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This isn't the scenario here though---there are no cases against specific people, only disputes *between* multiple people. We require that earlier steps of the dispute-resolution process be followed first, such as mediation. If these are unsuccessful, the matter goes to arbitration. The arbitration is thus arbitration of the dispute between two people, and is charged with resolving it in some way.
The proper analogy, as the name implies, is to arbitration hearings, not to court cases. It is standard practice in arbitration that sanctions may be levied against either or both of the parties to a hearing.
I think I can speak for Neutrality. His post on the request for arbitration page implies a case against a specific person at least as far as recusal goes:
" I'd only recuse if you were the respondent rather than the petitioner."
-- Silverback