A Refresher on Theory and Explanation
in Sociology
Micro-Macro Links in Sociology
Werner Raub
Workshop on Social Theory, Trust, Social Networks,
and Social Capital II
National Chengchi University – NCCU
April 2011
Agenda for the two
introductory sessions
• Basic features of problem-driven and
systematic (deductive) theory
construction, model building and
explanation in social science…
• … by way of examples
• Focus on micro-macro links in theory and
research in sociology
• Some “take home messages”
1
Sociological theory according to the
“analytical tradition”
• Sociology = research on social
phenomena (i.e., macro-phenomena) and
their social macro-conditions (“causes”);
compare Durkheim’s “minimal program”
• Sociological theory explains social
phenomena by showing how they come
about as (often unintended) results of
individual behavior that is affected by
social conditions.
Useful tools for summarizing and
reconstructing social science theory and
research
• Problems as a starting point for theory
formation and empirical research
P1

Problem
T1 
E1

Theory
Empirical Research
P2
...
New Problem
• Coleman’s scheme for macro-micro-macro
transitions
• A scheme representing the structure of social
science explanations
2
James Coleman (1926-1995)
Coleman’s scheme for macro-micromacro transitions
Social
conditions
Macro
outcomes
Macro
1
Micro
2
3
Individual
effects
Preferences,
information
1: Bridge
assumptions
3. Behavioral
theory
2. Transformation
rules
Coleman’s scheme and the structure of
explanations in sociology I
1. General laws
Explanans
2. Initial conditions:
Social conditions
Deduction
Description of the
phenomenon to be explained
Social phenomenon
Explanandum
Adequacy conditions for explanations
1.
2.
3.
4.
The explanandum is a logical consequence
of the explanans.
The explanans contains at least one general
law.
The explanans has empirical content (i.e., is
testable).
The explanans is true/empirically
supported.
(See Hempel & Oppenheim, Studies in the
logic of explanation, 1948)
48
Coleman’s scheme and the structure of
explanations in sociology II
Behavioral theory
(arrow 2)
Transformation rules
(arrow 3)
Bridge assumptions
(arrow 1)
Additional boundary
conditions
Initial conditions
• Macro-conditions (node A)
• Micro-conditions (node B)
Individual effects
(node C)
Individual effects
(node C)
Collective phenomena and
processes (node D)
Three examples
• Two highly simplified examples from Coleman
1990, 1987
• Max Weber: the spirit of capitalism
• Occurrence of a panic
• One more elaborate (though still highly
stylized) example
• Schelling’s model of residential
segregation
3
Max Weber: the spirit of capitalism
Protestant religious
doctrine
Capitalism
Macro
Micro
Economic behavior
Values
4
The panic example
Fire alarm in a crowded
theater
Panic or
order
Macro
Micro
Run to exit /
transfer control
conditionally
Utility structure for
alternative actions
5
A somewhat more complex example:
residential segregation
A sociologically uninformed
common-sense theory
versus
Schelling’s models of segregation
6
Examples of segregation phenomena
•
Segregation by ...
• ethnicity (race)
• religion
• wealth
8
Residential segregation: a (very) rough
definition
• Consider a city with X% ‘Whites’ and Y%
‘Non-Whites’
• The city consists of a number of
neighborhoods.
• ‘Perfect integration’ := Each neighborhood
consists of X% ‘Whites’ and Y% ‘Non-Whites’.
• ‘Perfect segregration’ := Each neighborhood
is either 100% ‘White’ or 100% ‘Non-White’.
• Roughly: A city is more integrated, the
‘closer’ the neighborhoods approximate the
case of ‘perfect integration.’ And a city is
more segregated the ‘closer’ the
neighborhoods approximate the case of
‘perfect segregation.’
10
Data on residential segregation:
United States, 1940-1960
• Indices of residential segregation by race, 109 cities,
for 1940, 1950, 1960.
Source: JS Coleman, Resources for Social Change: Race in
the US. NY: Wiley 1971, p. 9.
The indices are measures of the % of blacks who would have to
move in order to achieve residential homogenization by race. An
index of 0 would indicate no racial segregation among blocks. A
score of 100 would mean that each block is either all white or
all black.
