What are we asking about when we ask about the future?

A socio-epistemological perspective on probability questions

Gloria Origgi – InstitutNicod

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

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”

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

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.

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.

The emergence of probabilistic reasoning:

A different interpretation of the present:

not:

causallydetermined by the past

but:

counter-factually determined by the future

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

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.

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

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

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…

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”.

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 2Keynes: Subjective Probability - Popper

Propensity

Notorious Biases

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?

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%)

“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?

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

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?

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.

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!”

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.

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.

Conclusions

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