What kind of government do you want to live under? Yes, of course you asshole, we all want to be absolute dictator, but that's not how social contracts work. So let's try again - what kind of government does everyone want to live under?
Utilitarianism sounds like a sweet-ass basis for government. Why shouldn't a government try to satisfy as many rational desires of its constituents as possible? After all, democracy is all about the 'will of the people', and utilitarianism takes that vague phrase and literally fucking maximizes it. There's no denying, that's badass.
Except that when a government tries to maximize utility, it has to collapse everyone into one imaginary pool o' pleasure- suddenly running a government is like running a business in Burma - maximize profit/desire/magic/LeBron James/whatever you're after at all costs, and that's not the purpose of a government. Governments exist precisely because people are different, and have to be distinguished; if we were all the same it would be easy as fuck to resolve disputes.
Look, if you want fairness you're going to need a democracy, and you're going to need a system that applies to everyone equally. Why? Because here's the hard part - even though, we're all different, we all have to play by the same rules. You're not special, bro - or, if you still need the kindergarten version, we're all special, which is essentially the same thing with a fine layer of bullshit glazed over. So we have to find a social contract that everyone can agree to no matter what.
It seems like some people get a really, really shitty deal, doesn't it? Why the fuck would they agree to a social contract that puts them in that situation - and how could you know they would? Well, if you'll just step right over here behind this veil and we'll see.
What if you were one of those bros in a shitty situation? Or, even better, what if you had no fucking clue who or what you'd be? Sure, maybe now you want a government where one bro has all the power and gets all the bitches, but what if you didn’t know you were going to be that guy? What if you had to design a society and then someone else got to decide who you would be? What then?
Well, you'd sure as fuck want to guarantee yourself basic rights. Everyone wants those - we want the most extensive system of basic rights we can possibly guarantee everyone - that seems simple enough. But what can we say about those poor motherfuckers who end up poor? What system would they want?If they're anything like everyone, they want as much as they can possibly have - and if you knew you might be poor, you'd want to be as unpoor as possible. So if there has to be inequality, it should be distributed in such a way that the worst well-off are best-off. You know how poor everyone was in communist Russia? They were way the fuck poorer than America's poorest, which is why it's fine that in America, we have inequality. Is it perfect? No. But we're on our way.
Look, justice is about fairness. We have to provide fair opportunities, access to all social positions for everyone. If there is to be inequality, everyone must have access to all levels of the inequality - otherwise, there is no justice.