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Decoy Effects in Choice Experiments and Contingent Valuation: Asymmetric Dominance

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While a dominated choice involves a situation in which one option clearly dominates another on all relevant dimensions, an asymmetrically dominated choice typically arises where at least two options do not dominate each other and one (but not both) of those options does dominate a third option. We demonstrate that the introduction of such an asymmetrically dominated option can have a significant impact upon choices between non-dominated options within the same choice set for non-market goods. Furthermore, we show that this effect can then translate into significant impacts upon subsequent valuations for those non-dominated options.
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Asymmetric Dominance Effects in
Choice Experiments and Contingent Valuation
by
Ian J. Bateman, Alistair Munro
and Gregory L. Poe
CSERGE Working Paper EDM 05-06
Asymmetric Dominance Effects in
Choice Experiments and Contingent Valuation
Ian J. Bateman1, Alistair Munro2 and Gregory L. Poe3
1Centre for Social and Economic Research on the Global Environment
(CSERGE), University of East Anglia, Norwich, NR4 7TJ, UK
2Department of Economics, Royal Holloway University of London, UK
3Department of Applied Economics and Management, Warren Hall,
Cornell University, Ithaca NY 14853, USA
Author contact details:
Ian J. Bateman, e-mail: i.bateman@uea.ac.uk
tel: +44 (0)1603 593125, fax: +44 (0)1603 593739
Acknowledgements
Funding for this research was provided by the Programme for Environmental
Decision Making (which is funded by the UK Economic and Social Research Council:
ESRC), the Economics for the Environment Consultancy (EFTEC), and the USDA
Regional Project W-1133. Research assistance from Alex Arnell is gratefully
acknowledged as are discussions with Robin Cubitt, Paul Slovic, Chris Starmer,
Robert Sugden and participants in the Colorado University 2004 Workshop on
Environmental and Resource Economics and Cornell University’s AEM Departmental
Seminar. All errors are the authors’ responsibility
ISSN 0967-8875
Abstract
While a dominated choice involves a situation in which one option clearly dominates
another on all relevant dimensions, an asymmetrically dominated choice typically
involves more than two options in which at least two options do not dominate each
other but one (but not both) of those options does dominate a third option. We
demonstrate that the introduction of an asymmetrically dominated option can
significantly impact upon choices between non-dominated options within the same
choice set. Furthermore, we show that this effect can then translate into significant
impacts upon subsequent valuations for those non-dominated options. Such findings
are at odds with standard theory yet accord with a substantial number of findings
within the marketing and experimental economics literatures. More fundamentally
these results show that the introduction of alternatives which are, from a formal
perspective, irrelevant can significantly impact upon non-market valuation estimates
derived from both choice experiments and contingent valuation studies. We consider
the impact of such effects and their implications for future valuation research.
Keywords
Choice Experiment, Contingent Valuation, Asymmetric Dominance, Willingness to
pay, Lakes.
.
1
1. INTRODUCTION
In recent years, “anomalies” observed in contingent valuation (CV) exercises have informed
broader economic theory: the most noted example being the case of the disparity between
willingness to pay and compensation demanded, which was initially observed in, and
attributed to, hypothetical survey scenarios (Hammack and Brown, 1974; Brookshire,
Randall and Stoll, 1980; Rowe, D’Arge, and Brookshire, 1980), replicated in actual choice
frameworks (Knetsch and Sinden, 1984 amongst numerous others), and subsequently
incorporated into neoclassical (Hanemann, 1991) and Non-Hicksian theories of choice
(Tversky and Kahneman, 1990). A similar extension of hypothetical results to actual choice
situations has occurred in part-whole bias (Diamond and Hausman, 1994; Bateman et al.,
1997) and other-regarding behaviours (Kahneman and Knetsch, 1992; Palfrey and Prisbey,
1997).
In this paper we reverse this demonstrative flow by examining whether a particular choice set
phenomenon widely demonstrated in the marketing and psychological literatures, and borne
out in experimental economic settings and real market observations, carries over to
hypothetical non-market valuation and public goods choice settings. Our particular focus
here is on asymmetric domination effects. While a dominated choice involves a situation in
which one option clearly dominates another on all relevant dimensions, an asymmetrically
dominated choice typically involves more than two options in which one option is dominated
by at least one other option, but not by all options. Figure 1 illustrates asymmetric dominance
in the case where options vary along two dimensions. In this figure, d is dominated by t, but
not by c. An asymmetric dominance effect is an example of a broader class of decoy
phenomena (Herne, 1997, 1999), which refer to the effects on choices between two options
(the target: t and the competitor: c) that results from the introduction of an additional option
(the decoy: d). An asymmetric dominance effect is then said to occur if the addition of an
asymmetrically dominated decoy increases the share of the target (Huber, Payne, and Puto,
1982).
