I would argue that no one other than a supervisor or supervisors should be directly involved in the performance appraisal of a customer service representative. Other people, particularly customers, might be involved in an indirect way, but they should not be present for the actual performance appraisal.
The only people with a real right to evaluate a customer service representative’s performance are the representative’s supervisors and the customers that the representative serves. It is possible that coworkers would have a good understanding of how well the representative is doing his or her job, but it would not really be right to have coworkers evaluate one another since they would have an incentive to try to make one another look bad.
The supervisor, of course, must be the main player in the performance appraisal. It is not really possible to have customers present and it would also not be right to base a performance appraisal on the input of one or two customers. If customers’ opinions are to be taken into account, it should be through surveys. The firm might ask customers to rate the representative’s performance after they have been helped by that person. This is particularly easy to do if the help has been conducted online. In that way, the customers’ opinions could be part of the performance evaluation, but only an indirect part.