Viterbi Algorithm - Selecting survivor paths which both contain the same Hamming distance
Viterbi decoders are usually designed to take one of the two paths consistently versus the other in the case of a tie. This makes it a lot easier to do bit-exact non-regression testing of the implementation.

If the numeric precision of the input has enough resolution, the probability of a tie should be sufficiently small that it doesn't substantially impact performance to have this (presumably minuscule) bias. If there is not enough precision, then you will have non-trivial bias (and quantization noise), and such insufficient precision will  result in performance degradation, regardless of whether the bias is randomized or consistent.