Figure 1: Asymmetric Dominance
c
t
d
Attribute 2
Attribute 1
2
Decoy effects in general and asymmetric dominance effects in particular have attracted
attention of psychologists and experimental economists because rational choice theory
posits that preferences between two options should not depend upon the presence or
absence of any other options. It follows that if t is not chosen from a binary choice set B={c,
t}, then t cannot be the preferred choice in the more encompassing choice set E={c,t,d}. This
principle, known as expansion consistency (Sen, 1982) is embodied in standard models of
rational choice (Tversky and Simonson, 1993) and, given monotonicity, implies the absence
of asymmetric dominance effects. At an aggregate level, the parallel to the expansion
consistency restrictions on individual choice is the regularity condition (Huber, Payne and
Puto, 1982). Formally, letting C(B) = c denote that alternative c is chosen from the choice set
B and P(c, B) indicate the proportion of people for whom C(B) = c, the regularity condition is
defined as
P(c, B) > P(c,E) (1)
Regularity is a weaker condition than expansion consistency, because even when regularity
holds at the aggregate, individuals may still violate expansion consistency. Nevertheless,
from the perspective of choice experiments, regularity remains a minimally desirable
condition. It follows that failure of the regularity condition, in the form of an asymmetric
dominance effect may have serious consequences for the acceptability of choice
experiments.
Evidence of asymmetric dominance effects are widely demonstrated in the experimental and
consumer choice literature (see for example Huber, Payne and Puto, 1982; Ranteshwar,
Shocker and Stewart, 1987; Lehman and Pan, 1994). As an example, Rabin (1998)
discusses an asymmetric dominance experiment conducted by Simonson and Tversky
(1992) that examined choices between receiving $6 and a Cross pen. (Cross is a
manufacture of elegant pens in the United States)
“While only 36 percent of the subjects choosing only between the Cross pen
and $6 chose the Cross pen, 46 percent of subjects who were also given the
choice of a less attractive pen chose the Cross pen…the addition of an option
that compared unfavorably (as more expensive or lower quality) to an existing
option enhanced the perceived attractiveness of the existing option” (p. 38)
Other researchers have demonstrated that such effects appear to be general, and extend to
other choice situations such as political candidates (Pan, O’Curry and Pitts, 1995), job
candidates (Highhouse, 1996) and policy issues (Herne, 1997). While much of this research
has utilized hypothetical choice tasks, Simonson and Tversky (1992) and Herne (1999)
demonstrate that asymmetric dominance effects persist in choice experiments involving real
incentives. More recently asymmetric dominance effects have been observed in real markets
for commonly purchased goods. An interesting example of such phenomena is provided by
Doyle et al. (1999), who conduct a real world investigation regarding purchases of tins of
baked beans in a supermarket. Here the researchers initially monitored sales of two brands
of beans, both sold in the same large can size, over the course of a week. This showed that
one brand, which we can designate as Brand X, accounted for just 19% of sales despite
being cheaper than the leading brand. The researchers then introduced a decoy good,
namely a line of small tins of Brand X sold at the same price as a large can. Sales from the
following week showed that, while (unsurprisingly) no purchases of the decoy were made,
market share of Brand X had increased significantly (p = 0.034) to 33% of sales so cutting
sales of the leading brand from 81% to 67%.
The fact that the asymmetric dominance effect increases the relative, and in some cases the
absolute, proportion of choices favouring the more proximate target runs counter to the
“similarity hypothesis” that new items take share from existing items that are the most similar
(Tversky, 1972). Efforts by psychologists and market researchers to explain this
phenomenon can be broadly categorized as perceptual effects and decision-making
3
processes. With regards to the former, the addition of an asymmetrically dominated decoy
extends the unfavourable dimension of the target more than the favourable dimension,
making the target’s deficit in the unfavourable dimension seem less great (Huber, Payne and
Puto, 1982; Huber and Puto, 1983). Increased frequency of items in the dimension on which
the target is superior may increase the weight placed on that dimension (Huber, Payne and
Puto, 1982). With respect to decision-making processes, Simonson (1989) argues that
individuals seek to justify their choices in the face of uncertainty, especially in cases that they
may be concerned about external evaluation of their decisions: the target may be more
“attractive” because its superiority is unambiguous and independent of subjective
preferences; the target may be regarded as a “compromise” that combines desirable
attributes of the other choices. Underlying decision processes may be driven by an
“extremeness aversion” (Simonsen and Tversky, 1992) or the application of simplifying
decision heuristics to minimize decision costs (Wedell, 1991). Wedell (1991) identifies
further psychological, decision-making processes that may engender such effects.
