability to choose each one of options Proportional choice Try the better A (0.9) α(1 β/2) [0.54] α [0.9] B (0.8) β(1 α/2) [0.44] β(1 α) [0.08] None (1 α)(1 β) [0.02] (1 α)(1 β) [0.02] Why dynamics is robust? Because urban agents try the better opportunities in the same order, until the order is overturned. This makes choice quantitatively insensitive to small changes, but entails sudden and non-frequent qualitative changes. Residential dynamics in the city, which infrastructure does not change. Householders resettle in response to the characteristics of the neighbors U(H) H H U(H) A Probabilities of choice according to the Try the better heuristic Opportunity A B A B Utility at t Utility at t Utility at t Proportional choice versus Try the better (two versions) Proportional choice Try the better A Try the better to improve your situation NOTE: None of proportional choice algorithms (say, logit model) can result in essentially different chances of being selected for opportunities, which utilities are close. 9

The model outcome of try the better behavior of householder agents: Residential distribution is robust to the sudden changes in dwelling prices

claim: The dynamics of the city populated by the agents who apply the Try the better heuristic is robust Q. Why? A.

principle entails robust (and realistic) dynamics in Yaffo model Ok, Yaffo is an esoteric case, too specific for making general conclusions.

heterogeneity of the cities can be simulated on the base of the (1) Varying tolerance of the householders to their neighbors To reach likelihood

(3) Asymmetric relations rich avoid poor, but poor keep staying close to rich, if possible (4) Knowledge about the vacancies far away from the current

price, non-weighted mean of neighbors status over 7x7. To keep staying?

0 otherwise DU(c, A) = DU N (c, A) To occupy?

10 The model outcome of try the better behavior of householder agents: Residential distribution is robust to the sudden changes in dwelling prices Initial gradient of housing prices Initial distribution of agents economic status Proportional choice Try the better Try the better to improve Our claim: The dynamics of the city populated by the agents who apply the Try the better heuristic is robust Q. Why? A. Because the agents qualitative order of opportunities does not change with quantitative changes in opportunities utilities For example, Try the better principle entails robust (and realistic) dynamics in Yaffo model Ok, Yaffo is an esoteric case, too specific for making general conclusions. The data on Israeli cities support this view either Distribution of housing prices is averaged abruptly Stable population distributions The inherent heterogeneity of the cities can be simulated on the base of the (1) Varying tolerance of the householders to their neighbors To reach likelihood residential patterns, model householders must also possess all human features, we considered till now: (2) Try the better residential choice heuristic (3) Asymmetric relations rich avoid poor, but poor keep staying close to rich, if possible (4) Knowledge about the vacancies far away from the current location S(A) status, S Th (A) tolerance, S N (A) weighted over 7x7 mean of A neighbors status (weights decrease geometrically with distance), P(c) price, non-weighted mean of neighbors status over 7x7. To keep staying? Only the social component DU N (c, A) of disutility is considered: Social: DU N (c, A) = [S(A) S N (A)]*[1 - S Th (A)] If S(A) > S N (A) DU N (c, A) = 0 otherwise DU(c, A) = DU N (c, A) To occupy? The economic, U E (c, A), and social, U N (c, A), components of the utility U(c, A) of a cell c are considered: Economic: U E (c, A) = k*[s(a) P(c)] if S(A) - P(c) > k*s(a) U E (c, A) = S(A) P(c) if k*s(a) S(A) - P(c) > 0 U E (c, A) = 0 otherwise Social: U N (c, A) = S N (A) - S(A) if S N (A) > S(A) U N (c, A) = [S N (c) - S(A)]*[1 - S Th (A)] otherwise U(c, A) = U E (c, A) + U N (c, A) 10

Probability P L (c, A) that A will leave a cell c P L

A) if 0 DU(c, A) 1 P L (c, A) = PLeave if 1 < DU(c, A)

(c, A) = 0 if U(c, A) < U min P O (c, A) = U(c, A) U

min < U(c, g) Immigration: S t (A) ~ N(M t, STD t ), M

(A) < 1.96*STD t. In Israel factor g is close to 0.

9) Model patterns qualitatively reflect the

The results are robust regarding the distribution of

tolerance House prices Status mean 3x3 Status STD 3x3

2/Half 0.8 All Intolerant Mean STh of an agent.

tolerant 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.

status of neighbors We asked: Why human-driven city is

We answer: the results of choices of the agents

heuristics weakly depend on factors that influence

now: Why human-driven city can be predicted?

