Rényi entropy yields artificial biases not in the data and incorrect updating due to the finite-size data.

We show that the Rényi entropy implies artificial biases not warranted by the data and incorrect updating information due to the finite size of the data despite being additive. It is demonstrated that this is so because it does not conform to the system and subset independence axioms of Shore and Johnson [J. IEEE Trans. Inf. Theory 26, 26 (1980)IETTAW0018-944810.1109/TIT.1980.1056144]. We finally show that the escort averaged constraints do not remedy the situation.