I will consider the problem of estimating product preferences for
substitute goods or services, i.e., goods or services that serve the
same purpose, from a population of consumers. Here preferences are
elicited by questionnaires that pose a few choice tasks to
individuals from the population (respondents). Preference
elicitation by choice tasks is considered accurate since as it tries
to simulate real buying situations. The simplest choice task is a
pairwise comparison. To elicit a respondent's ranking of n
products completely n log(n) pairwise comparisons are
necessary. These are easily too many in settings where the
incentive for the respondent is not high though he might be willing
to answer a few questions truthfully. The standard approach to cope
with this complexity in marketing research is to aggregate the
answers of several (or all) respondents in order to estimate an
individual's complete preference ranking. I will describe such an
aggregation mechanism based on spectral clustering and prove its
validity in statistical model of population and respondents.
Joint work with Dieter Mitsche and Eva Schuberth (both from ETH Zuerich)