This discrimination claim is completely false, and our company is unwilling to consider any payment to the complainant. Isn’t mediation a waste of time?

Not necessarily. Some discrimination charges can be resolved without payment. If nothing else, the mediation can clarify the underlying facts.
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It is possible to resolve a discrimination charge in mediation without a monetary solution. It is often worth a relatively small investment of time to see if there is any common ground and to get a sense of the complainant’s understanding of what happened.  Sometimes mediation can facilitate a clarifying conversation that leads to resolution.