AN EMPIRICAL DEMONSTRATION OF
RISK-SENSITIVE FORAGING PREFERENCES
(Carco 1980)
Hanan Shteingart
Abstract
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Laboratory experiments shows preference
sensitive not only to mean but also to
variance.
The nature of preference is related to their
expected daily energy budget (?)
Foraging models should consider
environmental stochasticity
Introduction
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U(sik) = E[U(si, q, sk)] (DeGroot 1970; Keeney& Raiffa 1976)
Certainty equivalent s for probability distribution f(s)
means f(s) I s (I – indifferent)
U(s) must increase with reward size (U'(s) > 0).
(si, q, sj) - a reward of si units with probability q and sk with
probability 1-q
Risk aversion
sik < E[s] (= qsi + (1-q)sk)
U’’(s)<0
6.
Risk-prone
sik < E[s]
U’’(s)>0
Introduction – cont.
deterministic model  according to average rewards
Insensitivity to environmental variation (U"(s) = 0),
risk premium Y = E[s] – sik
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Y>0
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Y>0 avoids risk
Y<0 favor of risk
dY/dE(s)<0 decreasing risk aversion,
dy/dE(s) = 0 Constant risk aversion
'local risk aversion' as r(s) = -U"(s)/U'(s). (?)
Decreasing risk aversion r(s) > 0 and dr(s)/ds < 0.(?)
Methods
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5 birds
2 feeding stations
2 experiments:
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40 trials per experiment:
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1 hour starvation, 2 seed/min (req 1.39)
4 hours starvation, 1 seed/min (req 2.08)
20 training (10 each shuffled)
20 test
(si, 0.5, sk) – minimize estimation bias
Preference <> 14/20 (alpha = 0.05)
Methods – cont. Utility Estimation
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Becker et al. (1964).
U(0) = 0 and U(6) = 1
certainty equivalent U(s0,6) = E[U(0, 0.5, 6)]
= 0.5[U(0) + U(6)] =0.5
Estimate certainty equivalent for (0,0.5, s0,6)
(U=0.25) and (s0,6,0.5, 6) (U=0.75)
until confident
mean as the best estimate
Results
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Experiment 1 – risk aversion
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Experiment 2 – risk proneness
Discussion
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response to risk depends on a comparison
of energetic intake with energetic
requirements
energy/time as the random variable  U
has an inflection point (U" changes sign).
Utility theory is but one of many ways to
view choice, measurement, and optimal
decisions under stochasticity