It is evident, however, that the asymmetric dominance effect is not isolated to the human
psyche – it may be that we are “hard wired” to make choices using comparative, context-
dependent criteria rather than to value options independently. Shafir, Waite and Smith
(2002) note:
“We tested the choices of honeybees and gray jays in binary and trinary
contexts. According to the theories of rational choice and optimal foraging,
the subjective values assigned to two preexisting options should not be
affected by the presence or absence of a third option. However, our subjects
were affected by the presence of an asymmetrically dominated decoy just like
human subjects…” (p. 185)
Given the clear impact on familiar and regularly purchased products in humans and
replication in foraging by other species, we feel justified in investigating whether this effect
will replicate for less familiar environmental non-market goods for which preferences should,
if anything, be more malleable.
Our research extends the literature on asymmetric dominance in two key ways: first by
demonstrating that this phenomenon is exhibited in choices and expressed preferences for
non-marketed environmental goods. Perhaps more importantly, this research also provides
the first demonstration that values, and not just choices, are affected by the introduction of an
asymmetrically dominated decoy. Such a result is of general economic interest, but is
particularly critical in the context of the recent increased use of choice experiments in valuing
non-market goods, since it suggests that conjoint and other choice methods may be subject
to the same systematic biases documented in the psychology and marketing literatures. We
further argue that the findings presented in this paper provide a possible explanation of why
non-market values derived from choice experiments seem to exceed values obtained from
methods that elicit values for only one good (Cameron et al. 2002).
4
2. DESIGN AND HYPOTHESES
The data are taken from a study of proposed environmental management strategy options for
Ranworth Broad in East Anglia, U.K. (a Broad is a colloquial East Anglian term for lake). In
an in-person, on-site survey of visitors to the Broad, respondents were presented with
information concerning two distinct environmental attributes (A1, A2) which were increased
from present day levels by different extents: the first attribute (A1) concerned an increase in
the number of birds at the Broad; the second attribute (A2) concerned an increase in the
amount of plant cover at the Broad. Increases in attribute A1 were measured as numbers of
additional birds whereas increases in attribute A2 were measured as percentages over the
current level of plant cover. The analysis presented in this paper concerns responses to
linked choice and valuation questions, both concerning changes in bird numbers and plant
cover detailed above. The choice task was presented prior to the valuation task with a
principle aim being to see (i) if asymmetric dominance effects occurred in the former and if so
(ii) whether such an effect would then impact upon a subsequent valuation task concerning
the same provision change.
A split sample design was employed with one subsample being presented with a choice
between options c = (100, 30) and t = (150, 20), i.e. the choice set {c,t}. The second
subsample was offered an expanded choice set {c,t,d}, where d=(140, 15). Note that, as
demonstrated in Figure 2, d is dominated in both dimensions by t. In contrast the movement
in outcome space from c to d would involve an increase in A1 by 40 and a decrease in A2 by
15. Thus, d is dominated by t but not c.
Figure 2: Asymmetric dominance in the Ranworth Broad Choice Sets
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120 140 160
Increase in Bird Population (Numbers)
Increase in Plant Population (%)
In both subsamples, respondents made their decisions based upon numerical information
presented to them on a showcard (letters c, t and d were not used on the cards). The cards
were structured in a table format so as to make assimilation of the information as easy as
possible. In the choice task respondents were simply asked to identify their preferred option
c
t
d
5
from the two or three presented to them. The subsequent valuation exercise elicited
willingness to pay for the preferred option, payment being made via a general tax vehicle as
used in previous in-person CV survey research on the Norfolk Broads (Bateman et al., 1995).
These choice and valuation questions are reproduced in the Appendix to this paper.
The questionnaire survey was conducted at the Ranworth Broad Nature Reserve visitor
centre in the Norfolk Broads employing face-to-face interviewing techniques. Approximately
half of the questionnaires were completed within the visitor centre (beside the entrance) and
the other half outside the entrance as they entered the building. Members of the public who
agreed to respond to a ten-minute questionnaire were assigned at random to one of the two
treatments. The refusal rate was only 4 percent reflecting the prior commitment of visitors to
this area. A total of 294 subjects were interviewed. Prior to each decision task, all
respondents were provided with some background information to the scenario. This material
was designed so as to be as unbiased towards any particular attribute as possible.
