What does it mean to be a fair manager? When you have only two direct reports who are relatively equal in job responsibilities and performance level, you don't have to worry about it as much. As soon as you're dealing with different roles or different performance levels, though, things start to get complicated quickly. Here are some guiding principles to help you navigate when you need to treat people on your team differently but still want to be fair to all of them.
Fair doesn't mean equal.
Some managers get nervous about treating employees differently, so they try to treat them all exactly the same so that they can't be accused of favoritism or discrimination. This doesn't make sense, though. Employees are different. They and want different things from their manager, and you need and want different things from them. It doesn't make sense to say that no one on the team can work remotely because the front desk assistant can't be allowed to telecommute. It also doesn't make sense to put the same level of oversight and constraint on your proven top performer as you do on the rookie.
It is okay to treat people differently when it's based on the work.
Your goal as a manager is to provide an environment where your team can be as effective as possible. That means you need to look at what is going to enable and motivate each of your employees to do his or her best work. Any differential treatment needs to be based on the work and/or the employee's performance of that work. It's okay to say no to the employee who wants to take on more responsibility without having proven that they can handle the work they've already got. It's okay to not give a raise to a highly-paid employee who is doing the minimum (and only the minimum) for their job, while giving a larger-than-average increase to a new employee who has far exceeded the expectations of their role.
What you need to be clear on, for yourself and for your team, is what is most important for them to do/demonstrate/achieve. You can then reinforce the behaviors that align with that vision. If loyalty is most important, then you would give a raise to the twenty-year employee even if he's just doing the minimum. However, if results and taking initiative are what should be valued, then you wouldn't. There isn't necessarily a right answer: the key is to be clear, consistent, and transparent.
Make your decision criteria clear when giving perks or privileges to some employees and not others.
The reinforcement capability of your decisions depends on people actually knowing what you based those decisions on. If they don't realize that the reason you gave one person the option to work remotely two days a week when everyone else has to be in the office is because that person has consistently gone above and beyond to help the team succeed, they might think you're doing it because you like that person better. (Let's face it: it's easy to like people who are great team players and take initiative, so this isn't totally unfounded.) By specifying why you are doing what you're doing, you show that you are fair and hopefully motivate the other employees to work in ways that align with your vision if they're not already doing so.
Appearance is just as - if not more - important as intention.
Fairness is definitely in the eye of the beholder. It's just as important to look impartial as it is to actually be impartial (that is, making decisions based on work rather than personality or affinity). This is also a crucial part of creating an inclusive environment. Along with being transparent about your decisions, it's important to make sure you aren't appearing to favor or even just be closer to some employees than others. You are inevitably going to like some employees more than others, and that's okay as long as you don't make it obvious. If you care about being a fair manager, you will avoid socializing with individual employees outside of work. You should have an "all or none" policy - either you go to happy hour with the whole team, or you don't go. Either you have them all over for dinner, or you don't have anyone over.
This isn't just for the benefit of the "less-favored" employees, either. People perceived to be the "teacher's pet" are often ostracized in a way that affects their ability to be successful at work, so by distancing yourself you're helping everyone.
Treat employees differently when it makes sense, based on the work, and make it clear why you are doing so. You can reward great performance and inspire improvement, all while creating a fair and inclusive environment.