If somethingswingsthebalance, it is the thing thatcausesaparticularsituationtohappenor aparticulardecisionto be madeinsteadof othersituationsordecisionsthat arepossible:
使天平发生倾斜，起决定性作用
Thislatestelectionpromisemight justswingthebalancein the candidate'sfavour.最近作出的这一选举承诺可能会对选民抉择起到决定性的作用。