The phrase trips so glibly from the tongue that many take it to be definitive of utilitarian doctrine. Without ever pausing to think about what it might mean.
The phrase, of course, is Bentham's and not Mill's. It turns up in the second paragraph of the preface to his 'A Fragment on Government' (1776) :
"...it is the greatest happiness of the greatest number that is the measure of right and wrong...."
As a fundamental principle, the principle which indeed is the measure of right and wrong, this is hopeless. For it is not a single principle, but an unholy admixture of two quite different principles, principles which often point in different directions.
The 'greatest happiness' part is a maximising principle: it enjoins people to act so as to maximise human happiness produced.
But the 'of the greatest number' part is a principle of distribution: it enjoins people to act so as to spread happiness around as equally as possible.
Both admirable ethical principles no doubt. But they often clash. With the result that 'greatest happiness of the greatest number' fails to provide a guide for action in most cases.