Furthermore, it was emphasized that there were no correct answers and that the respondent
should respond according to their own preferences. As will be demonstrated later, the
random assignment of surveys provided samples with statistically identical characteristics.
Given this data, we examine four hypotheses. The first hypothesis is concerned with testing
the null hypothesis of description invariance, with the alternative hypothesis being that the
regularity conditions are violated. Formally,
Ho1: P(t,B) = P(t, E) HA1: P(t,B) < P(t, E)
Hypothesis Ho1 states that the probability of choosing the target good t does not vary
systematically according to whether or not the dominated decoy d is present or absent in the
choice set; it tests the standard assertion that d is an irrelevant alternative. Testing Ho1 is
accomplished by standard contingency table analyses to test whether the relative shares of t
and c change with the addition of an asymmetrically dominated decoy. A one-sided test of
proportions is used to explore the alternative hypothesis that the regularity condition is
violated for the target t.
The second hypothesis involves conditional tests of asymmetric dominance effects upon
choice. This is assessed by modelling individual choice as a function of covariates. Formally
this hypothesis is stated as follows,
Ho2: P(t,B; m) = P(t,E; m) HA2: P(t,B; m) < P(t,E; m) ,
where m is a vector of exogenously determined preferences and socio-economic
characteristics of the respondents. Adopting a random utility modelling framework, this
hypothesis test is conducted using a probit model in which the dependent variable is whether
t is chosen or not. The significance of the coefficient for the binary variable indicating
whether the decoy was present in the choice set provides the test of whether the null
hypotheses Ho2 can be rejected in a manner consistent with an asymmetric dominance
effect. This, in conjunction with the sign of the coefficient, provide insights into whether or
not the alternative hypothesis should be accepted.
Finally, in our last two hypothesis tests, we examine the procedural variance null hypothesis
that values are not affected by the addition of a decoy to the choice set. This investigation
takes two forms. First we focus on whether the “average” valuation is affected by the
addition of the decoy, where µ indicates that the preferred choice in a costless setting is the
choice being valued:
Ho3: V(µ(B)) = V(µ(E))
6
No alternative directional hypothesis is specified. Rejection of Ho3 simply provides an
indicator of whether the addition of an asymmetrically dominated decoy influences values
placed on the preferred option expressed by individuals without distinguishing between which
option, c or t, was chosen.
We next examine whether stated values for the preferred choice vary with the choice set.
Ho4: V(x,B) = V(x,E) for x = c, t
Because expectations associated with this test may depend upon the outcome of the
previous hypotheses, and because of the possibility of preference reversals (Lichtenstein
and Slovic, 1971; Irwin et al., 1993), no alternative directional hypothesis is specified at this
point. Nevertheless, the empirical direction of any impact remains a primary interest of this
research, as will be discussed.
The third and fourth hypotheses are evaluated following the treatment effects modelling
framework initially discussed in Barnow, Cain and Goldberger (1980). Although a full
information maximum likelihood estimator is used, this model is most readily described by
analogy to the well-known “two-step” selection model developed by Heckman (1976) wherein
z is an indicator variable for the presence or absence of a treatment. In our situation, z
distinguishes between the choice of t (z=1) or c (z=0), which is modelled in the “first step” or
selection model using a binomial probit model. The differentiating feature of the treatment
effects model from the standard selection model is that the treatment effect is endogenous in
the “second step” of the modelling process and all observations (rather than a selected
subsample) are included in the second step. Formally, following Greene (2002, 2003a,
2003b), letting WTP = the observed willingness to pay value and WTP* be the corresponding
latent variable, the specification of the tobit model1 with treatment effects is
],,,,0,0[~ ,
,0*z if 0
,0*z if 1
, z*
otherwise, *WTP WTP0, WTP* if 0 WTP
,*WTP
22
ρσσε
ε
δ
ε
u
Nu
z
z
u
z
=
>=
+=
==
++=
wα'
xβ'
where x and w are vectors of covariates and
δ
and,αβ are coefficients to be estimated.
The standard deviations are 22 and u
σσ ε
, and the covariance is 22
u
σρσ ε
(Green, 2002, 2003a).
1 44 of the 270 WTP responses were 0.00. Corrected ordinary least squares models, do not censor the WTP
data at zero, provide qualitatively the same results as reported for the Tobit specification are available from the
authors.
