Information cascade and division of cognitive labor

The value of informational cascade within scientific practiceThe sequential division of cognitive labor

The parallel organization of cognitive labor solution

Informational cascade and the division of cognitivelabor

Raphaël Künstler

University of Provence

6 december 2012

Raphaël Künstler titre court



Informational cascade and a scientific practiceThe positive value of IC for the scientific practiceThe negative value of IC for the scientific practice

Sommaire

1 The value of informational cascade within scientific practiceInformational cascade and a scientific practiceThe positive value of IC for the scientific practiceThe negative value of IC for the scientific practice

2 The sequential division of cognitive laborEmpty questionsThe sequential division of cognitive labor solutionThe inapplicability of this solution

3 The parallel organization of cognitive labor solutionEpistemic jumpsA prescription for the scientific practice to avoid IC’s badconsequences





Definition of informational cascade

Informational cascade is a sequence of decisions where it isoptimal for agents to ignore their own preferences and imitatethe choice of the agent or agents ahead of them[Bickhchandani, Hirshleifter and Welch] (1992)In order to apply this definition to epistemological contexts, wehave to assume a structural analogy between taste orpreference on the one hand, and belief on the second hand.Once this analogy is made, there are still several possible waysto apply IC to epistemological situations.





Three interpretations of informational cascades

1 An agent has an information p but still believes than ¬p2 An agent belives p but still accepts that ¬p3 An agent has an information q that gives him a good reason

for believing that ¬p, but still believes that q (because manypeople believe that p).

In this paper, I will use the third interpretation.





A dynamic representation of IC within an epistemic context

It is useful to represent the situation in a dynamic fashion.1 An individual has good reasons to believe that q, for instance,

he knows that p and that p → q.2 This individuals learns that everyone believes that ¬p.3 An informational cascade phenomenon occurs if this new

information leads this individual to accept that ¬p.

The no brainwashing assumptionAn individual who comes to believe that ¬p because of IC, stillbelieves that p → q and that p.





IC within a scientific context

1 Pedagogical context2 Heuristic context





The normative approach

1 A meaningful questions. Herding vs. IC : mechanical processvs. rational process.

2 An evaluative questions Ñ Following Goldman, the veritisticnormative question aims at estimating whether a practice islikely to procure or not true beliefs.

3 A prescriptive questions Ñ If a practice has a low veritisticvalue, we have to to wonder what to change to increase thisvalue.

4 What is the predictable outcome of scientific practice involvingIC ?

5 If IC has a low epistemic value and if it IC is unavoidable, howshould we organize scientific practice in order to save it fromthese bad consequences ?





The pedagogical context

IC can be regarded as a situation opposing laymen / experts.The consensus is regarded as a sign of truth.Such a reasoning is necessary to adopt a learning attitude.The student knows that there are reasons to renounce hisopinions, even though he still does not know what are thesereasons.





The heuristic context : an obvious answer ?

1 What is the epistemic value of this situation from the heuristicpoint of view ?

2 If this heuristic value is negative : how to avoid such asituation ?

A (simple) thought experiment on Galileo’s case.To prove that cognitive independence is an epistemic virtue, wehave first to prove that it has good epistemological outcomes.





Kuhn’s argument for the epistemic value of dogma inscientific practice

Popper’s rule : If the empirical consequences of a theory T arenot in agreement with the results of experiments, the theoryshould be rejected.Critique : Applying such a rule can lead the scientificcommunity to abandon an approximately true theory thatcould have been fixed with some corrections.To stick to one’s theoretical beliefs in spite of thecontradiction between the theory and empirical evidence istherefore increasing the chance of progress.Therefore, even if an agent knows that p and that T → ¬p,he should still believe that p.The consensus among the community helps its member to notfollow their private reasons.IC enhances scientific progress.





Three risks of informational cascade from the heuristic pointof view

All these risks follow from the fact that a dogma can be wrong.Therefore, an informational cascade involves the risk of acceptingas true a false proposition. The negative consequences of IC are thenegative consequences of accepting a false proposition in general.

1 Defending a false claim.2 Using a false proposition as a premiss for a demonstration.3 Raising an empty question.

The problem of IC for heuristic practiceIs the risk of raising empty questions outweighs the epistemicadvantage of IC within scientific practice ?




Empty questionsThe sequential division of cognitive labor solutionThe inapplicability of this solution

Sommaire








How to represent formally an empty question ?Hintikka’s Interrogative Model of Inquiry -1 (IMQ)

1 I know that someone murdered Dan Ackroyd. (Presupposition)2 Who murdered Dan ackroyd ? (Question)3 I know who murdered Dan Acroyd. (Desideratum)





How to represent formally an empty question ?Hintikka’s Interrogative Model of Inquiry-2

1 K (∃x)Px2 K (∃x1...∃xn)Px1∧, ...,∧Pxn(Question)3 K (∃x/K )Px) (Desideratum)





How to represent formally an empty question ?Hintikka’s Interrogative Model of Inquiry-3

K (∃x)Px

Kp

∃xPx

K (∃x1/KPx1) ∨ ... ∨ K (∃xn/KPxn)





How to represent formally an empty question ?An iterative model

1 We can order questions relatively to they rank.2 Definition : The question Qn is the question whose answer is

the presupposition of the question Qn+1.





