A Good Candidate is an alternative which is top ranked for at least half of the agents. Meanwhile, a Majority Winner is the alternative that is preferred by a majority of agents by pair-wise comparison to any other available alternative. Hence, to have a majority winner, the social majority relation must be acyclic, while in order to find a good candidate this condition is not necessary. In this note, we highlight the fact that there is a close relationship between the good candidate and a majority winner. In particular, they coincide for triples of alternatives whenever we work with a reduced profile of preferences where mutually exclusive preferences are removed. If the number of alternatives increases, then a condition by triples should be accomplished: an alternative should be the good candidate for any triple where it is. Furthermore, we propose a way to compute a majority winner via triples of alternatives.