Abstract: In the era of big data, the credibility of data experts in the public opinion field is manifested in two phenomena:one is the phenomenon of "Tacitus trap"-data experts cannot be trusted by the public no matter how hard they try; the other is the phenomenon of "the porcupine rule"-the public has to rely on data experts while questioning them. The reasons for the former phenomenon are as follows:experts cannot get rid of the influence of interests and powers; experts cannot solve contingency problems; data methods are irrational. The reasons for the latter are as follows:the high division of labor in modern society, the inability of intuition to give the public a sense of security, the need to urgently fill the vacuum of public trust, and the credibility of peer review. These two phenomena are contradictory and interdependent, showing that "objectivity" and "rationality" are only the rhetoric of identity of data experts in public opinion.