Massenzio - 2001 - An Interview With Claude Lévi Strauss
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Risk Sensitivity and Value among
Andean Pastoralists: Measures,
Models, and Empirical Tests
1
lawrence a. kuznar
Department of Sociology-Anthropology, Indiana
University, Purdue University at Fort Wayne, 2101 E.
Coliseum Blvd., Fort Wayne, Ind. 46805, U.S.A.
(kuznar@ipfw.edu). 9 i 01
Risk sensitivity has intrigued anthropologists because of
the role it can reasonably be expected to play in decision
making given the uncertainties of food supply and
weather patterns and the hazards that surround us (Win-
terhalder, Lu, and Tucker 1999, Douglas and Wildavsky
1982, Vayda and McKay 1975). Using data from Andean
herders, I will operationalize a denition of risk sensi-
tivity and demonstrate how risk sensitivity varies with
environmental and social variables. The potential ben-
ets of incorporating risk into models of economic be-
havior are obvious in the Andes. Andean mountain en-
vironments are cold, unpredictable, and limiting (Molina
and Little 1981:11516; Orlove and Guillet 1985:5; Brow-
man 1984:314; 1987; Goland 1993:318). Frequent
droughts, snows, and generally dry environments con-
strain the subsistence choices of Andean peoples, leading
ethnographers and archaeologists to assert that Andean
people will be risk-averse (Custred 1977; Gade 1975:94;
Browman 1984, 1987; Brush 1982; McCorkle 1987; 1990:
10; Guillet 1986:210; Goland 1993; Winterhalder 1994;
Isbell 1978; Hesse 1982; Aldenderfer 1998). The patterns
of risk sensitivity I present are consistent with research
in economics (Friedman and Savage 1948, Kahneman and
Tversky 1979, Bosch-Dome` nech and Silvestre 1999, But-
ler 2000, Morrison 2000), agricultural economics (Dillon
and Scandizzo 1978, Elamin and Rogers 1992, Zuhair,
Taylor, and Kramer 1992), biology (Real 1991, Stephens
1990), and human behavioral ecology (Winterhalder, Lu,
and Tucker 1999).
risk sensitivity in anthropology
Anthropologists have not overlooked the importance of
modeling decision making under uncertainty and risk
(Cancian 1972, 1980, 1989; Quinn 1978; Ortiz 1980,
2001 by The Wenner-Gren Foundation for Anthropological Re-
search. All rights reserved 0011-3204/2001/4203-0006$1.00
1. I am indebted to Alan Sandstrom, Rick Sutter, and Robert Jeske
for their comments on earlier drafts of this manuscript. Four anon-
ymous reviewers provided invaluable and constructive criticisms.
The term probability premium is borrowed from one reviewer.
Also, my gratitude goes to Malcom Dow and Roger Myerson for
exposing me to the mathematical foundations of economic theory.
The eld research would not have been possible without support
from Mark Aldenderfer and the Southern Peru Copper Company.
I thank the Aymara awatiri among whom I lived and worked. Of
course, I am solely responsible for the content of this paper.
Volume 42, Number 3, June 2001 F 433
Fig. 1. The sigmoid utility curve. Risk-preferring deci-
sion makers are represented by the convex portion of
the curve (origin to inection point), where a gamble
on winning or losing p is accepted because the poten-
tial gain a is greater than the potential loss b. Risk-
averse decision makers are represented by the con-
cave portion of the curve (inection point to end),
where a gamble on winning or losing p is rejected be-
cause the potential gain d is less than the potential
loss c.
1983; Gladwin 1975, 1989; Orlove 1986; de Garine and
Harrison 1988; Halstead and OShea 1989; Cashdan1990;
Winterhalder 1986a, b, 1990; Goland 1993; Fratkin 1991;
Smith 1991; Kuznar 1991a, b, 2000). One of the most
detailed studies is Frank Cancians (1972:14456; 1980:
171; 1989) pioneering work on the inuence of status on
risk taking among Mexican peasants. He points out that
very wealthy peasants are more likely to take chances
because their level of wealth is well above crucial thresh-
olds. Lower-middle-class peasants will also engage in
risky behavior because the prospect of entering a higher
wealth status is so near. Very poor and moderately
wealthy peasants will be averse to riskthe moderately
wealthy because they have too much to lose and the very
poor because they cannot afford to lose. Cancian (1989:
151) nds risk aversion to be widespread among mod-
erately wealthy peasants and rural farmers in India, Pak-
istan, Kenya, the Philippines, and the United States.
