Not only it depends on the meaning of fairness, but it also raises a bunch of questions/challenges on its own:

* How would you implement such a distribution?
* How to claim, through Internet that you are a different person?
* How to do this universally?
* How to avoid identity thief or coercing people to claim their share for you?

People verifying the authenticity of other people therefor get a form of control/power on them. This is against one of the core principle behind Bitcoin, namely decentralization.