Living for the greater good

Should have know this phrase long time ago, but better late then never... The phrase is "Living for the greater good." Previously, "Living for the sake of others" are commonly used. I think 'the greater good' is so much better and more appropriate than 'the sake of others.' Most leaders do feel responsible for their followers and thus in a way, they are living for the sake of their followers. Then, if two such leaders or groups are in conflict, they might end up fighting and this is bad. Still, aren't they living for the sake of others? However, by the standard of 'living for the greater good,' then something bad like fighting shouldn't be resulted, since this is surely not for greater good. The greater can be the 2 groups together. May be, the 'others' need to be quantified as 'other at the same level'. Eg. as a leader, representing a group, 'others' will mean other groups, but not others in the same group. Still, "Living for the greater good" is much clearer.