presentatie cost 2p - paris dauphine universitygold/cost_slides/amelie_vrijdags.pdf · amélie...

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Amélie Vrijdags – COST IC0602 International Doctoral School pag. 1

EMPIRICAL VALIDATION OF EMPIRICAL VALIDATION OF MEASUREMENTMEASUREMENT--THEORETICAL AXIOMS THEORETICAL AXIOMS

FOR DECISION UNDER COMPLETE FOR DECISION UNDER COMPLETE UNCERTAINTY.UNCERTAINTY.

Doctoral student: Amélie Vrijdags Promotor: Prof. Dr. T. MarchantSupervising committee: Prof. Dr. D. Bouyssou,

Prof. Dr. T. Marchant, Prof. Dr. Y. Rosseel, Prof. Dr. T. Verguts


OutlineOutline

• Introduction‣ Descriptive approach‣ Decisions under complete uncertainty‣ Axiom systems & empirical validation

• Experiment 1: testing transitivity of preferences‣ Design - analysis - results

• Planning ‣ Short-term‣ Long-term

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Normative approachNormative approach : how DMs SHOULD make decisions

Descriptive approachDescriptive approach : how DMs DO make decisions

� Behavioral models that fit empirical evidence

Introduction: Descriptive approachIntroduction: Descriptive approach


Introduction: Decision under complete uncertaintyIntroduction: Decision under complete uncertainty

Decision under complete uncertaintyDecision under complete uncertainty

Suppose no information about probabilities

Example:

Container A: Container A: red ticket red ticket --> win > win €€25 25 green ticket green ticket --> win > win €€100100

Container B: Container B: red ticket red ticket --> win > win €€50 50 green ticket green ticket --> win > win €€7070

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MaximinMaximin (pessimistic model)(pessimistic model)

A ≿ B iff min(A) ≿ min(B)

MaximaxMaximax (optimistic model)(optimistic model)

A ≿ B iff max(A) ≿ max(B)



MaxminMaxmin ordering ordering A ≿ mxn B iff max(A) > max(B) or

max(A) ~ max(B) and min(A) ≿ min(B)

MinmaxMinmax ordering ordering

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Let a(1) denote the largest element in A, a(2) denote the second largest element in A, etc.

Idem for b (i)

LeximaxLeximax

A ≿ B iff A = B or#A < #B and {a(i)} ~ {b(i)} , i = 1 ... #A or{a(i)} ~ {b(i)} ∀ i < j and {a(j)} > {b(j)} for some j

LeximinLeximin



Uniform Expected Utility (UEU) criterion:Uniform Expected Utility (UEU) criterion:

A ≿ B iff Σa∈A u(a)/#A ≥ Σb∈B u(b)/#B

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Representation theorems provide conditions for the numerical representation or measurement of the utility or attractiveness of alternatives

Goal empirical research: what numerical representations actually hold for human DMs + can be justified from observable choice behavior?

Introduction: axiom systems & empirical validationIntroduction: axiom systems & empirical validation



Some combinations form anaxiomaticalaxiomatical mathematical systemmathematical systemthat can be shown to guarantee the existence of a numerical representation

Structuralproperties of

decisions+

Behavioralproperties of

DMs

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2 Averaging• A ≿ B iff A ≿ A∪B iff A∪B ≿ B (A ∩B = ∅)

Exampleaxiom system characterizing UEU criterion

1 Weak order• Completeness A ≿ B or B ≿ AA for all A, B = ∅)• Transitivity A ≿ B, B ≿ C implies A ≿ C

Behavioral properties:Behavioral properties:

Example: (€20, €12) ≿(€5) iff (€20, €12) ≿(€20, €12, €5)I iff (€20, €12, €5) ≿(€5)



5 Bisymmetry• {a’} ∪ {a”} ~ {a} , {b’} ∪ {b”} ~ {b} , {a’} ∪ {b’} ~ {c’} , {a”} ∪ {b”} ~ {c”}implies {a} ∪ {b} ~ {c’} ∪ {c”}

4 Attenuation• A ~ B , #A > #B, (A ∩C = ∅ = B ∩C ),A ≿ C implies A∪C ≿ B∪C and A ≤ C implies A∪C ≤ B∪C

Behavioral properties:Behavioral properties:

3 Restricted Independence• A ≿ B iff A∪C ≿ B∪C (A ∩C = ∅ = B ∩C, #A = #B )

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8 Archimedeanness• Let {ci}, i = 1, 2, ... be a sequence where ci ∈ X for all i. Suppose a, b ∈ X , {a}> {b} , a ≠ ci ≠b for all i and {ci , a } ~ {ci+1 , b } for all i. If there is d, e ∈ X such that {d} > {ci } > {e} for all i, then the sequence is finite.

