Questions about the future are very often probability questions. Probability is a fascinating field of philosophical enquiry. On the one hand the philosophy of probability has concentrated on the double face of the concept. It is statistical, concerning itself with stochastic laws of chance processes. It is also epistemological, dedicated to assessing reasonable degrees of belief in propositions quite devoid of statistical background. On the other hand, it has concentrated on the relation between probability estimations and decision theory, that is, the utility functions associated with a certain outcome when a subject has to decide how to act upon an estimate of the future. We argue here that a deeper and, surprisingly neglected, philosophical issue about the double face of probability is the following: the probability of a fact and its impact (objective or subjective) are two distinct phenomena, sometimes confused when talking about probability. I can have a precise measure of the impact of a fact (if a tsunami takes place in Jakarta, there will be 5000 deaths) and yet have a much less precise measure of its probability. Impact questions and probability questions are often confused. We will provide example of this distinction and also, if, possible, some remedies.

1. What are we asking about when we
ask about the future?
A socio-epistemological perspective
on probability questions
Gloria Origgi – InstitutNicod

2. On ne saitjamaisexactementquand les gens
basculent d’un cotéoul’autre de la
vie, c’estunesomme de petitsriens qui
vousentraînent, calamités
imperceptibles, désastresindistincts.
Michaël Ferrier, Tokyo, Petits Portraits de
l’Aube, Arléa, Paris, 2010

3. Social Epistemology
The study of the social, cognitive, institutional
and cultural constraints on the
production, distribution and stabilization of
knowledge (valid, justified beliefs).
• Trust
• Reputation
• Indicators
• Predictive “style of thought”

4. Since the introduction of writing, at the end of
the 4th millennium BCE in Mesopotamia, our
cultural timeline is organized on a vertical
arrow:
past -> present ->future

5. A science of predictions?
• Probability calculus
• Pascal-Fermat correspondence in 1654:
• Division of the stakes, that is how to divide a
prize pot in a two-players game in which the
two players have won each a certain number
of rounds and the game is interrupted before
the end.

6. A Future-Oriented Solution:
• Pascal and Fermat famously solved the
problem by insisting not on the history of the
previous rounds, but on the probabilities of
winning future rounds were the game not
interrupted.
• The Beginning of Modern History of
Probability: it introduced the concept of
expectation, that is, of average payoffs in a
long run of similar gambles.

7. The emergence of probabilistic
reasoning:
A different interpretation of the present:
not:
causallydetermined by the past
but:
counter-factually determined by the future

8. Hacking: Probabilistic Reasoning as a
New “Style of Thought”
The difference from causal reasoning is that:
Instead of focusing on how a certain event
came to be, probabilistic reasoning focuses on
what could have happened instead

9. Probabilities and Causes
Probability teaches us to deal with states of
affairs we do not know either because of
ignorance or because they did not take place.
Counterfactual events do not have causal
power, because they don’t take place. They
are causally inert.

10. Probability is not just about the
Future:
• The unknown is everywhere, in all time
dimensions
• Taming the unknown means learning to care
about things we do not see, we cannot control
and therefore, we cannot determine their
causal powers on events

11. Present concerns with the Unknown:
• The existence of God (Pascal’s wage)
• The quick diagnosis of a patient’s illness in a
hospital’s emergency room (very present
problem!)
• The conditional probability of someone having
a certain condition (being a genius, being
rich, being infected by a disease) given the
evidence

12. Past concerns with the Unknown
• The probability that my mother was an
academic given that I am an academic
• The probability of being born with of a certain
distribution of genetic material in my DNA
given my present physical dispositions
• The probability of an historical event (the big-
bang, the extinction of dinosaurs) given the
present state of the world…

13. Different interpretations of probability:
1. A quasi-logical concept, which is meant to measure
objective evidential support relations. For
example, “in light of the relevant seismological and
geological data, it is probable that California will
experience a major earthquake this decade”.
2. An agent's degree of confidence, a graded belief. For
example, “I am not sure that it will rain in Canberra
this week, but it probably will.”
3. An objective concept that applies to various systems
in the world, independently of what anyone thinks.
For example, “A particular radium atom will decay
probably decay within 10,000 years”.

14. Subjective vs. Objective interpretations
of Probability
Hacking: “On the one side it is
statistical, concerning itself with stochastic laws
of chance processes. On the other side, it is
epistemological, dedicated to assessing
reasonable degrees of belief in propositions quite
devoid of statistical background”..
Condorcet: facilité, (stochastical) motif de croire
(epistemological)
Carnap: Probability 1 – Probability 2
Keynes: Subjective Probability - Popper
Propensity

15. Notorious Biases

16. Base-rate Fallacy
A cab was involved in a hit-run accident at night. Two
cab companies, the Green and the Blue, operate in the
city. You are given the following data:
• 85% of cabs in the city are Green and 15% are Blue
• A witness identified the cab as Blue. The court tested
the reliability of the witness and concluded that the
witness correctly identified each one of the two colors
80% of times and failed 20% of time
• What is the probability that the cab involved in the
accident was Blue rather than Green?

17. Solution
• In absence of the witness, the probability that of
the guilty cab being Blue is 15%, which is the base
rate of that outcome.
• If the distribution of cabs were 50/50, the base
rate would be uninformative and the only
relevant information would be the witness’
testimony.
• Bayes’s rule: combine the two: 41%.
• Most people ignore the base rate and go with the
witness (80%)

18. “Causal” Variant
• The two companies operate the same number of
cabs, but Green cabs are involved in 85% of
accidents
• A witness identified the cab as Blue. The court
tested the reliability of the witness and
concluded that the witness correctly identified
each one of the two colors 80% of times and
failed 20% of time
• What is the probability that the cab involved in
the accident was Blue rather than Green?

19. What Do People Say?
• The give a considerable weight to the base-
rate and ignore the witness. The car must
have been Green…
• Causal readingsuppresses statistical one

20. Gambler’s Fallacy
You are playing at the Casino de Monaco and
red has come out 6 times. What is more
probable that, in the next game: red or black?

21. The Gambler’s Fallacy is a Causal
Fallacy
• The gambler thinks that black is more
probable because red came out 6 times.
• A tendency to think that past events have a
causal power on future events.
• Statistics says that “in the long run”, in a series
of trials, the average value comes closer to the
expected value (law of large numbers)
• But it insists on the independence of trials.

22. Causal readings and the Future
• What do we want to predict?
– Rare, extreme events
– Black Swans
• The problem with the unbiased readings is
that they allow you to predict only a uniform
future.
• You will never be able to say “I thought so!”

23. Predictions, probabilities and utilities
• Estimate the probability of an event x
• Estimate the utility u(x) of the event x, that
is, what is the best course of action I can
choose given the risks (decision theory). I can
calculate if it is rational, for example, to bet on
a horse, given the probability of its winning
the race.
• Estimate the impact of x, that
is, independently of my course of action.

24. We can predict impact of x better than
x and act upon it
• The probability of a tsunami in Naples is 0.2
• The impact of a tsunami in Naples is
independent of its probability: it will cause
1000 casualties and more than one hundred
million dollars of physical damages.
• Acting upon impact can be easier than acting
upon probabilities of an event.
• Impact of rare events.

25. Conclusions
Some biases in reading the future are perhaps
cognitively bad, but epistemologically
necessary.