We present a semantic criterion for fairness notioins for multiparty interaction. We show that if a fairness notion violates the criterion, then no deterministic algorithm for multiparty interaction scheduling can satisfy the fairness requiement. Conveersely ,the implementation is possible if the criterion is obeyed .Thus, the criteriion is sufficient and necessary to appear in the literature. We then use this criterion to examine several important fairness notions, including strong interaction fairness, strong process fairness, weak process fairness, U-fairness, and hyperfairness. All, except weak process fairness, fail to pass the criterion.
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