In the popularly used ranking method of peer rating, the exclusion of the evaluations/marks given to oneselves is intuitively appealing and has been actually practiced, since a person/university/country typically is biased in favor of itself. This short paper shows that this apparently reasonable principle of self-exclusion may give unacceptable rankings. In particular, it may rank B over A despite the fact that everyone including B ranks A over B. An impossibility theorem (in two versions) is proved, showing that, if the self-awarded marks are excluded, no method of ranking can satisfy some compelling conditions like monotonicity, neutrality, and weak unanimity. Some proposals to overcome the difficulty are discussed. While no ideal proposal has been discovered, some may be practically acceptable in most cases. Received: 5 November 2000/Accepted: 15 May 2002
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