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The role of perceived acceptability of alternatives in identifying and assessing choice set
processing strategies in stated choice settings: the case of road pricing reform
David A. Hensher
Chinh Ho
Institute of Transport and Logistics Studies
The University of Sydney business School
The University of Sydney NSW Australia
David.Hensher@sydney.edu.au
Chinh.Ho@sydney.edu.au
Version: 1 July 2015 (revised 24 August 2015) accepted 29 September 2015
To appear in Transportation Research Part E
Abstract
In designing choice experiments, it is common to present a number of alternatives to a
respondent and have them choose the most preferred alternative. However, respondents may
ignore one or more alternatives which they deem unacceptable for various reasons. This
possibility aligns with the idea of the ‘consideration set’ which influences the choice of an
alternative given the choice set of interest. This paper uses an endogenous choice set model to
investigate the influence that contextual effects and socioeconomic characteristics play in
explaining variations in the choice sets considered by respondents when they reveal their
preferences.
Keywords choice of choice sets, processing strategies, acceptable alternatives, random
parameters, stated choice, road pricing, elasticities.
Acknowledgment The research contribution is linked to an Australian Research Council grant DP140100909
(2014-2016) on ‘Integrating Attribute Decision Heuristics into Travel Choice Models that accommodate Risk
Attitude and Perceptual Conditioning’. The comments of Bill Greene are appreciated as are the very useful
comments of four referees and the editor-in-chief Jiuh-Biing Sheu on various versions of this paper.
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1. Introduction and Conceptual Context
Stated choice modelling focuses primarily on identifying the role of a set of attributes and
attribute levels in establishing individual preference as an alternative/complementary
approach to revealed preference modelling. In stated preference studies, a choice experiment
is designed to ensure that the combinations of attribute levels that describe alternatives are
optimal in a statistical sense; however, the number of alternatives is usually pre-defined in
stated choice experiment and this carries forward to the modelling stage without sufficient
consideration of the behavioural implications of the relevant choice set. Typically, the
number of alternatives presented in a choice experiment (i.e., the size of the choice set) is
fixed and individuals are asked to choose the best alternative amongst this set of alternatives
or to rank the full set as if all alternatives are relevant. This includes experiments where the
number of alternatives is varied across choice scenarios or across respondents but fixed
within each choice scenario for each respondent.
In contrast to this common practice in stated choice modelling, respondents may not consider
some alternatives imposed in a choice task, and thus assuming all designed alternatives are
relevant to each respondent may not reflect the way in which respondents process the
information and reveal their preference. This paper proposes the use of an additional response
question related to the perceived acceptability of each alternative on offer in establishing
individual preference. This approach is along similar lines of supplementary questions that
reveal the extent to which specific attributes are attended to or not in attribute processing (see
e.g., Hensher 2010, 2014). The inclusion of the acceptability of an alternative in choice
models is effectively an additional endogenous choice response (Hess et al. (in progress) and
Rose et al. (2015)). Most importantly, the acceptability of each alternative provides a
response metric that can guide us in establishing the subset of alternatives that matter in
narrowing down the preferred alternative. This is known as the ‘choice of choice sets’
problem (as mentioned by Louviere and Hensher in 1983) and is typically neglected in choice
modelling. Regardless of what information is used to construct a choice set response, without
such knowledge it is not possible to establish, from the full set of alternatives, which subset
of alternatives are processed in making a preferred choice, and indeed in establishing a rank
order for a behaviourally meaningful set of alternatives. The small but growing literature on
the perceived acceptability of each alternative posits that when making decisions, people first
identify an acceptable set of alternatives, known as a consideration set in the broader
literature (especially in marketing research), and it is from this reduced set that the final
choice is made1. This is also in line with the literature on choice set formation set out in the
context of revealed preference data (see Manski 1977 and Swait and Ben Akiva 1987).
Despite frequent mention of these features of choice modelling, the great majority of applied
choice modelling (using stated choice data in particular) ignores this stage of the choice
making process. This might suggest that there is a view that modelling choices with
endogenous choice set is either too difficult or that it has little significance in the
determination of the choice outcomes of interest. Evidence from a recent study by Rose et al.
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In stated choice studies which impose a set of alternatives it is normal practice to ask which alternative is
preferred. What we have done however is to proceed with that question but to add in the addition question to
identify which alternatives in the set are acceptable. We could have asked these questions in the reverse order
but did not do so, and although the reverse order might be interesting, we are of the view that the responses for
only three alternatives are likely to be the same (at least for the majority of respondents). A sequence test is a
good topic for future research.
