  Personality quiz is a powerful tool that enables costumer segmentation by
actively asking them questions, and marketers are using it as an effective
method of generating leads and increasing e-commerce sales. In this paper, we
study the problem of how to select and sequence a group of quiz questions so as
to optimize the quality of customer segmentation. We assume that the customer
will sequentially scan the list of questions. After reading a question, the
customer makes two, possibly correlated, random decisions: 1) she first decides
whether to answer this question or not, and then 2) decides whether to continue
reading the next question or not. We further assume that the utility of
questions that have been answered can be captured by a monotone and submodular
function. In general, our problem falls into the category of non-adaptive
active learning based customer profiling. Note that under the our model, the
probability of a question being answered depends on the location of that
question, as well as the set of other questions placed ahead of that question,
this makes our problem fundamentally different from existing studies on
submodular optimization. We develop a series of question selection and
sequencing strategies with provable performance bound. Although we focus on the
application of quiz design in this paper, our results apply to a broad range of
applications, including assortment optimization with position bias effect.