7
3. RESULTS
3.1 Regularity Test of Asymmetric Dominance Effects on Choice Shares: H1
Table 1 details the choice shares for the various options offered to our two choice task
subsamples. Consideration of these findings reveals clear evidence of asymmetric
dominance effects. When no decoy is included in the choice set, the choice between target
and competitor are approximately evenly split. With the addition of the asymmetrically
dominated decoy, it is evident that the choice shares change substantially with the proportion
of respondents choosing t increasing noticeably. Only one of the respondents acted
“irrationally”, choosing the decoy rather than the preferred alternative. This individual is
excluded from subsequent analyses. Using standard chi-square tests, the choice shares of c
and t are significantly different (Table 1a data: =
2
1
χ
11.14, p < 0.01; Table 1b data:
=
2
1
χ
8.91, p<0.01) across choice sets. This leads to a rejection of the null hypothesis Ho1,
indicating that the addition of an asymmetrically dominated decoy does indeed affect the
choice shares. A one-sided test of proportions indicates that the alternative hypothesis, that
the regularity conditions with respect to t, are violated, a finding that demonstrates that
asymmetric dominance effects carry over to violations of the regularity conditions in choices
involving environmental goods.
Table 1: Choice Shares by Choice Set
(Cell contents are counts with corresponding subsample proportions given in parentheses)
c t d
All Data
{c,t} 72 (50%) 72 (50%) -----
{c,t,d} 46 (31%) 103 (69%) 1 (<1%)
Respondents Reporting WTP
{c,t} 62 (48%) 68 (52%) -----
{c,t,d} 42 (30%) 97 (70%) 1 (<1%)
Note: As defined in the text and demonstrated in Figures 1 and 2, c refers to the competitor, t refers to
the target, and d refers to the decoy. Note that d is asymmetrically dominated by t.
3.2 Conditional Tests of Asymmetric Dominance Effects on Individual Coice: H2.
For both the ‘With Decoy’ and ‘No Decoy’ subsamples, Table 2 provides, descriptive
statistics for the exogenous choice covariates included in the econometric analysis. These
include standard demographic and socio-economic characteristics such as gender, age and
income. Also included are indicators of how frequently the individual uses the resource and
membership in environmental organizations. Using Chi-square contingency table analyses
for the binary variables and independent difference of mean t-tests for the continuous
variables, none of the covariates used were found to be significantly different between the
‘With Decoy’ and ‘No Decoy’ subsamples.
Binomial Probit selection models allowing for exogenous socio-economic covariates are
provided in Table 3 using both the full sample and the observations for which WTP values
were reported. The “long” analyses includes all the aforementioned covariates, regardless of
significance level. The “short” analysis retain only those that passed a pre-test criteria of 20
percent: i.e., income, and membership in specific environmental organizations. The two
membership covariates tend to shift choices in alternative directions: membership in the
Royal Society for the Protection of Birds (RSPB) is associated with a rise in the likelihood of
choosing the alternative that favoured birds (a reassuringly common sense result);
membership in less specific “Green” organizations such as Friends of the Earth is correlated
with choosing the competitor (more plants – again this seems a plausible and interesting
8
result). As might be expected for a costless choice, income is not significant in any of the
selection models.
Table 2: Descriptive Statistics
Mean (s.d.) Mean (s.d.)
Variable
All
Respondents
“No
Decoy”
Sample
“With
Decoy”
Sample
Respondents
Reporting
WTP
“No
Decoy”
sample
“With
Decoy”
sample
With Decoy
(binary, 1 if{c,t,d,},
zero if {c,t})
0.508
(0.501)
0 1 0.519
(0.501)
0 1
Household Income
(continuous, set at
midpoint of income
brackets)
25,145
(14,183)
23,976
(14,473)
26,275
(13,852)
25,000
(14,174)
23,923
(14,565)
26,000
(13,778)
Frequent visitors
(binary, 1 if
visits/year > 2, zero
otherwise)
0.184
(0.388)
0.188
(0.392)
0.181
(0.386)
0.193
(0.395)
0.192
(0.396)
0.193
(0.396)
Gender
(binary, 1 if female,
zero otherwise)
0.495
(0.501)
0.500
(0.502)
0.490
(0.502)
0.496
(0.501)
0.500
(0.502)
0.493
(0.502)
Age
(continuous, in years)
41.57
(16.87)
41.31
(16.88)
41.82
(16.91)
41.10
(16.97)
40.51
(16.92)
41.65
(17.06)
RSPB
(binary, 1 if member
of the Royal Society
for the Protection of
Birds, zero
otherwise.)