How to represent formally an empty question ?An iterative model-Example

1 I know that Dan Ackroyd is either dead or alive.2 Is Dan Ackroyd dead ?3 I know that Dan Ackroyd is dead.4 I know that Dan Ackroyd is either murdered or not.5 Has Dan Ackroyd been murdered ?6 I know that Dan Ackroyd has been murdered7 I know that someone murdered Dan Ackroyd. (Presupposition)8 Who murdered Dan ackroyd ? (Question)9 I know who murdered Dan Acroyd. (Desideratum)





Definition of a sequential organization of cognitive labor

It is wrong always, everywhere, and for anyone to believeanything on insufficient evidence.

Clifford (1877) The Ethic of Belief.

Sequential organization of cognitive laborDo not raise a question Qn before being sure of the truth theanswer to the question Qn−1





An example : Descartes’s representation of history of science

"The aim of our studies should be to direct the mindwith a view to forming true and sound judgementsabout whatever comes before it""Thus, all Philosophy is like a tree, of whichMetaphysics is the root, Physics the trunk, and all theother sciences the branches that grow out of thistrunk, which are reduced to three principal, namely,Medicine, Mechanics, and Ethics. By the science ofMorals, I understand the highest and most perfectwhich, presupposing an entire knowledge of the othersciences, is the last degree of wisdom."





Does this rule implies to renounce to IC ?No : even if the common opinion is true, the possibility remains thatan individual could have reasons to have doubt about this opinion.





The problem of time

The pause of History as a consequence of Descartes’ method.Maybe it is necessary to raise the question to know who killedDan Ackroyd before knowing that he has been killed.But if someone renounces Clifford’s principle, one has also toaccept that he might be raising a false question. Therefore, herenounces to reach epistemic goals (he is not intellectuallyvirtus anymore).William James’s solution : we can pragmatically decide tobelieve something, but for epistemic reasons.




Epistemic jumpsA prescription for the scientific practice to avoid IC’s bad consequences

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A requirement so that IC can be regarded as epistemologically goodin heuristic scientific contextsIt must be possible to be rational to ask who murdered Ackroydeven though we do not know that he is dead

Definition-epistemic jumpTo raise a question Qn without having answered the question Qn+1





In order to accommodate IC with the temporal dimension ofscience, we need to raise two questions :

1 How is it possible to raise a question while doubting the truthof its presuppositions ? (Epistemic jump)

2 How can such a decision can be successful ? (or avoid failure)(safety net)





Cases of epistemic jumps

What is the weight of phlogisticon ? (Guyton deMorveau)What is the position and the mass of Vulcain ? (LeVerrier)





New examples of epistemic jumps

Is there an ignored particle which would beresponsible for the mass of objects ?What is the mass and the position of the planet thatdisturbs the orbit of Uranus ?





Exposition of the problem

1 The main idea : TO APPLY TECHNICAL REASONING TOQUESTIONS-TREE

2 The axiom of technical reasoning (Aristotle-Kant) :3 [U(p) ∧ K (q ⇒ p)]→ U(q) (with U a utility function, ⇒ a

causal relation and K representing a belief state)4 By recursivity, this kind of reasoning can convert a causal

sequence into a practical sequence.5 [U(p) ∧ K (q1 →, ...,→ qn → p)]→ U(q1)





1 How to apply the analysis of practical deliberation to inquirystrategies ?

2 We can consider a sequence of questions as a kind of causalknowledge.

3 If there is a epistemic state (or meta-epistemic state which hasthe form :

4 K ∗ (K1 → Q1 →, ...,→ Kn → Qn)

5 Then :[K ∗ (...Ki → Qi →, ...,→ Kn → Qn) ∧ U(Qn)]→ U(Qi )





The Belgium bookmakerDefinition

A belgium bookmaker is a bookmaker who designed a gamewhere a rational player would always win.Let us suppose a process with several possible outcomes andpropositions. The actual outcome verifies only one of thesepropositions.Rule 1 : bets on several outcomes are allowed (it is possible toavoid any risk).Rule 2 : the reward of correctly betting must be superior tothe cost of avoiding any risk.Can we apply this if, following Hintikka, we consider inquiry asa game against nature ?





The Belgium bookmakerApplication to the safety net problem-Rule 1

1 It is possible to run simultaneously research programs bearingon opposite premisses.

2 We can use the decision tree as an organizational tree.





The Belgium bookmakerApplication to the safety net problem-Rule 2

1 The problem of collective payoffs.2 The problem of individual payoffs.





Assume that a radical climate change would produce a worldflooding WL, and, in the actual world, WL is either possible ornecessary.Assume that there is a technology t1 that enables humanity tosurvive in WL, and a technology t2 that enables humanity toprevents that WL occurs. T is the set of all possibletechnologies.�WLf → ¬♦t2Therefore, if �WL, the question of discovering a technology t2is empty.If, on the opposite, ♦t2 ∧ ¬ML, the question of discovering t1is empty.The two research programs are playing a 0-sum game againstone another.But from the social welfare point of view, the cost of runningthe two programs at the same time is higher than the cost ofrunning both of them at the same time.





The parallel organization of cognitive laborSplit the community into as many groups as there as possiblequestions and let the IC phenomenon occur in each of thesecommunities.

The core of the research program plays involuntarilythe function of the antecedent and maybe falsequestion.The search for auxiliary hypotheses plays the functionof the secondary question.


Information cascade and division of cognitive labor

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