“The Greater Good,” often “For the Greater Good” was an idea developed Goderic’s Hollow in the summer of 1899 by Albus Dumbledore and Gellert Grindelwald which advocated wizard supremacy “for the greater good” of the world (DH18).
Dumbledore and Grindelwald’s plans to achieve the Greater Good by wizarding takeover involved locating and using the Deathly Hallows (DH35). The Life and Lies of Albus Dumbledore by Rita Skeeter has a chapter entitled “The Greater Good”, quoted in its entirety in DH18, discussing Albus Dumbledore’s friendship with Gellert Grindelwald. While Albus Dumbledore disavowed the idea of wizard supremacy, “For the Greater Good” became Gellert Grindelwald’s mantra, and it is carved into the entrance at Nurmengard Prison (DH18).
In Dumbledore's obituary, Elphias Doge described his late friend as "working always for the greater good" (DH2).