On rare events and the economics of small decisions

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On rare events and the economics of small
decisions Ido Erev, Technion

• Examples Using safety devices, cheating in
  exams, selecting among websites, stopping at red
  lights, continue listening.
• Why small
• Can be studied in the lab.
• Can be predicted with simple models with high ENO
  (Erev, Roth, Slonim Barron)
• Can be important.

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Are small decisions similar to large
decisions? According to the common assumption
large decisions can be studied by focusing on the
way people decide based on descriptions of the
possible payoff distributions. For example 3000
with certainty 4000 with probability 0.8 0
otherwise We believe that this paradigm is a
useful simulation of the last stage in large
decisions, but it is not clear that it trigger
tendencies that are similar to the tendencies
that affect small decisions. In many settings
small decisions are made based on personal
experience without explicit descriptions of the
payoff distributions.


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Experimental research highlights large
differences between decisions from descriptions
and from experience
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Experimental research highlights large
differences between decisions from descriptions
and from experience
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• This pattern can be explained with the assertion
  that rare events are overweighted when they are
  presented, but are forgotten when they are not
  (in decisions from experience).
• In decisions from experience people deviate from
  maximization in the direction of the alternative
  that leads to better outcome most of the time.
• This pattern was observed in a wide set of
  paradigms
• Search paradigm (Fujikawa Oda, 2004 Barron
  Erev, 2003)
• Sampling and a single choice (Hertwig et al.,
  2004 Ert et al., 2004)
• Signal detection (Erev, 1998)
• The joint effect of description and experience
  (Yechiam et al., 2005)
• Relatively simple models allow useful prediction
  of behavior (Erev Barron, 2005)

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Pessimistic interpretation In natural decision
problems people rely on descriptions and
experience. Thus, the two biases are likely to
cancel each other out. So, the experimental
examples are interesting, but can be ignored when
decisions outside the laboratory are
considered. Under an optimistic interpretation
the coexistence of the two biases magnifies the
importance of the behavioral approach. It
suggests that understanding of the conditions
under which the two biases occur can be very
useful.
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Gentle enforcement of safety rules (Erev
Rodansky, 2004) Enforcement is necessary Workers
like enforcement programs Probability is more
important than magnitude Large punishments are
too costly therefore, gentle enforcement can be
optimal
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Cheating in exams (Erev, Ingram, Raz Shany,
2005)
Consider a situation in which a rule enforcement
unit has limited capacity. For example, it can
punish, on average, only M violators. Assume
further that the number of potential violators
(subjects of the rule) is NgtM, the cost of
obeying the rule is C gt 0, that the fine for
violators (when punished) is F gt C, and that
(F)(M/N) lt C. i.e. N 100 students, M 10
fines, F Fine of 7, C cost of obeying
5. This game has at least two Nash
equilibria. In the first, no agent violates the
rule. In the second equilibrium all the agents
violate the rule.
Relative value of violation
C-F(M/N) 0 C-F
Proportion of violators
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Under a gentle solution, the enforcement unit can
employ a gentle ZT policy that use moderate fines
(C lt F lt C(N/M)). Under this solution the unit
declares that the first M violators will be
punished. Given this declaration no one will be
motivated to be the first violator. As a result
no violation is the unique equilibrium of the
game. A field experiment To evaluate this
solution, we used it to try to reduce cheating
during university exams. The experiment was
conducted during final semester exams of
undergraduate courses. Traditionally,
instructions for exam proctors included the
following points (1) The students ID should be
collected at the beginning of the exam, (2) A
map of students seating should be prepared.
To facilitate the implementation of gentle ZT in
the experimental condition we simply changed the
second instruction to proctors (2e) A map of
the students seating should be prepared 50
minutes after the beginning of the exam.
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Other examples Two-stage lottery promotion
(Haruvy Erev, 2006) The effect of rare
terrorist attacks (Yechiam et al., 2005). The
effect of immediate feedback on the decision to
practice. The value of free sampling (Ert et al.,
2006). Risk attitude in time saving decisions
(Munichor et al., 2006). In summary, Paris
Hilton and Amnon Rapoport are correct, but small
decisions can be interesting.
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Reinforcement learning among cognitive strategies
(RELACS)Erev Barron (2005)Basic ideaThe
optimal strategy in decisions from experience is
situation specificSlow best reply (Stochastic
fictitious play) (9) or (100, .1 0)Fast best
reply (11) or (10)Best reply to pattern People
learn among the reasonable strategies
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The Equivalent Number of Observations of
Descriptive models Ido Erev, Al Roth, Bob Slonim
and Greg Barron Assume that you are asked to
predict behavior in a new environment (e.g., the
proportion of violations of safety rules given a
new rule enforcement policy). Learning models
can be used to drive ex ante prediction. This
prediction can be described as the modelers
prior opinion. When observations concerning
behavior in the new situations are available, the
prior opinion can be revised. We show that the
optimal revision is given by the rule RevPred
W(Prior) (1-w)(Obseved) Where W ENO/(ENO
n) ENO is the model equivalent number of
observations And n is the number of observations
of behavior in the new situations