11
Data on residential segregation in the
US, 2005-2009
• The New York Times offers a resource
providing quite up to date and
comprehensive data on residential
segregation in the US, see:
http://projects.nytimes.com/census/2010/explorer
• Screening this site is recommended!
Residential segregation: some types of
problems
1. Descriptive problems
Trends over time
Cross-section: comparing North and South
2. Explanatory problems – our focus
Why is residential segregation rather stable over time?
Why are there hardly any differences in residential
segregation between North and South?
3. Problems of institutional design
How to reduce or mitigate residential segregation?
4. Normative problems
How much residential segregation is normatively
acceptable?
What are acceptable costs of reducing or mitigating
residential segregation?
12
Residential segregation: possible causes
•
Actors’ preferences and perceptions
– Prejudice
– Perception of unwelcome by-effects
of integration
•
Constraints
– income inequality / prices on the
housing market
– legislation
Etc.!
13
Common sense-theory
% of whites
approving
integration
residential
segregation
14
The stability of residential segregation
over time: sketch of an explanation
Common sense-theory:
• percentage of whites
residential
approving residential integration   segregation 
Antecedent condition:
• In the US (North and South), the percentages of whites
approving residential integration has been appr.
constant between 1940 and 1960.
______________________________________________
• In the US (North and South), residential segregation has
been appr. constant between 1940 and 1960.
Note: We shall see that this explanation is not adequate!
15
Similarities in residential segregation
between North and South: sketch of an
explanation
Common sense-theory:
• percentage of whites
residential
approving residential integration   segregation 
Antecedent condition:
• In the US (between 1940 and 1960), there are no
systematic North-South differences in the percentage of
whites approving residential integration.
______________________________________________
• In the US (between 1940 and 1960), there are no
systematic North-South differences in residential
segregation.
Note: We shall see that this explanation is not adequate!
16
Science as a systematic
test of theories
17
The logic of empirical tests of theories
4.1
1
Propose a theory / hypothesis
2
Derive empirically testable implications
3
Compare these implications with data
Corroboration
4.2
Refutation
of the theory
of the theory
18
Table I-3 and I-25 combined. Indices of residential
segregation by race, 109 cities, for 1940, 1950,
1960, and percentage of whites who approve
residential segregation in 1942, 1956, June and
December 1963, 1965, 1968ª
ª Source: For residential segregation see Table I-3. For attitudes towards residential
integration the question asked was, “ If a Negro with the same income and
education as yours moved into your block, would it make any difference to you?”
Data on 1942, 1956, 1963 from Paul B. Sheatsley (1996, Table I, p. 222). Data on
1965, 1968 by personal communication from Paul B. Sheatsley (July 1, 1969)
unpublished data from NORC surveys of October 1965 and April 1968.
19
An empirical test of the common sensetheory of residential segregation
1. Common sense-theory (hypothesis):
% of whites
residential
approving residential integration   segregation 
2. Implications:
Trend: If the percentage of whites approving integration
increases in the US (North and South) between 1942 and 1956
as well as between 1956 and 1963, then residential segregation
decreases in the US (North and South) in both periods.
Comparison North-South: If the percentage of whites approving
integration is higher in the North than in the South of the US in
the forties, fifties, and sixties, then residential segregation is
lower in the North than in the South of the US in all three
periods.
3. Comparison with data (from Coleman, 1971 and Sheatsley, 1966).
4.
Refutation of common sense theory of residential segregation.
20
Schelling’s models of segregation
23
Thomas Schelling
24
Residential segregation:
summary of the problem situation
25
Schelling’s game
1. Initial state (residential integration)
•
•
•
•
•
Unidimensional town: from left to right,
70 pieces (households) are spread out
in a line.
Two ethnicities: each piece is black or
white
The color of each piece is decided by
throwing a dice.
1,2,3: black piece
4,5,6: white piece
26
2. Definition of the neighborhood of a piece
(neighborhood of a household)
• The neighborhood of a piece consists of
the piece itself, the four pieces to the left,
and the four pieces to the right
• Pieces near the end of the line have less
neighbors (alternative: circle)
oo#o#oo##
Neighborhood
27
Neighborhood and interdependence
• Neighborhood of a piece = neighborhood
of a household
• Note: interdependence between
households: if A and B are neighbors,
(color of) A affects composition of B’s
neighborhood and vice versa
• Interdependence as a social condition for
residential segregation in addition to
preferences and perceptions of actors
28
3. Moving pieces I
• The game proceeds in rounds (segregation as
a dynamic process).
