1. Probability and Causality
in the Social Sciences
Federica Russo
Center Leo Apostel, VrijeUniversiteitBrussel&
Centre for Reasoning, University of Kent

2. Overview:
Probability: syntax and semantics
Probability: my preferred perspective
(Old) results, very briefly
New ideas in progress
Dispersion and variation
Individual and population
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3. PROBABILITY:
‘SYNTAX’ AND ‘SEMANTICS’
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4. A metaphor
Syntax: axiomatisation
Kolmogorov, by and large accepted
Semantics: interpretation
3 major schools:
Logicist
Physical (frequentist and propensity)
Epistemic interpretation (Bayesian)
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5. One approach to probability
What is the meaning of probability?
Not in an ‘absolute’ sense
But relatively to a given scientific context
For instance
Emigration rates in a region and propensity of farmers
migrate (wrt other occupations)
The probability that my gastric ulcer is due to
HelycobacterPilori rather than stress given positive results
at the test
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6. How I got to probability
Accounts of causality
Probabilisticaccounts of causality
Accounts of probability
Statistical studies of populations
Probabilistic models
Accounts of probability
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7. The
philosophical
The empirical problem of
problem of causality
causality
Probabilistic
models in
social
science
Probability and causality
in the social sciences 7

8. A TASTE OF ARGUMENTS
PREVIOUSLY DEVELOPED
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9. Janus-faced probability
A long history, since Pascal and Laplace; the duality
emerged later; plans for unifications
Who’s in the driver’s sit?
Frequency-driven epistemic probabilities
Degrees of belief are shaped upon knowledge of frequencies
Credence-driven physical probabilities
Credence in the truth of a proposition fixes the chance of the
event (as long as evidence does not contradict)
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10. Frequency-driven
epistemic probabilities
Account for different types of probabilistic causal
claims
because they are Janus-faced
Make sense of learning from experience
because they incorporate empirical constraints
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11. Objective Bayesianism
and hypothesis testing
Hypothesis testing compares hypotheses with data
Null hypothesis: observed variation is chancy
Alternative hypothesis: observed variation is real
Test statistic
Null hypothesis is accepted/rejected depending on the
chosen p-value
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12. Probability in hypothesis testing
Evaluate the probability to obtain the sample if the
hypothesis is true
The probability of a hypothesis is single-case
Meaningful for Bayesians, meaningless for frequentists
Probability of which hypothesis? Null or alternative?
Objective Bayesianism treats them on equal footing, unless
evidence suggests otherwise
A problem of evidence, not of type of error
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13. NEW IDEAS TO BE DEVELOPED
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14. Suggested reading
Daniel Courgeau
Probability and
Social Science
(Springer, 2012)
•For the philosopher of
probability interested in
probabilistic approaches in
social science
•For the practicing social
scientists interested in the
foundations of probability
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15. DISPERSION AND VARIATION
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16. Population science studies …
Births, deaths, and migration flows which affects the
population.
The probability of fertility, mortality and migration
[Courgeau 2012, 198]
A tight knot between probability and modelling
in population science
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17. Dispersion
2 meanings of dispersion
PROB: Spread of observations around their central value. Measured
by e.g. variance, standard deviation, variation coefficient …
SOCSC: As heterogeneity, in sub-populations the variable’s mean
and variance are strongly dispersed
Courgeau:
a historical reconstruction of how dispersionPROB,SOCSCis used in
various methods in population science
Here: bring these arguments a step forward
Why is dispersion so important?
From descriptive to causal analysis
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18. Variation
In reasoning about
cause-effect
relations, what notion
guides this reasoning?
Regularity?
Invariance?
Production? ...
Hunting for a rationale
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19. Rationale vsdefinition
Rationale:
a principle/notion/concept underlying
decision/reasoning/modelling
Definition:
A description of a thing by means of its properties or if its
function
Here:
hunting for the notion underlying model building
and model testing: rationale, not definition
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20. Variation in causal models
If we had to be precise:
A statistical model in the form of a set of probability
distributions
A vector X of variables; A vector Θ of parameters …
A decomposition of X in a sequence of marginal and
conditional components
… we’ll take the shortcut
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21. Variation in structural models
Consider a structural equation
Y = X+
Are there meaningful co-variations between X and Y?
Are these variations chancy or causal?
hypothesis testing; invariance; exogeneity
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22. Dispersion ⇄ Variation
A purely probabilistic The analogue concept
description of the regimenting causal
population analysis
PROB: How observations are How the probability of a
spread around a value variables changes with
SOCSC: How variables’ other variables’ change
parameters are dispersed
in sub-populations
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23. INDIVIDUAL AND POPULATION
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24. The concept of population
“Aggregate of individuals which conform to a given
definition” [Ryder 1964, quoted in Courgeau 2012, p. 196]
Spatial and temporal specificity
Example criteria: political, economic, religious, social, …
Overlapping populations
Here, physical probability, mainly frequentist
Measure general characteristics of groups
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25. The concept of individual
Individuals in a population
Only a small number of phenomena
and of characteristics of these individuals
“We shall create an abstract fictitious individual, the
statistical individual, as distinct from the observed
individual. The statistical individual will experience event
that obey the axioms of probability theory chosen to treat
the observations” [Courgeau 2012, p.197]
Thus we can also study individual-level data (and the effects of
aggregate characteristics on them)
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26. How can we go back
to the observed individual?
Actuarial cases
How much should my car insurance be?
Socio-economic intervention
How likely is this unemployment programme
to work for Mr Rossi?
Epidemiology and medicine
If I take contraceptive pill X, will Idevelop thrombosis?
Did working at Eternit cause Mr Rossi and Mr Bianchi to
develop lung cancer?
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27. The population to help the individual?
How can we combine knowledge of aggregates to
calculate single-case probabilities?
Objective Bayesianism:
“Degrees of beliefs should be probabilistic, calibrated with
evidence, and otherwise equivocal.” [Williamson 2010]
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28. To sum up
Many ways of looking at probability – the one I like:
What probability in a given scientific context?
In the past, explored links between frequencies and objective
Bayesianism
To have a grip on empirical data
To revisit hypothesis testing
Courgeau’s book prompts new paths of research
Dispersion and variation
Statistical individual, population, and observed individual
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29. To conclude
An exercise that shows
Useful interactions between probability
theory, population science, and philosophy
How intertwined descriptive and causal analysis are
How much abstract theory and empirical data help
each other in constructing knowledge
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