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Many companies and organizations have been collecting personal data with the aim of sharing it with partners. To prevent re-identification, the data should be anonymized before being shared. Although many anonymization methods have been proposed thus far, choosing one from them is not trivial since there is no widely accepted criteria. To overcome this situation, we have been conducting a data anonymization and re-identification competition, called PWS CUP, in Japan. In this paper, we introduce a problem appeared at the competition, named an excessive anonymization, and show how to formally handle it.