Socialism may be 'fair', but it is not right. Rightness is different than fairness, which I would define as everyone being equal. If everyone is equal economically [except the leaders, of course!] then there is no incentive to do anything. Why should any person do their best when someone else who is slacking off is just as well off as them?
It doesn't matter who runs it; socialism is inherently flawed in that it punishes creativity and hard work and rewards laziness.