The sacking of Natalia Kills and Willy Moon as judges on X Factor brings a sharp ending to a series of scandals for which TV3 has been attempting to apologise.

First, TV3 "apologised" for any "hurt or distress" caused by footage of contestant Shae Brider describing his criminal conviction for manslaughter.

In the second case, Moon swore at Tracey Neal-Gailer in a bakery. After she took her story to the media, X Factor issued a news release saying "Willy regrets the incident took place and he will be more thoughtful in his choice of language in future."

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Moon later denied any regret and then contradicted himself by claiming both that Neal-Gailer was lying and that her "lies" proved his original vulgarities correct.

On Sunday night, Kills and Moon abused a contestant, Joe Irvine, who Kills described as "disgusting" and "creepy".

TV3 put a statement on Facebook saying "TV3 does not condone bullying", which the Herald called a "forced apology". Yesterday Moon and Kills were sacked.

Perhaps we might shrug our shoulders, mutter something deprecating about what passes for entertainment these days, and resolutely turn our attention elsewhere. But before doing so, it is worth considering the questions these events raise about the nature and purpose of public apologies.

TV3's interventions are recent examples of a range of more or less fulsome apologies from a variety of public individuals and institutions. In all three cases, TV3 responded to bad behaviour by offering a public statement conveyed through TV broadcasts, news releases and social media. All three cases have been described as "apologies". But are they? Should we dignify these statements with that description? I think not. False characterisation debases the coinage.

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An apology is a way for the offender to acknowledge wrongdoing. An apology will say what was done, describe it as wrong, and acknowledge responsibility for it. It is usually offered by the offender. Third-person apologises aren't unknown. But when I apologise for someone else, for example if I apologise for my child's rude behaviour, I don't "own" that rude act. Instead, I communicate to my audience that I am responsible for correcting my child's behaviour.

So, how do TV3's statements stack up? In the case of Shae Brider, TV3's statement focused on the "distress or hurt" caused to the family of the dead man. It is common for public apologies to focus on the reactions of those injured. But that focus is usually wrong. Spin-doctors will instruct clients to redirect attention away from wrongdoing in a sympathetic manner. But good PR problem-management doesn't make an apology and it is mealy-mouthed to misconstrue the problem as the hurt feelings of the victims. Apologies respond to wrongdoing. In the Brider case, TV3's "apology" concerned the wrong thing.

The second case takes us further away from the paradigmatic apology. TV3's apology for Moon's vulgarity did not concern something TV3 did. TV3 did not, like a parent, need to accept responsibility for Moon's behaviour. Moon is an adult who was off camera and on his own time.

Now, TV3 could rightfully condemn Moon's act, as could anyone. But by trying to convey regrets that Moon clearly did not feel, TV3 tried to deflect attention from Moon's character. In this case, the apology came from the wrong agent and shows how a corporate apology can serve as "cover" to permit those who are culpable avoid responsibility. Moon did wrong. It was up to him to make redress. TV3 might be learning.

In the most recent case TV3 did not apologise for the wrong thing, nor did it come from the wrong person. In this case TV3 is, like a parent with a cheeky child, in a position of responsibility for Kills' and Moon's behaviour. Their abusive rant occurred during the show. TV3 choose to put that rant on air. Therefore, it would be appropriate for TV3 to apologise for its (former) employees' treatment of Joe Irvine.

TV3's Facebook statement condemning bullying is clearly not an apology. But it's more important that TV3 fired its boorish employees. The sincerity of that move will depend on whether TV3 puts in place procedures and standards to prevent future abuse.

Dr Stephen Winter is a senior lecturer in Political Theory at the University of Auckland. He's recently published Theorising the Political Apology, in the Journal of Political Philosophy, 2015.