This paper presents the results of an experiment where respondents were given two versions of two real-life controversies involving comments made by public figures. Approximately half of the participants read a story that made it appear as if the person had apologized, while the rest were led to believe that the individual stood firm. In the first experiment, involving Rand Paul and his comments on the Civil Rights Act, hearing that he was apologetic did not change whether respondents were less likely to vote for him. When presented with two versions of the controversy surrounding Larry Summers and his comments about women scientists and engineers, however, liberals and females were much more likely to say that he definitely or probably should have faced negative consequences for his statement when presented with his apology.
An apology experiment: “Does Apologizing Work? An Empirical Test of the Conventional Wisdom”, Hanania 2015:
My regular recommendation for apologies is Aaron Lazare’s book, “on apology”. Which gave me a solid understanding on what apologies are and are for.