1) Tagliabue could agree that there are conflicts and recuse himself.

2) Tagliabue could say that he believes that the he can be a neutral arbitrator, and the union could disagree and ask him to recuse himself.

3) Tagliabue could convince all parties he can be neutral, which is unlikely given the union's position.

4) Tagliabue and the league could simply do nothing and move forward with the appeal.