• At the beginning of each round, each piece in
a neighborhood where more than half of the
neighbors have the opposite color is marked
• Preferences of households: avoid a
minority situation
• Social condition: composition of
neighborhoods
• Individual motives (avoiding a minority
situation) versus collective effects
(segregation)
• Order of moving: marked pieces move in turn,
counting from left to right.
29
Moving pieces – interpretation
• The preference of households to avoid a minority
situation is consistent with different more specific
assumptions:
• One prefers segregated over integrated
neighborhoods (“white prejudice”)
• One prefers an integrated (50-50)
neighborhood to any other other composition
as long as one is not in the minority situation
(“preference for residential integration”)
• One is indifferent with respect to to
neighborhood composition as long as one is
not in the minority situation
• Hence, Schelling’s rules and assumptions are
consistent with the assumption of preferences for
integration!
30
An observation on the “spirit” of
Schelling’s models
• Schelling’s rules and assumptions are in a
sense very “optimistic” with respect to
“prospects for residential integration”
• He tries to show precisely that extreme
residential segregation can emerge even
under seemingly favorable conditions for
integration
• Complex relationship between individual
motives (avoiding minority situation) and
collective effects (extreme residential
segregation)
• Residential segregation as an unintended and
unfavorable (suboptimal) outcome for the
actors
31
Moving pieces II
• How pieces move: a piece moves to the
nearest point between two other pieces
to the right or to the left where it is not a
minority.
• Interpretation
• Moves are costly; costs increase in
distance
• No scarcity on the housing market
• No legal or economic constraints to
choosing certain neighborhoods
• No discrimination on the housing
market
32
Moving pieces III
• If the neighborhood of a marked piece has
changed such that not more than half of the
neighbors have the opposite color when the
turn to move comes, the marked piece does
not move after all
- Interdependence between households.
• End of a round: each piece that has been
marked at the beginning of the round has had
a turn to move
• End of the game: each piece has a
neighborhood with at least half of the
neighbors of the same color (or: there are no
suitable places to move to)
33
Example (compare Schelling 1969: 490,
1971: 149-151)
1.
Start situation:
o#ooo##o#oo##oo###o##o##oo##oo##oo##o#o#oo###
o##ooooo###ooo#oo##o#o##o
2.
Situation after round 1
oooooooo####o#########oooo##ooo#o#o###o#####
####oooooooooooooooo######
3.
Situation after round 2
oooooooo###############oooooooooo###########
####oooooooooooooooo######
34
Important features of Schelling’s model
• The model shows that high levels of
segregation can result from rather
tolerant individual preferences
• High levels of segregation can result from
both tolerant and intolerant preferences
• Schelling makes the micro-macro link
explicit
• The model allows for derivation of new
implications
35
“Changing support for integration” and
“differences in support for integration”
•
•
Background: the data on residential
segregation for the United States
Question: how to conceptualize
“increasing support for integration
within a region” and “differences in
support for integration between
regions” within Schelling’s model?
36
“Changing support for integration” and
“differences in support for integration”
•
•
•
Consider the following preferences for
neighborhood composition that are all
consistent with a 50%-threshold for moving:
Most preferred is...
1. complete segregation...
2. much segregation...
3. some segregation...
4. perfect integration...
and in all cases 1 – 4 one moves as soon as one
is in the minority position
Clearly, “support for integration” increases
when preferences shift from 1 to 4
NOTE: under each of the 4 types of preferences,
extreme segregation results
36
Schelling’s model versus the “common
sense theory”
• Schelling’s model improves on the common sensetheory in two respects:
• Empirically: Schelling’s model is consistent
with a ‘weak’ relation between prejudice and
segregation.
• Over time increasing support for integration
need not reduce segregation.
• Two regions that differ with respect to
support for integration can be similar with
respect to segregation levels.
