There are many alternatives, just none that work.
The "greatest good for the greatest number" exists most successfully in capitalist democracies.
Whilst I have views as to why this is, I'm not an economist.
(It's still true though).
Is there an alternative to a capitalistic society?
Sure, there is always feudalism, Sharia, communist autocracy, or monastic society... I'll take capitalism.
Capitalism is an economic form. Not a governmental form.
Here's a little primer I found: