For instance, you might have a majority of six, but those in the 'out' group still have somebody to talk to. A variety of people may be better than a crew of one sex, one race or one nationality. I would guess that the first trip to Mars probably will be multicultural with at least two languages and include at least one woman. The compatibility of crew members can be evaluated in advance. Russians, the world's leaders in long-term space flight, pay much attention to how cosmonauts get along and base crew selection, in part, on compatibility.
Crew members work together for a year before launch, and if tensions develop, are broken up.