• Theoretically: Schelling’s model (but not the
common sense-theory) is consistent with the
“minimal program of sociology”: explaining
macro-phenomena as a result of macro-conditions
and incentive-guided (goal-directed) behavior
37
Table I-3 and I-25 combined. Indices of residential
segregation by race, 109 cities, for 1940, 1950,
1960, and percentage of whites who approve
residential segregation in 1942, 1956, June and
December 1963, 1965, 1968ª
ª Source: For residential segregation see Table I-3. For attitudes towards residential
integration the question asked was, “ If a Negro with the same income and
education as yours moved into your block, would it make any difference to you?”
Data on 1942, 1956, 1963 from Paul B. Sheatsley (1996, Table I, p. 222). Data on
1965, 1968 by personal communication from Paul B. Sheatsley (July 1, 1969)
unpublished data from NORC surveys of October 1965 and April 1968.
38
Some further questions on Schelling’s
models
• Does segregation always emerge? And how stable
is integration?
• Integrated initial states
#0#0#0#0#0 ...
0#0#0#0#0# ...
...
• Probability for such states is very small
• These states are unstable under “external
shocks” such as “forced movements” or inand out-migration of households
• Note: the final states in Schelling’s model are
stable relative to such “external shocks
Schelling’s model: unrealistic and
simplifying assumptions
1.
2.
3.
4.
One-dimensional town
Order of moving
Two groups of similar size
Homogeneity assumption with respect to:
• Neighborhood size
• Preferences of neighborhood composition
5. No scarcity on the housing market
6. No legal or economic constraints to
choosing certain neighborhoods
Problem: derive implications of more realistic
and less simplifying assumptions
39
A two-dimensional variant
Initial Situation
Resulting Situation
40
Reconstruction of Schelling’s model
41
Schelling’s model and Coleman’s scheme
42
Social change in Coleman’s scheme
43
Recent literature on residential segregation
• Fossett, Mark (2011) Generative models of
segregation: Investigating model-generated
patterns of residential segregation by
ethnicity and socioeconomic status,
forthcoming in Journal of Mathematical
Sociology 35(1) – up to date extension of
Schelling-type models; will be available on
Studion
• Bruch, Elizabeth & Robert Mare (2009)
Segregation Dynamics, pp. 269-293 in Peter
Hedström & Peter Bearman (eds.) The Oxford
Handbook of Analytical Sociology, Oxford:
Oxford University Press.
44
Conclusions:
Some “take home messages” for theory
construction and model building in sociology
45
Some general features of theory construction
• The P-T-E-scheme: Sociology starts from
Problems, Theories provide tentative
solutions (answers) to these problems, and
Empirical research is used to scrutinize (test)
the adequacy of these answers. Research
typically generates new problems, initiating a
new P-T-E-sequence.
• The logical structure of theories, hypotheses,
and explanations
• The logic of empirical tests of theories
46
Coleman’s scheme for macro-micromacro transitions
Social
conditions
Macro
outcomes
Macro
1
Micro
2
3
Individual
effects
Preferences,
information
1: Bridge
assumptions
3. Behavioral
theory
2. Transformation
rules
Coleman’s scheme and the structure of
explanations in sociology II
Behavioral theory
(arrow 2)
Bridge assumptions
(arrow 1)
Initial conditions
• Macro-conditions (node A)
• Micro-conditions (node B)
Individual effects
(node C)
Transformation rules
(arrow 3)
Additional boundary
conditions
Individual effects
(node C)
Collective phenomena and
processes (node D)
A brief note on terminology:
theory – hypothesis – explanation –
testable implication
1.
Two (different) meanings of “theory”
(a) A set of hypotheses (other label for “hypothesis”:
proposition)
•
Note: sometimes, such a set of hypotheses is “structured” in the
sense that there are some “basic” hypotheses (often labeled
“axioms”), while other hypotheses (sometimes labeled “lowerlevel hypotheses”) are implications of the basic hypotheses /
axioms.
(b) An explanation
2. Two (different) meanings of “hypothesis”
(a) An element of a theory in the sense of 1.a above.
(b) An empirically testable implication that follows from a theory
and additional assumptions.
