Your point about Wizard dominance being FOR THE MUGGLE'S OWN GOOD -- this, I think, is the crucial point. Yes, we have been given power and yes, that power gives us the right to rule, but it also gives us responsibilities over the ruled. We must stress this point, it will be the foundation stone upon which we build. Where we are opposed, as we surely will be, this must be the basis of all our counterarguments. We seize control FOR THE GREATER GOOD. And from this it follows that where we meet resistance, we must use only the force that is necessary and no more. (This was your mistake at Durmstrang! But I do not complain, because if you had not been expelled, we would never have met.)
- —One of Albus Dumbledore's letters to Gellert Grindelwald in their school years as they plotted Muggle domination.[src]
"For the Greater Good" is a phrase that Gellert Grindelwald used to justify his horrific actions in the 1940s global wizarding war and it was engraved it over the entrance of Nurmengard, the prison he constructed to house those who opposed him. It expressed his belief that what he was doing was to be of eventual benefit to everyone, but that a small number of people would have to suffer to bring these benefits about.
History of the phrase
When Grindelwald visited Godric's Hollow in the 1890s, he struck up a friendship with the young Albus Dumbledore and told him about his plans to overthrow the International Statute of Wizarding Secrecy and establish a regime in which wizards were placed above Muggles. Within these talks, Grindelwald said that the regime would be for the Muggles' own good, and Dumbledore wrote a letter in which he said:
"Yes, we [wizards] have been given power and, yes, that gives us the right to rule, but it also gives us responsibilities over the ruled... We seize control for the greater good. And from this it follows that...we must use only the force that is necessary and no more."
After Dumbledore severed ties with Grindelwald following a duel that claimed the life of his younger sister, the motto became Grindelwald's alone. Dumbledore's actions after these incidents show that he did not wholly reject the philosophy that he himself had inspired Grindelwald to use. On the one hand, he made a plan by which Harry Potter would have to suffer a great deal of hardship and death to bring about Lord Voldemort's downfall. On the other hand, he delayed in telling Harry about why Lord Voldemort had tried to kill him as a baby, indirectly resulting in Sirius Black's death.
- Harry Potter and the Deathly Hallows (First appearance)