Winterhalder, Lu, and Tucker (1999) review recent op-
timal-foraging applications that incorporate risk and pro-
pose that much risk-sensitive behavior can be under-
stood by employing a sigmoid utility curve to model
peoples preferences. Utility is a measure of a persons
satisfaction with a good or some decision. As far back
as 1738, the mathematician Daniel Bernoulli (1954
[1738]) noted that utility does not necessarily vary 1:1
with quantities of actual goods. Milton Friedman and
Leonard Savage (1948) recognized that peoples utility
functions for some good (for example, wealth) tend to be
sigmoid, or S-shaped.
In the sigmoid curve (g. 1), the rst part of the curve
is convex and the last part concave. Convex utility
curves correspond to a preference for risky prospects. For
instance, individuals of wealth status w, offered an even
chance of either increasing or decreasing their wealth by
p, will take the gamble because if they win their wealth
status will increase by a, a greater gain than the loss b.
In contrast, risk-averse individuals at wealth status x,
offered the same gamble, will reject it because the most
they can gain is d, which is less than the potential loss
c. Friedman and Savage saw the sigmoid utility curve as
a reasonable description of how peoples risk sensitivity
changes with wealth. People with convex utility func-
tions aspire to the next-highest class and therefore are
willing to take a chance at a perceived higher increase
in utility from a gamble. In contrast, people in a com-
fortable wealth class are reluctant to risk what they have
for a comparatively small increase in utility.
Winterhalder (1986a, b, 1990) and Goland (1993) em-
ploy an approximation to a sigmoid utility curve in their
Z-score model of risk-sensitive decision making. Win-
terhalder (1986a:374) begins by dening risk as the
probability of falling below a xed minimum require-
ment (m). This might be starvation or some less cata-
strophic but signicant cost to tness or adaptation.
The model is so named because minimum requirements
are standardized with the common Z-score. In this model
people will make decisions to exploit a set of resources
so that they minimize the probability of falling below
the minimum requirement (measured as some standard
deviation below the mean). Goland (1993) conducted an
empirical test of the Z-score model in two Peruvian agro-
pastoral communities and found that peasants dispersed
their elds to reduce variance in yield because stochastic
shocks that reduce yield (frosts, hail, droughts, theft) are
unevenly distributed across the landscape.
While yielding important insights, anthropological ex-
plorations of risk sensitivity do not all agree, and they
generally fail to consider the subjective component of
decision making. Optimal-foraging theory applications
are consistent with research in biology: some species of
animals, including people, close to a starvation income
tend to take chances in order to obtain enough food (Win-
terhalder, Lu, and Tucker 1999:317, 332, 334). In con-
trast, Cancians statements on class and risk sensitivity
can be translated into the sigmoid utility curve in gure
2, where poor peasants are risk-averse (have a concave
utility function) while upper-class peasants prefer risk
(have a convex utility function). Furthermore, most ap-
plications are tied to etic measures of value (e.g., star-
vation thresholds, actual variances in income), which
people do not necessarily perceive accurately. Peoples
perceptions of the actual variances of events can be very
subjective, and most people in most economies are not
so concerned with starving as with maintaining or gain-
ing in social status (Douglas and Wildavsky 1982:71;
434 F current anthropology
Fig. 2. Translation of Cancians (1972, 1989) theory of
peasant risk sensitivity.
Smith and Mandac 1995; Bar-Shira 1992). A more thor-
ough consideration of economic utility theory will re-
solve these problems and increase the generality of both
optimal-foraging applications and Cancians results.
utility theory
Utility theory provides a means of monitoring how peo-
ple perceive risk and of measuring subjective values by
taking advantage of an individuals perception of risk
(von Neuman and Morgenstern 1944, Luce and Raiffa
1957, Myerson 1979). The application of utility-theory
methods does not require that decision makers have any
explicit idea of probability or make explicit mathemat-
ical calculations (Rapoport 1966:30). They need only
make decisions based on their subjective perception of
probabilities. It is assumed by this method that a deci-
sion makers preferences are complete, transitive, and
continuous (von Neuman and Morgenstern 1944, Luce
and Raiffa 1957, Myerson 1979). Completeness means
that a decision maker can compare any alternatives un-
der consideration. Transitivity means that a decision
maker who prefers A to B and B to C will also prefer A
to C. Continuity means that a decision makers utility
increases continuously such that if A is preferred to C,
any option B that is ranked between A and C can be
represented by a randomized combination of A and C.
