Institut für Politikwissenschaft
Schwerpunkt qualitative empirische Sozialforschung
Goethe-Universität Frankfurt
Fachbereich 03
Prof. Dr. Claudius Wagemann
Qualitative Comparative Analysis (QCA)
and Fuzzy Sets
29 April 2013:
The Analysis of Necessary and Sufficient
Conditions
Sufficient Conditions
X
Y
0
0
Situation not relevant (but allowed)
0
1
Situation not relevant (but allowed)
1
0
Situation NOT allowed
1
1
Situation allowed
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
2
Asymmetry for Sufficient Conditions
02.05.2013
Y=1
Cases
Cases
Y=0
Cases
No Cases
X=0
X=1
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
3
Venn Diagram for Sufficient Conditions
Y
X
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
4
Sufficient Conditions in csQCA
1
Cases
allowed
Cases
allowed
Y
Cases
allowed
0
0
02.05.2013
Cases NOT
allowed
Sufficient Condition
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
1
5
Sufficient Conditions in fsQCA
1
Cases
allowed
X<Y
Y
Cases NOT
allowed
X>Y
0
0
02.05.2013
Sufficient Condition
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
1
6
Example for a Sufficient Condition
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
7
Necessary Conditions
X
Y
0
0
Situation not relevant (but allowed)
0
1
Situation NOT allowed
1
0
Situation not relevant (but allowed)
1
1
Situation allowed
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
8
Asymmetry for Necessary Conditions
02.05.2013
Y=1
No Cases
Cases
Y=0
Cases
Cases
X=0
X=1
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
9
Venn Diagram for Necessary Conditions
X
Y
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
10
Necessary Conditions in csQCA
1
Cases NOT
allowed
Cases
allowed
Y
Cases
allowed
0
0
02.05.2013
Cases
allowed
Necessary Condition
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
1
11
Necessary Conditions in fsQCA
1
Cases NOT
allowed
X<Y
Y
Cases
allowed
X>Y
0
0
02.05.2013
Necessary Condition
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
1
12
Rules on Sufficiency and Necessity
• Sufficiency
Membership scores in the condition are smaller
or the same as in outcome (X  Y)
XY
• Necessity
Membership scores in the condition are larger or
the same as in outcome (X  Y)
XY
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
13
Sufficient and Necessary Conditions
X
Y
0
0
Situation not relevant (but allowed)
0
1
Situation NOT allowed
1
0
Situation NOT allowed
1
1
Situation allowed
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
14
Symmetry (!) for Necessary and
Sufficient Conditions
02.05.2013
Y=1
No Cases
Cases
Y=0
Cases
No Cases
X=0
X=1
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
15
Venn Diagram for Necessary and
Sufficient Conditions
X=Y
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
16
Example
Conditions
Outcome
Cases
A
B
C
Y
ARG
1
1
1
0
PER
1
0
0
0
BOL
1
1
0
0
CHI
0
1
0
1
ECU
1
0
0
0
BRZ
0
1
1
1
URU
1
0
1
1
PAR
0
0
1
1
COL
VEN
0
1
0
1
0
1
1
0
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
Y = stable democracy
A = violent breakdown
B = ethnic homogeneity
C = fragmented party system
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Example
Conditions
Complements
Outcome
Cases
A
B
C
~A
~B
~C
Y
ARG
1
1
1
0
0
0
0
PER
1
0
0
0
1
1
0
BOL
1
1
0
0
0
1
0
CHI
0
1
0
1
0
1
1
ECU
1
0
0
0
1
1
0
BRZ
0
1
1
1
0
0
1
URU
1
0
1
0
1
0
1
PAR
0
0
1
1
1
0
1
COL
VEN
0
1
0
1
0
1
1
0
1
0
1
0
1
0
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
18
Example
Conditions
Combinations
Outcome
Cases
A
B
C
AB
ABC
~BC
Y
ARG
1
1
1
1
1
0
0
PER
1
0
0
0
0
0
0
BOL
1
1
0
1
0
0
0
CHI
0
1
0
0
0
0
1
ECU
1
0
0
0
0
0
0
BRZ
0
1
1
0
0
0
1
URU
1
0
1
0
0
1
1
PAR
0
0
1
0
0
1
1
COL
VEN
0
1
0
1
0
1
0
1
0
1
0
0
1
0
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
19
Solution of the Analysis
~A + ~B*C → Y
“INUS” conditions:
Insufficient but
Necessary part of a condition which is itself
Unnessary but
Sufficient for the result
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
20
Any Necessary Condition?
Conditions
Outcome
Cases
A
B
C
Y
ARG
1
1
1
0
PER
1
0
0
0
BOL
1
1
0
0
CHI
0
1
0
1
ECU
1
0
0
0
BRZ
0
1
1
1
URU
1
0
1
1
PAR
0
0
1
1
COL
VEN
0
1
0
1
0
1
1
0
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
21
Any Necessary Condition?
Conditions
Unions
Outcome
Cases
A
B
C
A+B
~A + C
A+B+C
Y
ARG
1
1
1
1
1
1
0
PER
1
0
0
1
0
1
0
BOL
1
1
0
1
0
1
0
CHI
0
1
0
1
1
1
1
ECU
1
0
0
1
0
1
0
BRZ
0
1
1
1
1
1
1
URU
1
0
1
1
1
1
1
PAR
0
0
1
0
1
1
1
COL
VEN
0
1
0
1
0
1
0
1
1
1
0
1
1
0
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
22
Solution of the Analysis
~A + C  Y
Also:
(~A + C) * (~A + ~B)  Y
“SUIN” conditions:
Sufficient, but
Unnecessary part of a factor that is
Insufficient but
Necessary for the result
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
23
Example
Conditions
Outcome
Cases
A
B
C
Y
ARG
0.8
0.9
1
0.1
PER
0.7
0
0
0.2
BOL
0.6
1
0.1
0.3
CHI
0.3
0.9
0.2
0.6
ECU
0.9
0.1
0.3
0.4
BRZ
0.2
0.8
0.9
0.7
URU
0.9
0.2
0.8
0.8
PAR
0.2
0.3
0.7
0.9
COL
VEN
0.2
0.9
0.4
0.7
0.4
0.6
1
0.3
02.05.2013
Qualitative Comparative Analysis (QCA) and
Fuzzy Sets
Y = stable democracy
A = violent breakdown
B = ethnic homogeneity
C = fragmented party system
24