Performance Appraisal CAN be fair when the following criteria exist
The basis of the appraisal is known, shared, agreed and even developed jointly between the employee and the manager
When the basis of the appraisal is given in advance before the appraisal period starts so that the employee is fully aware of what is expected/required from him/her
When the appraisal process itself is done jointly by the manager and the employee at the same time without anything decided in advance by the manager only before setting with the employee
When the appraisal process is transparent and straight forward with no hidden agendas, bias pro or against the employee.
When performance appraisal is based on facts and figures through a numeric/qunatitiative measurement system whose input come from daily/weekly/monthly performance reports filled by the employee and verified/approved by the manager on regular basis.
This is the minimum that I can think of right now.
If you need further elaboration/explanation ... let me know !