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(2015) rejects the latter explanation. Using an acceptability response to define choice sets of
interest, Rose et al. find a large number of differences between parameters associated with
the alternatives deemed to be acceptable and those deemed to be unacceptable by the
respondent. They show that joint estimation allows the modeller to overcome potential
endogeneity bias that may exist between the final choice made and the acceptability
responses, where the latter conditions the relevance of an alternative. The authors also
conclude that what might be thought of as preference heterogeneity may be linked to the
overall acceptability of an alternative.
What concerns us in the contribution of Rose et al. (2015) is that the acceptability of each
alternative is combined with its rank order to define the set of elemental alternatives for
jointly estimating alternative acceptability and choice. This modelling technique does not
account for the role that choice set formation plays in arriving at the selection of an
alternative. This paper focuses on the higher level of choice set formation which conditions
the lower level in a ‘nested’ structure of choosing a particular alternative. It differs from the
choice set generation methods proposed by authors such as Ben Akiva and Boccara (1995) in
that we treat the choice of choice sets as integral to the overall utility maximising framework
and not a conditioning set of exogenous rules.
2
The approach presented in this paper differs from previous contributions in that we use the
responses on the acceptability of each alternative to identify a choice set considered by the
respondent and formulate a model to predict both responses: the subset of alternatives
considered and the final choice. From a choice task of J alternatives imposed on the
respondent, we may construct up to 2
J
subsets of alternatives with different combinations of
acceptable alternatives. These subsets are referred to as outcomes of candidate choice set
processing strategies (CCSPSs), and only one of these subsets is considered by the
respondent when they make their final choice. This is in line with the idea of consideration
sets.
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Previous studies combined each alternative on offer with an acceptability response in
defining a universal choice set and estimating parameters which can be generic or specific
across an acceptability/certainty scale. These studies are interested in establishing different
sets of parameters for different levels of acceptability/certainty, assuming the relevance of all
alternatives offered in the experiment. In contrast, the current paper focuses on likely reasons
for each imposed alternative being processed (up to a probability) where the sub-set of
alternatives together with the alternative itself defines a choice response. The growing
literature on process heuristics offers up many possible explanations for choice set selection,
but one of particular interest in the context of choice experiments is the application of
context-dependent heuristics such as extremeness aversion and compromise (proposed by
Simonson and Tversky (1992) and Tversky and Simonson (1993)), that take into account the
variations in attribute levels across a set of alternatives predefined in a choice experiment
(Hensher 2014). Such context-dependent heuristics are an important feature of the empirical
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We are not able to conclude that our joint approach is empirically better than approaches in which exogenous
rules are imposed to define eligible alternatives in choice set generation, but it has the appeal of being more
general than approaches which select a few criteria to screen alternatives.
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Another way of including the acceptability of an alternative at the time of modelling is to assign a zero
probability to alternatives that have been deemed to be out of the acceptable consideration set (Gilbride and
Allenby 2004, Horowitz and Louviere 1995). However, asking whether an alternative is acceptable or not does
not preclude the possibility that the alternative was actually considered when the final choice was made, and
hence does not necessarily suggest that the alternative should be assigned a zero choice probability. Although, if
at least one other alternative is deemed to be acceptable, then any unacceptable alternative would be expected to
have a probability close to zero, and its treatment as outside of the final choice set has greater behavioural merit
than maintaining its presence.
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inquiry into some rules that might be adopted in ‘screening’ hypothetical alternatives,
especially in the context of a reference or status quo alternative that reflects real market
experience. We examine these possible processing rules through innovative ways of
introducing attributes into the utility expression of each ‘alternative’ as defined by a choice
set, such as the attribute range across the alternatives in a choice set.
Extremeness aversion or the compromise effect can be explained as follows. If an extreme
alternative is defined as one with both the best value on a subset of attributes, and the worst
value on other attributes, then a specific form of extremeness aversion known as the
compromise effect is said to occur (see also Leong and Hensher 2015). That is, the inclusion
of an extreme alternative in the choice set causes the pair-wise choice share of the
compromise or the in-between alternative to increase, relative to the other extreme
alternative.
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It is also normally supposed that a “betweenness inequality” holds in choice
making, in which the middle alternative (for example, in a three alternative choice set) loses
relatively more than an existing extreme alternative when another extreme alternative is
introduced (Tversky and Simonson 1993). Under this condition, the compromise effect can
be seen as a violation of the betweenness inequality and its existence is generally attributed to
a consequence of loss-aversive behaviour (Kivetz et al. 2004, 2008). There is a hint here of
the nature of acceptability of an alternative in preference revelation and the refinement of
choice set selection. The statistical design of choice experiments does not account for the
possible set of underlying behavioural processing strategies that respondents adopt in choice
revelation, something that has to be taken into account in modelling.
