Why would you want to be paid fairly? Aim to get paid what you want - not what some group of people decide is "fair". If you don't get what you want, that's not the end of the world, just gives you goals to strive for.
Also, never let people who pay you tell you what is fair. You only talk about what you think you're worth, and what they are willing to pay -- if there's overlap then great, otherwise no cigar.
And final point to OP of thread
> How can I come up with what is a fair raise?
You search inside your soul and find a number that below which you'll feel bad (resentful/undervalued/cheated/etc) and above which you'll feel good (well-compensated/proud/valued/etc). That is the number you aim for
But yeah you should also consider both party's BATNA when deciding how hard to push.