Provided that a decision makers preferences meet these
requirements, researchers can use utility-theory meth-
ods to monitor preferences and to model decision mak-
ing. In the application of utility theory I present below,
I address the validity of each of its axioms for my par-
ticular case study.
Economists, taking an explicitly deductive approach,
tend to rely for its validity more on the theorys axio-
matic foundations than on empirical demonstrations
(Perry 1998, Paris and Caputo 1993). When economists
do test utility theory, it is often in experiments con-
ducted in industrialized Western societies (Kahneman,
Knetsch, and Thaler 1990, Cubitt and Starmer 1998,
Bosch-Domene` ch and Silvestre 1999, Butler 2000). Some
experimental economists have focused on violations of
utility-theory assumptions. Many of these limitations
were detailed in a seminal article by Daniel Kahneman
and Amos Tversky (1979) in which they noted common
violations of utility theory such as unequal weighting of
losses versus gains, overweighting of certain outcomes
over probabilistic ones, and failure to consider common
features of prospects relevant to the calculation of their
value. Other researchers have built upon this foundation
(Karmarkar 1979, Tversky and Kahneman 1992, Cubitt
and Starmer 1998, Butler 2000, Morrison 2000). Despite
various limitations, utility theory appears valid when its
assumptions can be met, and violations of assumptions
can often be overcome with modications to utility
functions (Kahneman and Tversky 1979, Tversky and
Kahneman 1992, Butler 2000). As Morrison (2000:194)
notes, despite the limitations of utility theory, a clearly
superior model has not yet been identied.
In contrast to critical experimental studies, actualistic
studies by agricultural economists (Bar-Shira 1992,
Smith and Mandac 1993, Dillon and Scandizzo 1978,
Elamin and Rogers 1992, Zuhair, Taylor, and Kramer
1992) tend to support the t between utility theory and
peoples actual behavior. For instance, Bar-Shira (1992)
found that, when a feasible solution to a land allocation
problem for farmers exists, risk aversion coefcients can
be assessed and people behave in accordance with utility-
theory predictions. Zuhair, Taylor, and Kramer (1992)
found that utility functions provided accurate predic-
tions of harvesting strategies among Sri Lankan peasants.
Other researchers have applied these methods success-
fully among slash-and-burn horticulturalists and agrar-
ian peasants in northeastern Brazil (Dillon and Scandizzo
1978) and the Philippines (Smith and Mandac 1992).
Some anthropologists have considered utility theory.
Harold Schneider (1974) explicitly used utility theory as
the basis for his formalist approach in economic anthro-
pology. Sutti Ortiz (1980, 1983) took into account sub-
jectivity in peoples values for goods and in their eval-
uations of probabilities to discuss the potentials and
limitations of economic methods in anthropology. Be-
cause of the empirical and cross-cultural nature of their
eldwork, anthropologists can make potentially impor-
tant contributions to utility theory by testing its foun-
dations empirically in contexts sensitive to cultural and
social variables.
utility theory in practice
Utility-theory methodology involves presenting decision
makers with options, or lotteries, that have different
long-run expected utilities. Expected utility, E[u], is im-
portant because a probabilistic return (e.g., a 50%chance
of winning $100) either rewards an individual or not,
depending on whether the event (winning) occurs. How-
ever, if the trial is repeated many times, the expected
return will equal the prize multiplied by the probability
Volume 42, Number 3, June 2001 F 435
table 1
High-Sierra Utility Interviews
Herder/Sex
Preference Ranking
Probability
Premium
b
Goats Sheep Cows
1/m b c 1 0.45
2/m 1 c c 0.49
3/f b 1 c 0.45
4/m b 1 c 0.45
5/f c 1 b 0.0
6/m c b 1 0.45
7/m 1 c c 0.4
8/m 1 c c 0.3
9/f b c 1 0.35
10/f b c 1 0.4
11/m 1 c c 0.4
12/m b b 1 0.45
Aggregated animal
values
a
4 6b 2c 3 2b 7c 5 b 6c
a
The sum of the values assigned to each rank for each animal over the set of herders interviewed.
b
A measure of risk sensitivity in which the value represents the additional probability, X, that a decision
maker required to be indifferent between a certain prize of 50 animals and a lottery with probability 0.5
X of winning 100 animals. Positive values indicate risk aversion, zero values risk neutrality, and negative
values risk-preferring attitudes.
of winning (0.5 # $100 p$50). The techniques of utility
theory are easily adapted so that they can be applied
among Andean pastoralists for monitoring risk
sensitivity.
