Many Hassidic Rebbes tackled the apparent change in HaShem's thought process, as if the Rabbis (chas v'shalom) were saying HaShem made a mistake. Of course He doesn't make mistakes, He's beyond time and infallible, so the concept of a mistake makes no sense in the context of HaShem. So what's the Midrash coming to teach us?
The Noam Elimelech has a unique take on this: He explains that there was no change, that the world still functions according to Din. But in order that the world would be able to exist, the Tzaddikim emerge in great Gevurah, great might, ascend to the root of all Din, and overcome and master the Judgement. Essentially the whole system works based on Gevurah or Din. Rachamim is the term for the victory of the Tzaddikim's Holy Gevurah over the natural Din HaShem bestowed within the system. This, he explains, is why the word 'partnered' (שתף) is used in the midrash as opposed to another word. HaShem allows the Tzaddikim through their great Holiness and desire to become partners in sustaining the world.