They are resolved clockwise, yes, but you have to wait the end of the effect to have the winners.
In your example (Sheriff dies), if Deputy dies Renegade wins, if Deputy keeps alive Outlaws win.
Approccio professionale a Bang? Prova le BANG! Utility
Professional approach to Bang? Try the BANG! Utility
Bang! Stats Database *Agg. The Duel 2015* e MyBang
Bang! Stats Database *Upd. The Duel 2015* and MyBang