The rst step in applying utility-theory methodology
was to establish whether it was warranted. The Aymara
herders I interviewed in southern Peru had no trouble
rank-ordering their preferences among different animals,
satisfying the completeness axiom. The herders also
demonstrated the transitivity axiom by consistently or-
dering their preferences among the different herd ani-
mals they had available to them. Finally, herders com-
prehended the choice between a certain prize of animals
and a lottery that offered the chance of winning animals
(some herders had actually played lotteries), and so the
continuity axiom also seemed reasonable.
In order to measure a herders risk sensitivity, I pre-
sented a herder with a choice of prizes, either a particular
number of animals of that herders preference or a lottery
ticket that offered the possibility of winning a larger
number of animals of that kind. I varied the probabilities
assigned to the lottery ticket until the herder had dif-
culty choosing between the prizes (see Dillon and Scan-
dizzo 1978 and Zuhair, Taylor, and Kramer 1992 for sim-
ilar applications). If, for instance, a herder was indifferent
between a certain prize of 50 animals and a ticket that
offered a 50% chance of winning 100 animals, then that
herders value for animals was risk-neutral because the
expected utility of a 50% chance of 100 animals was 50,
the same as the certain prize. However, if a herder re-
quired a higher probability of winning 100 animals, say,
75%, then this indicated risk aversion; the herder re-
quired a higher chance of winning the uncertain yet
larger prize than what simple expected utility predicts.
The probability above or below a risk-neutral expecta-
tion required for the decision maker to take a gamble is
called the probability premium (see n. 1); in this case it
was 25%. If a herder preferred to take, say, a 30% chance
of winning 100 animals rather than take 50 animals for
certain, this would indicate risk-preferring behavior, and
the probability premium would be negative, 20%. The
probability premium is a measure of a decision makers
sensitivity to risk; negative values indicate a willingness
to bet on long shots, a zero value indicates risk neutral-
ity, and a positive value indicates risk aversion.
Comparing the relative values of different animal spe-
cies is methodologically more complicated. Theoreti-
cally, animal values can be estimated in a similar appli-
cation of utility-theory methodology. An accessible
description of this method is found in Rapoport (1966:
30), and I have used this method to assess the relative
values of herd animals among Aymara pastoralists (Kuz-
nar 2000). However, the method can be limited if the
arbitrary value of zero is assigned to the least preferred
animal as I have done, for this implies, probably contrary
to fact, that the animal has no value to a herder. An
alternative is to aggregate animal values over all herders
preferences. For each herder, one assigns a value of 1 to
the highest-ranked animal and arbitrary values b and c
to the second-highest-ranking and the least preferred an-
imal respectively. Then one can sum the rankings for
each of the animals over the set of herders (see tables 1
and 2). Quantitative estimations of animal value are de-
rived by inserting values for b and c. The limitation of
this method is that the values for b and c are arbitrary.
The advantage is that one avoids undervaluing low-rank-
ing animals. I will use this aggregation method and then
perform a sensitivity analysis in which values of b and
436 F current anthropology
table 2
Puna Utility Interviews
Herder/Sex
Preference Ranking
Probability
Premium
b
Llamas Alpacas Sheep
1/m b 1 c 0.20
2/f b 1 c 0.15
3/m b 1 c 0.45
4/m b 1 c 0.40
5/m b 1 c 0.2
6/f b 1 c 0.00
7/m b 1 c 0.30
8/m b 1 c 0.35
9/m 1 b c 0.25
10/m 1 b c 0.25
11/m 1 b c 0.45
Aggregated animal
values
a
3 8b 8 3b 11c
a
The sum of the values assigned to each rank for each animal
over the set of herders interviewed.
b
A measure of risk sensitivity in which the value represents the
additional probability, X, that a decision maker required to be in-
different between a certain prize of 50 animals and a lottery with
probability 0.5 X of winning 100 animals. Positive values indi-
cate risk aversion, zero values risk neutrality, and negative val-
ues risk-preferring attitudes.
c are varied and values in Kuznar (2000) are used to check
the robusticity of my ndings.
In generating my nal data, I had to take care that
respondents were giving me their actual preferences in-
stead of the result of their own optimizing calculations.