0.177
(0.383)
0.153
(0.361)
0.201
(0.402)
0.178
(0.383)
0.169
(0.376)
0.186
(0.390)
Greens
(binary, 1 if member
of green
organizationa, zero
otherwise)
0.191
(0.394)
0.188
(0.392)
0.195
(0.397)
0.185
(0.389)
0.177
(0.383)
0.193
(0.396)
n 293 144 149 270 130 140
a. “Green” organizations include Greenpeace, Friends of the Earth, and WWFN.
9
Table 3: Selection Equation, Binomial Probit (target = 1, competitor = 0)
Estimated Coefficient –
All Data (s.e.)
Estimated Coefficient –
Respondents Reporting
WTP (s.e.)
Variable
Long Model Short Model Short Model Long Model
Constant -0.117
(0.279)
-0.164
(0.173)
-0.199
(0.288)
-0.201
(0.182)
With Decoy
(binary, 1 if{c,t,d,}, zero
if {c,t})
0.512
(0.159)** 0.512
(0.158)**
0.521
(1.67)**
0.522
(0.166)**
Household Income
(continuous, set at
midpoint of income
brackets)
0.00000793
(0.00000601)
0.00000776
(0.00000579)
0.0000118
(0.00000642)
0.0000109
(0.00000612)
Frequent visitors
(binary, 1 if visits/year
> 2, zero otherwise)
-0.0667
(0.222)
-0.134
(0.234)
Gender
(binary, 1 if female,
zero otherwise)
0.0425
(0.160)
0.063
(0.167)
Age
(continuous, in years)
-0.00150
(0.00471)
-0.00081
(0.00489)
RSPB
(binary, 1 if member of
the Royal Society for
the Protection of Birds,
zero otherwise.)
1.058
(0.252)** 1.046
(0.250)**
1.106
(0.272)** 1.081
(0.268)**
Greens
(binary, 1 if member of
green organizationa,
zero otherwise)
-0.956
(0.211)** -0.960
(0.209)**
-0.976
(0.223)** -0.982
(0.221)**
n 293 293 270 270
Note: * and ** denote 5% and 1% significance levels, respectively. Standard errors in parentheses.
Given these covariates, the probit results demonstrate significant impacts of adding the
decoy to the choice set (p < 0.01) as demonstrated by the coefficient on the With Decoy
variable. As such, Ho2, the null hypothesis of no asymmetric dominance effect, can be
rejected. The positive and significant sign on the With Decoy variable further suggests that
asymmetric dominance effects observed in other choice settings can be extended to the
realm of tradeoffs between environmental goods.
3.3 Expansion of the Choice Set and Average WTP – H3
Willingness to pay values by choice set and choice are provided in Table 4. Examination of
this 2X2 matrix of values suggests that WTP for t is higher than WTP for c, and that the
addition of the decoy increases the WTP for t. There appears to be a smaller downward
effect on WTP for c when an asymmetrically dominated t is added.
10
Table 4: Mean WTP Values (£’s) by Choice Set and Choice (s.d.)
C t
{c,t} 15.45
(21.31)
18.49
(24.10)
{c,t,d} 13.81
(18.42)
24.61
(30.33)
Note: As defined in the text and demonstrated in Figures 1 and 2, c refers to the competitor, t refers to
the target, and d refers to the decoy. Note: d is asymmetrically dominated by t. Standard errors are in
parentheses.
Table 5: Treatment Effects Model, Corrected Tobit Specification
Tobit Regression, Accounting for Treatment Effect
Coefficient Estimates (s.e.)
Average Value Shift Value Shift by Choice
Variable
Long Model Short Model Long Model Short Model
Constant 2.67
(6.87)
5.69
(5.44)
4.96
(6.87)
8.15
(5.48)
Chose T -31.16
(5.84)** -30.97
(5.67)** -34.30
(6.31)** -34.09
(6.18)**
With
Decoy
9.58
(4.08)** 9.57
(3.93)**
D(Chose
C),
D(decoy)
6.40
(9.20)
6.45
(8.96)
D(Chose
T),
D(decoy)
16.23
(6.15)** 16.24
(6.06)**
Income 0.000841
(0.000133)** 0.000838
(0.000118)** 0.000818
(0.000132)** 0.000813
(0.000117)**
Frequent
Visitor
22.94
(4.31)** 23.55
(4.31)*** 22.97
(4.32)** 23.58
(4.31)**
Gender
(female
=1)
2.86
(3.60)
2.72
(3.56)
Age 0.041
(0.102)
0.047
(0.100)
RSPB 10.95
(4.88)* 10.62
(4.77)* 8.91
(4.88) 8.57
(4.80)
Greens -13.41
(5.38)** -13.27
(5.28)*
-11.31
(5.33)* -11.18
(5.20)*
σ
28.32
(1.12)** 28.30
(1.11)** 28.26
(1.15)** 28.24
(1.14)**
ρ
0.809
(0.0474)** 0.807
(0.0473)** 0.813
(0.0480)** 0.810
(0.0471)**
N 270 270 270 270
Log
Likelihood
Function
-1196.69 -1197.32 -1195.91 -1196.53
Note: * and ** denote 5% and 1% significance levels, respectively. Standard errors in parentheses.
