Abstract
The plurality rule for molecular sequences is a consensus function ℘ which maps each profile of lengthk (i.e., each sequence ofk bases appearing at an aligned position ofk molecules) to a set of consensus results (i.e., ambiguity codes) that are descriptive summaries of the profile. Since the plurality rule ℘ is a median procedure, its results are solutions of an optimization problem that is well known and intensively studied in the theory of social choice. However, ℘'s behavior for long profiles according to its behavior for short profiles. Because consistency is a desirable feature of consensus functions, we explore the boundaries of its applicability to ℘. We distinguish between two types of consistency, weak and strong, and we apply them to profiles and consensus results as well as to ℘ itself. For ℘ we obtain simple characterizations of weakly consistent profiles, of weakly consistent results, and of strongly consistent results.
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