Should you apologise?

If the issue in question is a big deal, the first variable (D) immediately raises the stakes. However, raising the stakes can lead you to apologise with more sincerity or to absolutely refuse to make amends (conversely, if the issue is not such a big deal, your entrenched stance on apologizing or not will be reduced).

Later in the equation we see that if the person accuses you unjustly, you will be highly unlikely to apologise. For example, if he/she blames you for running over his/her mother with the new SUV and you did not in fact run over his/her mother with said SUV, you will likely be righteous in your defence.

However, if the issue is not a big deal, even if you are not actually at fault you might as well apologise if the person demands it. Of course, as these variables interact with each other, you will find a delicate balance.

Raising the level of perceived responsibility will make you increasingly likely to apologise until it reaches the point of persecution at which time any further increase in perceived responsibility past your actual responsibility makes you less likely to apologise.