11
The selection model described above was expanded to the treatment effects framework by
including the predicted choice as an endogenous variable in the second stage Tobit
regression. In the “Average WTP” regression, depicted in the lefthand columns of Table 5,
WTP is the dependent variable, and the independent variables include the set of covariates
in the long model discussed above. In addition, the “treatment” variable (i.e. the choice of c
or t as represented by “Chose t”) is included as an endogenous variable as previously
specified – that is the predicted value for “Chose t” from the “first stage” probit analysis is
used as an endogenous variable in the “second stage” Tobit analysis.2
Evaluating first the socio-economic covariates, only gender and age do not pass the pre-test
significance level of 20 percent. Hence they are not included in the short Tobit model.
Income and frequency of visits are each significant and positive, reflecting standard
expectations for WTP. WTP is positively correlated with membership in the RSPB, and
negatively correlated with membership in a Green organization.
Focusing on the With Decoy effect, we see that adding a decoy is correlated with a positive
and significant increase in WTP. This suggests that, on average, the addition of a decoy to
a choice set will elevate the WTP function for the remaining options in the choice set. The
existence of a treatment effect is indicated by the positive and significant ρ.
3.4 Expansion of the Choice Set and Conditional WTP: H4
The last two columns of Table 5 provide the corrected Tobit estimates in the treatment
effects model that distinguishes between the preferred choice (i.e. c or t) for which values
were subsequently elicited. We focus on the coefficients of the binary variables D(chose c),
D(decoy) and D(chose t), D(decoy), which replace the With Decoy variable in the previous
analyses. These variables, in conjunction with the Chose T variable, allow us to isolate the
WTP values for each of the quadrants in Table 3. If we define D(chose t) = 1- D(chose c),
then the four possible combinations are provided below.
c t
B ={c,t} Chose c = 1
D(decoy) = 0
Chose t = 1
D(Decoy) = 0
E={c,t,d} Chose c = 1
D(decoy) = 1
Chose t = 1
D(decoy) = 1
As such, c=C(B) serves as the baseline in the regression. Our interest at this point is on the
binary variables represented in the shaded portion of the above. That is, relative to the
baseline, D(chose c)/D(decoy) isolates the effect on WTP of adding the decoy for those
individuals that chose c. Similarly, D(chose t)/D(decoy) isolates the effect on WTP of adding
the decoy for those individuals that chose t.
As indicated in Table 5 the sign of the decoy effect is positive in both cases. WTP for c is not
significantly affected by the addition of the decoy to the choice set. However, the decoy
effect on WTP for t is large and statistically significant at the 1% level by the addition of the
decoy to the choice set. To put this is in an economic perspective, note that the size of the
decoy effect on WTP is of a similar order of magnitude to the impact of being a frequent
visitor to the area. Again ρ is significant, indicated the presence of a treatment effect.
Using sample means of the covariates associated with each of the samples corresponding to
the 2X2 matrix above, the estimated conditional willingness to pay values (and
corresponding standard errors) are 13.52 (0.09), 14.14 (0.09), 10.46 (0.15) and 22.63 (0.10)
for the No Decoy/Chose c, No Decoy/Chose t, With Decoy/Chose c, and With Decoy/Chose t
2 As noted previously the econometric estimation was conducted using full information maximum likelihood
procedures developed in Greene (2002).
12
samples, respectively. These predicted, sample specific and treatment corrected values,
mirror trends observed in the raw data: the addition of a decoy has a strong upward effect on
WTP for the target; there is evidence of a downward effect on WTP for the competitor for this
sample.
13
4. DISCUSSION
Using a data set from a study of water quality management in the U.K., this research
demonstrates that the asymmetric dominance decoy effects widely observed in the
psychological and marketing literatures are also manifested in environmental management
choice situations. In itself this raises substantial concerns about the robustness of values
from choice based non-market valuation elicitation approaches to changes in the choice set.
Importantly, we demonstrate that this choice anomaly carries over to valuation exercises.