This was accomplished by identifying the forage needs
of different species of animals and what forage resources
herders possessed. These discussions, which generated
self-reports of aspirations and assets, were supplemented
by my own detailed mapping and analysis of the vege-
tation and forage potential of the communities in which
I worked (see Kuznar 1991c, d, 1994, and, for maps and
forage data, 1995).
I examined risk sensitivity in two Andean herding
communities located in contrasting environmental set-
tings, one in the high sierra (2,500 m3,800 m above sea
level) and one in the Andean puna (3,800 m4,500 m
above sea level). Both communities lie along the Ro
Asana in the Department of Moquegua, eastern Mariscal
Nieto Province, Peru. The environment in this region is
arid, and the landscape is dominated by bunch grasses
and xerophytic shrubs (Kuznar 1995, 1999, n.d.). The
high-sierra community is located between 2,500 m and
3,800 m above mean sea level and is characterized by
deep valleys, steep terrain, and seasonal rains. Pastor-
alists move up and down high-sierra valleys seasonally
with their herds of goats, sheep, and cattle. The average
family owns 142 goats, 13 sheep, and 4 cows (Kuznar
1993:259). Herders raise these animals primarily for
meat, although the milk of females whose offspring die
is an important secondary resource.
A number of hazards afict high-sierra herds, among
them theft, drought, and predation. For instance, Win-
terhalder (1994) and Kuznar (1990, n.d.) provide mea-
surements on the predictability of rainfall in the Andes
based on information theory (Colwell 1974). In general,
the annual predictability of rainfall in highland areas is
less than 50%. In the communities I report here,
droughts, although infrequent, can claim up to 60% of
a herd, and predation is a constant low-level threat,
claiming 4% to 8% of a herd annually (Kuznar 1991c:
97; 1994:60; 1995:44, 47, 50). According to herders state-
ments and some personal observations, theft accounts
for 10% to 20% of herd losses in the high sierra (see also
Custred 1974:287; Orlove 1980).
The puna community is above the high-sierra com-
munity in the Andean high-altitude plain between 3,800
m and 4,400 m. The puna is too high for effective goat
and sheep herding, and therefore indigenous herd ani-
mals, the llama (Lama glama) and the alpaca (Lama pa-
cos), are the primary animals herded in this zone. Llamas
are large and provide transportation for goods to lowland
markets where puna pastoralists can obtain agricultural
products in trade. In addition to transportation, llamas
provide meat and wool for making bags and ropes. Al-
pacas produce valuable wool that herders trade and use
in the manufacture of blankets and clothing. Family
herds in this puna community average 82 alpacas, 22
llamas, and 8 sheep. The primary hazards that afict
herds in the puna include snow, drought, predation, and
theft. Snow is the most severe hazard, with families los-
ing up to 50% of their herd in a severe snow year. People
mitigate other hazards by effective defense of herds with
dogs and family networks that cooperate for defense
against rustlers.
The presence of clear, unpredictable hazards in these
two communities makes them good candidates for in-
vestigating risk sensitivity. Two Aymara assistants and
I interviewed 12 herders among the high-sierra families
(50% of adults and adolescents) and 11 herders in the
puna community (17.5% of adults). These communities
were very small, so the sample should capture results
generalizable to the communities as a whole. More in-
terviews in larger communities would be ideal. However,
the relationships I investigate turn out to be extremely
strong and highly statistically signicant, despite the
small sample size. Assessing the representativeness of
my data will require further research.
risk sensitivity in aymara herders
High-sierra pastoralists are extremely risk-averse (table
1). Only one individual in the sample is risk-neutral, and
no one prefers risk. The average probability premium is
0.38 (i.e., a person requires near 90%certainty of winning
a large prize of 100 animals before abandoning a certain
prize of 50 animals), with a coefcient of variation of
34.2%. In general, high-sierra pastoralists prefer cows to
goats, and sheep have the lowest preference (table 1).
There are interesting trends in animal preference by gen-
der (table 3). According to womens statements, they pre-
fer animals with a direct domestic household use, such
as sheep that produce wool and cows that produce milk.
Volume 42, Number 3, June 2001 F 437
table 3
Animal Values
a
by Sex of Herder
Animal
Sex of Herder
One-
tailed T
Statistic d.f. Probability Male Female
Alpacas 0.83 1.00 0.905 9 0.190
Llamas 0.67 0.50 0.904 9 0.190
Sheep 0.18 0.40 1.545 21 0.069