I can't remember anymore as do not have a partner, however with friends, family it all depends on the situation - I don't feel you can always say one thing or another for this question as it is too complex and depends so much on the situation.
I have just about been the one to make that first move, maybe 25% not.
So I think not a bad track record.
It really does depend also on what was said, and how badly things turned out.
Even when I know I am not in the wrong, I just have to say something most of the time.
If I thought it would do more damage to say something, that it would or could be taken badly....then I have backed away.
There are people like say my brother who all his life has believed he is in the right, so that's a no-win situation, and by giving in one will just make him even more difficult to deal with.
For my part, it depends entirely on the nature of the conflict. If the problem or situation was undoubtedly caused by me, I think it’s but fitting to initiate contact and say sorry to the aggrieved party. However, if such were not the case, then I shall wait for the other person to apologize. If they don’t know, that still won’t stop me from moving forward and striving to be a better person.
I do not think that any one person should always be the one to make a move to resolve conflict. My husband and I very rarely disagree, but when we do, we immediately realise that we have said the wrong thing and possibly hurt the other person, and we apologise. I have learnt a lot from my parents dysfunctional conflict resolution technique of ignoring each other and not talking for approximately a week. It was very tense for us all living in this environment. I vowed never to be as childish as them. We communicate about everything. Sometimes it is better to agree to disagree rather than try to change the other person towards your way of thinking, especially when they are reluctant to do so.
I have learnt a lot from my daughter who has no qualms about apologising when she has said something hurtful. Despite appreciating it is not easy to say sorry as that stupid “EGO” comes in the way. Slowly I am overcoming it especially, when I am in the wrong. Most of the time though I have learnt to talk less especially with people with whom friction is easy.