Specifically, we find that the average value reported is larger when a decoy is included in the
choice set. This we term an absolute valuation decoy effect. Given that typical choice
experiments are replete with options which to a greater or lesser degree dominate other
options in the choice set, this may lead to stronger preferences being expressed in favour of
a given option than might be expected if that option had been valued directly without
dominated comparators. This type of comparison between choice and direct valuation is
precisely what occurs in studies which compare choice experiment with contingent valuation
estimates of goods. Such studies typically find that choice experiment values exceed those
estimated by contingent valuations (Adamowicz et al, 1998; Hanley et al., 1998, 2003;
Cameron et al., 2002; Foster and Mourato, 2003).
In addition to the absolute valuation decoy effect, this research demonstrates that the trade
off, or relative values, may be affected by the addition of decoy options. Specifically, in our
example, while WTP for the competitor, c, was not significantly affected by the addition of the
decoy, WTP for the target, t, was significantly affected, thereby changing relative values.
This suggests that marginal valuations from choice set experiments will be affected by the
addition of asymmetrically dominated decoy options. Such evidence suggests that one of
the purported advantages of choice set experiments, that marginal rates of substitution
between choices can be directly estimated, may not be robust.
Taken together this research suggests that biases or anomalies found in other choice
settings will also be found in choices regarding public environmental goods. One perspective
of this result is positive: hypothetical decisions about public issues are subject to similar
inconsistencies that are found in everyday decisions involving real commitments. However,
these results also suggest caution as researchers endeavour to expand non-market
valuation analyses into decision settings involving wider and more varied choice sets.
Because of the potential to affect values in known directions it is incumbent upon
researchers to carefully consider, and be prepared to defend, the specific design of choice
sets and to consider tests of robustness of WTP estimates from alternative choice set
designs.
14
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16
Appendix: Reproduction of choice and valuation questions
Text in bold type was read out to survey respondents. Regular type indicates instructions to
interviewers.
Ranworth Broad is one of 26 owned by the Norfolk Wildlife Trust that will benefit from
National Lottery funding. The funding on this reserve will create larger areas of open
fen, increasing the range of plants, birds and animals together with new interpretative
displays giving visitors an insight into the way people have created a landscape in
which wetland wildlife has benefited.
7. This card (SHOW CARD 4/5) illustrates the result of three/two possible
management schemes where the numbers of birds and water plants have
increased from present day levels to different extents. Assuming that the cost of
achieving each scheme is the same, please indicate which scheme you would
prefer to see implemented at Ranworth Broad.
Card 4 shown Card 5 shown
(with alternative d) (without alternative d)
Scheme A (c) Scheme A (c)
Scheme B (t) Scheme B (t)
Scheme C (d)
CARD 4
Scheme Increase in bird population from
present day (numbers)
Increase in amount of plant cover
from present day (% cover)
A (c) 100 30
B (t) 150 20
C (d) 140 15
CARD 5
Scheme Increase in bird population from
present day (numbers)
Increase in amount of plant cover
from present day (% cover)
A (c) 100 30
B (t) 150 20
(Cont.)
8. Now suppose that the scheme at Ranworth Broad is not lottery funded and
the numbers of birds and water plants does not change from the present
day. Considering the other expenses that you have made, I would like to ask
you what is the most your household would be prepared to pay, if anything,
each year in extra taxes per year in order to attain you preferred option.
When considering you response you should bear in mind that any money
you offer will be spent on that scheme only and nothing else.
Response: £ ________________ per year
or: p. _______________ per year
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Findings that challenge several normative assumptions of consumer choice have been documented in the literature on the attraction effect. There has been ample previous empirical evidence supporting the attraction effect. However, there is some concern that findings were generated only in hypothetical choice experiments. The choice of political candidates in elections presents a more complex and “real world” choice setting in which to reexamine the attraction effect. In this article, we report two studies that provide evidence of the attraction effect in the choice of political candidates in the 1994 Illinois State primary election and the 1992 U.S. Presidential election.
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Consumer choice is often influenced by the context, defined by the set of alternatives under consideration. Two hypotheses about the effect of context on choice are proposed. The first hypothesis, tradeoff contrast, states that the tendency to prefer an alternative is enhanced or hindered depending on whether the tradeoffs within the set under consideration are favorable or unfavourable to that option. The second hypothesis, extremeness aversion, states that the attractiveness of an option is enhanced if it is an intermediate option in the choice set and is diminished if it is an extreme option. These hypotheses can explain previous findings (e.g., attraction and compromise effects) and predict some new effects, demonstrated in a series of studies with consumer products as choice alternatives. Theoretical and practical implications of the findings are discussed.