•
Note: there is no “true” meaning of “theory” or of
“hypothesis” (and in the literature you may encounter
additional meanings not mentioned above). Often, you will
have to conclude from the context, which meaning an
author has in mind.
49
The logic of empirical tests of theories
4.1
1
Propose a theory / hypothesis
2
Derive empirically testable implications
3
Compare these implications with data
Corroboration
4.2
Refutation
of the theory
of the theory
18
The logic of empirical tests of theories
• Note: testing theories empirically is a complex
enterprise involving more than “directly”
confronting a theory or hypothesis with empirical
findings:
• Theories have to be reconstructed in a
systematic way so that testable implications
can be derived.
• Derivation of testable implications: “sociology
in action” (and science generally) typically
involves argumentation, that is, the derivation
of implications from assumptions – doing
sociology (and science in general) is more than
producing theories and empirical evidence, it is
also about the links between theories and
evidence.
50
Theoretical models
• The “T” in a P-T-E scheme is often a
theoretical model.
• A theoretical model comprises two elements
(compare the explanations and the
explanandum of a deductive explanation):
1. A set of (often relatively abstract and
almost always simplified) assumptions.
2. Implications of these assumptions
Note: a major task involved in model
building is to show that these
implications do indeed follow from the
assumptions
52
Theoretical models
•
After a model has been constructed (= the
assumptions have been introduced) and analyzed (=
implications/hypotheses have been derived), two
further steps typically follow:
1. Derivation of testable implications for empirical
research (note: this is part of the “E” in the P-T-E
scheme) as well as derivation of policy
implications
2. The method of decreasing abstraction –
elaborating and improving the model in a
stepwise fashion: step by step, simplified
assumptions are replaced by more realistic ones,
while checking the implications of more realistic
assumptions (leading question: how robust are
the implications of the model relative to
modifications of assumptions of the model?)
53
Assumptions on individuals: goaldirected (incentive guided) behavior
• Actors have:
• Alternative actions,
• Goals, i.e., they evaluate the possible
outcomes of their actions,
• Expectations (or information) on the
“states of the world” (for example,
expectations on certain “contingencies” or
on the behavior of other actors).
• They choose the action that seems most
appropriate, given their expectations, to
realize their goals.
54
What is taken into account at the macro
level?
• Relations (networks) and
interdependencies between actors
• Institutions (in the sense of organizations
as well as rules and norms)
• Aggregate effects (frequencies, averages,
variance distributions)
• Collective phenomena as unintended
consequences of incentive-guided
behavior.
Related research programs in the
landscape of the social sciences
1. Scottish moralists (A. Smith, D. Hume, etc.)
2. (Contemporary) sociology
• Analytical sociology, broadly conceived
• US: J. Coleman, D. Heckathorn, M. Macy etc.
• Europe: R. Boudon, K.D. Opp, H. Esser, A. Diekmann, R.
Ziegler, J. Goldthorphe, P. Hedström, P. Abell, ICS, etc.
(structural-individualistic approach)
• Intersection of analytical sociology and network theory (R.
Burt, M. Granovetter, etc.)
• Social exchange theory (P. Blau, G. Homans, etc.)
3. Political science
• Economic theory of politics; public choice (K. Arrow, A.
Downs, J. Buchanan & G. Tullock, M. Olson, W. Riker, P.
Ordeshook, etc.)
59
Related research programs in the
landscape of social sciences
.
Economics
• Economic approach to human behavior (G. Becker etc.)
• New institutional economics (R. Coase, O. Williamson, D.
North, etc.)
5. Also
• Social psychology: research on social dilemmas (R. Dawes
etc.)
• Interdisciplinary research on incentive-guided behavior,
bounded rationality, etc. (H. Simon, D. Kahneman, A.
Tversky, etc.)
• Game Theory and its application in various social sciences
(T. Schelling, R. Selten, J. Harsanyi, D. Kreps, etc.)
60
Some books with a similar perspective on social
science theory and research
61
An advanced textbook and a handbook
62
Some modern classics
• Robert K. Merton, Social Theory and Social Structure, rev
and enl. ed. New York: Free Press 1968 (original 1957)
63
Some modern classics
64
Some modern classics
65
Coleman, Foundations of Social Theory
66
Two recent books that elaborate on
various topics that have been discussed
67