  A number of applications involve sequential arrival of users, and require
showing each user an ordering of items. A prime example (which forms the focus
of this paper) is the bidding process in conference peer review where reviewers
enter the system sequentially, each reviewer needs to be shown the list of
submitted papers, and the reviewer then "bids" to review some papers. The order
of the papers shown has a significant impact on the bids due to primacy
effects. In deciding on the ordering of papers to show, there are two competing
goals: (i) obtaining sufficiently many bids for each paper, and (ii) satisfying
reviewers by showing them relevant items. In this paper, we begin by developing
a framework to study this problem in a principled manner. We present an
algorithm called SUPER*, inspired by the A* algorithm, for this goal.
Theoretically, we show a local optimality guarantee of our algorithm and prove
that popular baselines are considerably suboptimal. Moreover, under a community
model for the similarities, we prove that SUPER* is near-optimal whereas the
popular baselines are considerably suboptimal. In experiments on real data from
ICLR 2018 and synthetic data, we find that SUPER* considerably outperforms
baselines deployed in existing systems, consistently reducing the number of
papers with fewer than requisite bids by 50-75% or more, and is also robust to
various real world complexities.