7 Restricted Solvability• For all A, B in Pn(X) and c*, c* in X, A ∪{c*} > B > A ∪{c*} implies

there is c in X such that A ∪{c} ~ B.

6 Certainty Equivalence• For all A in Pn(X) there is a in X such that A ~ {a}.

Structural properties:Structural properties:


Validation of individual axioms:Validation of individual axioms:+ Detailed focus on what appears valid and what is in need of change + Clear directions for theoretical research- Comparison competing theories can become tedious

Validation of entire representation as a whole:Validation of entire representation as a whole:+ Possibility of direct comparison of competing theories- What is wrong exactly if representation does not fit the data?


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�� Decision under risk: lots of empirical research

� Decision under complete uncertainty: not one empirical study up to date


Main goal doctoral thesis = empirical validation of theories Main goal doctoral thesis = empirical validation of theories for decision under complete uncertainty through examination for decision under complete uncertainty through examination of individual axiomsof individual axioms

11stst axiom = axiom = TRANSITIVITYTRANSITIVITY

A A ≿ B, B B, B ≿ C implies A C implies A ≿ CC


STIMULI:STIMULI:

A = (€56, €12) EV* = €34B = (€43, €17) EV* = €30C = (€30, €21) EV* = €25.5A ≿ B, B ≿ C, C ≿ A according to LPH LS with €5 < ∆Land PH

A’ = (€42, €9) EV* = €25.5B’= (€31, €13) EV* = €22C’= (€22, €16) EV* = €19A’ ≿B’, B’ ≿ C’, C’ ≿ A’ according to LPH LS with €4 < ∆P and PH

*Expected Values were calculated under the assumption of a uniform probability distribution

Experiment 1 Experiment 1 –– testing transitivity of preferences: Designtesting transitivity of preferences: Design

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PROCEDURE:

• Forced choice task• Presentation:

X = ( 13 , 31 ) N = ( 8 , 47 )

• 1 practice block (10 trials), 11 experimental blocks (261 trials)• 1/5 participants plays 1 of chosen gambles for real money• # subjects = 8

Experiment 1 Experiment 1 –– testing transitivity of preferences: Designtesting transitivity of preferences: Design


Inconsistent responses: viability of orderInconsistent responses: viability of order--constraints implied constraints implied by axiom? by axiom? --> need for statistical method> need for statistical method

�� Counting # violating patternsCounting # violating patterns�� Iverson & Iverson & FalmagneFalmagne (1985): Likelihood ratio test(1985): Likelihood ratio test�� Since 2005: Bayesian machinery (Karabatsos, Since 2005: Bayesian machinery (Karabatsos, MyungMyung,..),..)�� BayesBayes Factor (Factor (DesimpelaereDesimpelaere & & MarchantMarchant, 2006):, 2006):

P[P[≿T∈A | n ] / P[P[≿T∈A* | n ]

Experiment 1 Experiment 1 –– testing transitivity of preferences: Analysistesting transitivity of preferences: Analysis

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Experiment 1 Experiment 1 –– testing transitivity of preferences: Resultstesting transitivity of preferences: Results

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Subject

5.726338ABC C’B’A’6 7 6 6 6 6

9.151815ABC A’B’C’11 9 7 11 10 11

9.786321ABC A’B’C’11 10 11 11 10 11

2.6631E-08ABC A’B’C’10 11 2 10 11 2

9.661132ABC A’B’C’7 8 8 11 10 9

1.809843ABC B’C’A’10 8 5 9 11 10

9.772648ABC A’B’C’11 11 10 11 11 10

7.62291ABC A’B’C’11 8 6 10 10 11

Bayes factorMax Lik WORaw data (n)


TransitivityTransitivity of of preferencespreferences is a is a plausibleplausible conditionconditionforfor decisiondecision underunder complete complete uncertaintyuncertainty

Experiment 1 Experiment 1 –– testing transitivity of preferences: Conclusiontesting transitivity of preferences: Conclusion

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In the shortIn the short --term:term:

•• Further exploration of transitivity:�Use of more than 2 triples, sets with more than 2 elements�Transitivity of indifference

• Empirical validation of other axioms, starting with UEU criterion• Situation specificity? -> include decisions under risk

Further researchFurther research


In the longIn the long --term:term:

• Inclusion of losses and mixed consequences

Further researchFurther research

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Thank you for your attention!!Thank you for your attention!!

presentatie cost 2p - paris dauphine universitygold/cost_slides/amelie_vrijdags.pdf · amélie...

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