Solomon's Paradox
Solomon's paradox is the finding that people reason better about someone else's problem than about their own. Igor Grossmann and Ethan Kross demonstrated it in 2014 across three experiments with 693 people. It is named after the biblical king whose judgement was famous in public and poor at home. It is a gap in the quality of reasoning, not a gap in how harshly people treat themselves, and the two must not be run together.
What it is
Given a friend's relationship trouble, most of us admit what we do not know, accept that things will change, take the other person's view seriously and look for a compromise. Given the identical trouble in our own life, we do less of all four. Those four moves are what the researchers scored, and the bundle is what the literature calls wise reasoning: intellectual humility, recognising that situations change, seeing another perspective, and searching for resolution.
Grossmann and Kross put people in front of a relationship conflict, either their own or someone else's, and scored how they talked it through. The advisers reasoned more wisely than the sufferers, and the sufferers were the same people. In the later studies the researchers asked participants to think about their own problem as an outside observer would, and the gap closed. The fix was free, and it was a change of vantage point rather than a change of information. See self-distancing for the lever itself.
What it does not measure, and this distinction is load-bearing. Grossmann and Kross measured wisdom of reasoning, not harshness. People reason less wisely about themselves. That is not the same as saying they are crueller to themselves. The kindness gap is widely reported experience, supported indirectly by the self-criticism literature; the reasoning gap is the measured thing. No clean experiment was located that asks the same person to write advice to a friend and to themselves about the same situation and then scores both for harshness.