11 Probability P L (c, A) that A will leave a cell c P L (c, A) = 0 if DU(c, A) < 0 P L (c, A) = PLeave*DU(c, A) if 0 DU(c, A) 1 P L (c, A) = PLeave if 1 < DU(c, A) P Leave - maximum unconditional probability to leave the cell. Probability P O (c, A) that A will occupy a cell c P O (c, A) = 0 if U(c, A) < U min P O (c, A) = U(c, A) U min if U min U(c, A) 1 - U min P O (c, A) = 1 if 1 - U min < U(c, g) Immigration: S t (A) ~ N(M t, STD t ), M t =Mean city,t, STD t = g*m t, truncated to keep S t (A) < 1.96*STD t. In Israel factor g is close to 0.8, always remains within (0.7, 0.9) Model patterns qualitatively reflect the experimental data. The results are robust regarding the distribution of the level of tolerance in the population (and all the other parameters, besides P Leave ). Agents status Status STD S Th Agent status Agent s tolerance House prices Status mean 3x3 Status STD 3x3 All tolerant Uniform [0,1] Half 0/Half 1 Half 0.2/Half 0.8 All Intolerant Mean STh of an agent. Agents located within the strange neighborhoods are tolerant Agent's status - Mean status of neighbors We asked: Why human-driven city is robust? We answer: the results of choices of the agents operating in the city according to Try the better heuristics weakly depend on factors that influence utilities quantitatively, but not qualitatively We ask now: Why human-driven city can be predicted? If we correctly guess the main factors that govern agents choice we could simulate the dynamics of the real-world city - minor factors do not change the order of utilities 100% - Sth = % - Sth = 0.0; 50% - Sth = % - Sth = 0.2; 50% - Sth = 0.8 Uniform 100% - Sth =

12 Residential distribution in the city VARYING HOUSEHOLDERS TOLERANCE and ASYMMETRIC RELATIONSHIPS are the sources of residential heterogeneity and entail simultaneous homo- and heterogeneity of the residential distribution in the city. TRY THE BETTER CHOICE BEHAVIOR and KNOWLEDGE ABOUT DISTANT AREAS (we did not discuss in this lecture) entail robustness of the urban residential dynamics to unknown distribution of the tolerance level in the population From residential to urban dynamics Residential dynamics in the city, where infrastructure is in development (Yet theory ) Extension of the model of housing Two types of agents: Householders and Developers Our interviews with developers confirm that they think of themselves as optimizers. Q. What do they optimize? A. Profits. Q. How do they optimize? A. By setting the prices of apartments. Q. Why they can be wrong? A. Because they do not know about decisions of the other developers Model of developers and householders in the city The city consists of building sites (of varying size and shape), each belonging to some developer agent. Each site can be built up Depending on demand, the developer continuously reestimates the price of the new construction and potential profit If it is worth developing, the developer builds the site and the newly built dwellings are offered to householder agents. 12

Two sites for development (marked red) Is it worth it for the constructor to take a risk?

status neighborhood 1.5 1.5 RUN RUN 1.0 10.00 1.0 10.00 9.00 9.00.5 8.00.5 8.00 7.00 7.00 0.0 6.00 0.0 6.00 -.5 5.00 4.

13 Two sites for development (marked red) Is it worth it for the constructor to take a risk? Try the better heuristic: Developer s profit Project located within low status neighborhood Project located within high status neighborhood RUN RUN B2P B1P ITER ITER No profits till high status neighborhood is filled Agents status Irrational developers become bankrupt Urban sprawl with developers and householders Agents status Buildings Price Buildings Price t 1 t 2 Wrong developer s decision t 1 t 2 Wrong developer s decision 13

The conclusion of the householders-developers model: Sales and profits in the low status neighborhood remain low as long as dwellings of the better situated project are not filled.

14 The conclusion of the householders-developers model: Sales and profits in the low status neighborhood remain low as long as dwellings of the better situated project are not filled. This brings one more argument in favor of the robustness of the city development: In reality, developers understand customers choice behavior and do not create unrealistic opportunities PROPER URBAN MODEL MUST BE ROBUST to the lack of knowledge regarding most of the dependencies and parameters. Requirement of robustness is equivalent to thinking about urban system as understandable We must shape our models to follow this imperative, and build them in a way that measurable parameters only influence model output quantitatively The phenomena that help in constructing robust models (and partially are confirmed experimentally): Bounded rationality of residential choice (rough reaction to just main factors) Asymmetry of interactions Knowledge of distant/global information! תודה רבה 14

OBEUS. (Object-Based Environment for Urban Simulation) Shareware Version. Itzhak Benenson 1,2, Slava Birfur 1, Vlad Kharbash 1

OBEUS. (Object-Based Environment for Urban Simulation) Shareware Version. Itzhak Benenson 1,2, Slava Birfur 1, Vlad Kharbash 1 OBEUS (Object-Based Environment for Urban Simulation) Shareware Version Yaffo model is based on partition of the area into Voronoi polygons, which correspond to real-world houses; neighborhood relationship