Decision making under uncertainty and beyond 20

Decision making under uncertainty and beyond
20 March 2015
HEC Porte de Champerret
6-14 Avenue de la Porte de Champerret - 75017 Paris
Workshop organised by GREGHEC (HEC Paris & CNRS) and the Economics and Decision
Sciences Department Seminar, HEC Paris, with the support of the Labex EcoDec.
Preliminary Programme
9h00-9h30
Welcome Coffee
9h30-10h15
Graham Loomes (Warwick), Looking for ‘Ambiguity Attitude’ in a Strategic
Setting (w/ Zhihua Li and Ganna Pogrebna).
10h15-11h
Stefan Trautmann (Heidelberg & Tilburg), Dynamic consistency & fairness
(w/ Gijs van de Kuilen).
Coffee Break
11h30-12h15
Thomas Epper (St Gallen) Generalized homothetic preferences
12h15-13h
Massimo Marinacci (Bocconi), Uncertainty attitudes and justifiability (w/
Pierpaolo Battigalli, Simone Cerreia-Vioglio and Fabio Maccheroni).
Lunch
14h30-15h15 Uzi Segal (Boston) Preferences over Randomized Alloaction Mechanisms
(w/ David Dillenberger).
15h15-16h
Stefania Minardi (HEC Paris) Subjective Contingencies and Limited
Bayesian Updating (w/ Andrei Savochkin).
Coffee Break
16h30-17h15
Aurélien Baillon (Erasmus), Bayesian markets for unverifiable truths.
17h15-18h
Soo Hong Chew (Singapore), TBA.
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Abstracts
Aurélien Baillon (Erasmus), Bayesian markets for unverifiable truths
Subjective data play an increasing role in modern economics. For instance, new welfare
measurements are based on people’s subjective assessments of their happiness or their life
satisfaction. A problem of such measurements is that people have no incentives to tell the
truth. To solve this problem and make subjective assessments incentive compatible, I
introduce a new market institution, called Bayesian markets.
On Bayesian markets, agents trade an asset whose value is the proportion of people
answering Yes to a given question. Only those answering Yes have the right to buy the asset
and those answering No the right to sell it. Bayesian updating implies that “Yes” agents
predict a higher value of the asset than “No” agents do and, consequently, “Yes” agents want
to buy the asset while “No” agents want to sell it. Conditions ensuring truth-telling are
established in the paper.
Bayesian markets reward truth-telling the same way as prediction markets (betting markets)
reward people for reporting their true subjective probabilities about observable events. Yet,
unlike prediction markets, they do not require events to be objectively observable. Bayesian
markets apply to any type of unverifiable truths, from one’s own happiness to beliefs about
events that can never be observed.
Soo Hong Chew (Singapore), TBA.
Thomas Epper (St Gallen) Generalized homothetic preferences
We introduce a general characterization of Allais paradoxes. Our characterization motivates a
generalized homotheticity condition (gHT) which precludes particular Allais paradoxes while
permitting others. Preferences are homothetic if a probabilistic mixture of two lotteries with a
specific third lottery (or a specific set of lotteries) does not revert preferences.
gHT contains existing proposals to weaken independence as special cases. For example, if the
homothetic center, i.e. the third lottery with which the original two lotteries are mixed, is the
worst lottery in the choice set, it precludes the classic common ratio effect. If the homothetic
center lies at infinity, it precludes the classic common consequence effect. If the homothetic
center is one of the original two lotteries, it is equivalent to betweenness. If the homothetic set
consists of all lotteries in the n-simplex, it is equivalent to mixture independence. If gHT
holds for comonotonic sets, it is equivalent to comonotonic independence.
We derive a number of key results. First, mixture independence holds for any subdomain of
the n-simplex if there exist at least two distinct homothetic centers for which gHT holds.
Second, there is no preference relation characterizing both, common ratio violations and
common consequence violations simultaneously over a relevant domain of the simplex.