Given the interest in incorporating the endogenous acceptability response into choice models,
we assess model options within the random utility maximisation (RUM) framework. A
number of models have been developed at the alternative-level, allowing for the estimation of
non-random parameters or random parameters. Candidate methods of interest are mixed logit
and latent class models. The latent class model offers a framework within which to
investigate many forms of attribute processing (Hensher 2010); however, the latent class
approach is limiting when the focus is on understanding the role of specific alternatives in
establishing acceptable choice sets. This is because it is not feasible to associate latent classes
in a behaviourally meaningful way with combinations of alternatives that define potential
choice sets considered by the respondent. In order to give some behavioural structure to each
class (similar to imposing constraints of attributes in specific classes), this model form would
have to be interpreted as a probabilistic decision process (see Hensher 2014). Given all
possible candidate choice sets (or classes), we are interested in estimating the probability that
each of the candidate choice sets is adopted (i.e., the class assignment probability) as opposed
to treating the consideration set as known (i.e., probability =1) and the probability that each
of the alternatives is ranked as most preferred given the class they belong to (conditional
alternative probability). To do so, we would have to specify a latent class model with a
number of restrictions based on the presence or absence of an alternative in each candidate
choice set. This model will result in a singular variance matrix of parameters, as might be
expected, since it involves an exact mapping of the restrictions imposed on the utility
function of the same alternative that belongs to multiple candidate choice sets. A more
appealing way to do this is a standard random (or fixed) parameter logit model with error
components applied in this paper in which the error components are used to capture the
correlation across overlapping choice sets (i.e., subsets with common alternatives).
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This notion of “extremeness” might be distinguished from “dominating/dominated” alternatives, in which all
attributes of an alternative are better/worse than a competing alternative.
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The CCSPS approach proposed in this paper enables efficient implementation of RUM for
any choice set size since the emphasis at the upper level of the decision structure is on the
choice of CCSPSs, and not of alternatives; however this is jointly estimated with the choice
of best elemental alternative amongst those imposed in the experiment. The attribute
descriptions of each elemental alternative are embedded in the CCSPS model together with
explanatory variables designed to capture process heuristics such as extremeness aversion
and to identify other possible ways in which the attribute levels are processed in establishing
the acceptability of particular alternatives in defining a CCSPS. Examples are the range,
maximum and minimum levels and deviation of levels from the best or worst level of an
attribute across the full set of alternatives on offer, and the set deemed acceptable. Such an
approach (aligned with context dependency) is a way of identifying the role of particular
attribute processing strategies within and between alternatives in defining choices sets for
subsequent model estimation.
The paper is organised as follows. We begin with the conceptual positioning of the proposed
acceptability approach, followed by the context in which we empirically develop the CCSPS
model. We then present the model findings, followed by an assessment of the main
behavioural outputs. The paper concludes with the main findings and suggestions for ongoing
research.
2. Conceptual Positioning of the Proposed Acceptability Approach
Hensher and Louviere (1983), in one of the very earliest choice experiments, show that an
‘ideal’ choice experiment is defined as one in which “… the basic elements of the choice
process are abstracted and everything is controlled to permit unbiased estimates of choice
strengths and choice probabilities.” (p.228). Such an experiment would normally consist of a
set of J alternatives (j=1,2,…,J) and different subsets of these J alternatives which simulate
“availability” (although not strictly acceptability) or variance in choice sets. To ensure that
the choice of alternatives is independent of the presence or absence of alternatives in choice
sets (a condition satisfied when all alternatives appear equally often) and are also balanced
with respect to the presence and absence of all other alternatives, we would need to design
the choice experiment to satisfy this condition. A complete factorial design is likely to be too
large, but a 2
J
fractional factorial design can ensure a balanced occurrence of the
presence/absence of alternatives in choice sets.
A choice set designed under these conditions will be one of all universal finite choice sets
where each alternative appears equally often, 2
J
/2 or 2
J-1
times, and each other alternative
occurs 2
J-1
/2 or 2
J-2
times when each other alternative occurs (or does not occur). Each
individual is likely to have a different rank ordering of the alternatives which results in a
distribution of choices over any sample of individuals. This distribution is assumed to be
explained by the utility version of Luce’s choice axiom (McFadden 1974). A discrete choice
model that is estimated on such data will obtain a distribution of choice probabilities
associated with each choice set that sum to 1.0 across all choice sets for an individual.
Although the theoretical and methodological merits of such a design that is capable of
studying the ‘choice of choice sets’ are appealing, the design of the great majority of choice
experiments typically results in a fixed choice set or partial structuring of alternatives which
not only induces correlation across offered choice sets (the latter is not a concern when