Asymptotically optimal assignments in ordinal evaluations of proposals
Author(s)
Advisor
Aykanat, CevdetDate
2009Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
In ordinal evaluations of proposals in peer review systems, a set of proposals
is assigned to a fixed set of referees so as to maximize the number of pairwise
comparisons of proposals under certain referee capacity and proposal subject
constraints. The following two related problems are considered: (1) Assuming
that each referee has a capacity to review k out of n proposals, 2 ≤ k ≤ n,
determine the minimum number of referees needed to ensure that each pair of
proposals is reviewed by at least one referee, (2) Find an assignment that meets
the lower bound determined in (1). It is easy to see that one referee is both
necessary and sufficient when k = n, and n(n-1)/2 referees are both necessary
and sufficient when k = 2. It is shown that 6 referees are both necessary and
sufficient when k = n/2. Furthermore it is shown that 11 referees are necessary
and 12 are sufficient when k = n/3, and 18 referees are necessary and 20 referees
are sufficient when k = n/4. A more general lower bound of n(n-1)/k(k-1)
referees is also given for any k, 2 ≤ k ≤ n, and an assignment asymptotically
matching this lower bound within a factor of 2 is presented. These results are not
only theoretically interesting but they also provide practical methods for efficient
assignments of proposals to referees.