Third, imposing additional restrictions on top of gHT directly leads to a number of
representations. For example, adopting a generalized version of Bergson's theorem, i.e.
additive separability together with gHT and standard axioms, is equivalent to rank-dependent
utility with a quadratic probability weighting function. Finally, preferences can be recovered
from choices using triangulation. We derive novel and direct tests of gHT and large domain
of theories it encompasses.
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gHT helps to understand the drivers of various behavioral patterns documented in the
literature. For example, we find that preferences for late resolution of uncertainty and
preferences for one-shot resolution of uncertainty are driven by certain violations of gHT, and
do not depend on other characteristics of the representation.
Also, gHT is crucial for the aggregation of preferences. Representative agent results are
systematically biased as compared to population means if gHT fails.
In the outcome domain, gHT is a key condition for the axiomatization of the Stone-Geary
utility function (which underlies the linear expenditure system) and quasilinear utility
function (which underlies the Marshallian supply/demand framework).
Graham Loomes (Warwick), Looking for ‘Ambiguity Attitude’ in a Strategic Setting
Joint with Zhihua Li and Ganna Pogrebna.
To date, most experimental investigations of ambiguity have focused upon individual
decision making in non-strategic environments. However, much uncertainty in life relates to
the behaviour of others in interactive environments. This paper considers the implications of
subjective expected utility theory (Savage, 1954) in a co-ordination game environment where
ambiguity arises from uncertainty about the actions of other players. In this environment, a
large majority of individuals violate subjective expected utility theory. We discuss three
possible explanations of the observed behaviour: nonlinear transformation of probabilities;
noise in responses; and/or systematic biases in the way that individuals generate subjective
probabilities.
Massimo Marinacci (Bocconi), Uncertainty attitudes and justifiability
Joint work with Pierpaolo Battigalli, Simone Cerreia-Vioglio and Fabio Maccheroni.
An action is justifiable if it is a best reply to some belief. We show that higher risk/ambiguity
aversion enlarges the set of justifiable actions.
Stefania Minardi (HEC Paris) Subjective Contingencies and Limited Bayesian Updating
Joint work with Andrei Savochkin.
Abstract TBC
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Uzi Segal (Boston) Preferences over Randomized Alloaction Mechanisms
Joint work with David Dillenberger.
A group of n individuals needs to allocate n goods of two types among its members. Each of
them has the same stochastic preferences, where with probability q he prefers the first type to
the second. We consider two familiar mechanisms, each consists of two stages.
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Random Top Cycle (TC): In the first stage, the allocation of the goods among the
agents is randomly determined. In the second stage, the entire profile of preferences
is revealed. Those who like their holding will keep it. The rest will trade such that
people on the long side of the market will be randomly chosen to trade with all
individuals on the short side of the market.
•
Random Serial Dictatorship (SD): In the first stage the order of the agents is
randomly determined. In the second stage, the entire profile of preferences is
revealed. The agents then choose the goods according to the order determined in the
first stage. A person will get his desired outcome if when his turn arrives such a unit
is still available.
It is well known that in both procedures, the probability of receiving the desired good is the
same. We show that under plausible assumptions, the recursive model of Segal (1987,1990)
predicts that one procedure (TC) is systematically preferred to the other. These preferences
can also address the phenomenon of ambiguity seeking in the context of decision making
under uncertainty.
Stefan Trautmann (Heidelberg & Tilburg), Dynamic consistency & fairness
Joint work with Gijs van de Kuilen
Literature on fairness preferences distinguishes between outcome fairness, concerning the
final allocation of payoffs, and process fairness, concerning the expected allocation of
payoffs. It is not obvious, however, whether process fairness can consistently be
implemented. Once uncertainty is resolved and outcomes are determined, the ex-ante
procedurally fair decision maker may become consequentialist ex-post, and reconsider her
choice on the basis of the observed outcomes. We present experimental evidence on dynamic
consistency in a setting that is unfavorable to process fairness: a significant share of people
subscribes to process fairness both before and after the resolution of uncertainty.
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