The obvious action would be to not play favorites from the get-go. However, if members of a team voluntarily communicate with their manager at different frequencies/levels, soon enough there will be a self-selected discrepancy in employee engagement. This might not be an issue, but it could sow the seeds of contempt in a workplace under pressure. How to mitigate this?
You've combined two different issues - favoritism and engagement.
I agree that the employees will communicate at different levels and frequencies, leading to more or less engagement. But frequent engagement isn't the same as favoritism. Favoritism can be displayed even in limited engagement.
So the key is that, regardless of the frequency of engagement, the manager needs to be cognizant of the "quality" and "type" of engagement, and make sure that he/she is being objective in that.
But even here, nothing is really ever fair and equal. Besides the frequency of engagement, the team will self-select based on abilities and actions. The manager will have to navigate that bias as well, in the same way.
I believe that whenever favoritism happens, is because there aren't candid and objective processes to:
Having that said, any people-related matter is liable for bias, therefore bear in mind that some bias will always exist. Is your duty to reduce it as much as possible, and some actions could be taken:
I believe these are good paths to follow towards lowering bias and all its derivations (favoritism, engagement, commitment... you name it).