I think that more than "political system" it is a consequence of group dynamics.
Too few: If you have a duumvirate, you have two personalities in direct conflict and no counterbalancing system:
Either one of them is the "senior" member and the other is the "junior", and both accept the situation: but in this case we will often not consider that a duumvirate but the senior member being the ruler and the junior member a supporter.
They do not accept a hierarchy between them; the two members see themselves as equal in power. That often leads to conflict (conspiracies, civil wars, ...) making the duumvirate an unstable solution, as any of the members may believe at any time that they are capable of removing the other one.
The only stable variation would need well defined spheres of influence of each member (e.g. a civil leader and a religious leader), and even those situation lead to conflict.
Too many: with 4 or more, the ruling group can split themselves into groups/factions, with each group selecting its own leader (you could consider Julius Caesar Civil War a case of that). That devolves into a duumviare or triumvirate.
In opposition, in a triumvirate, in the case of conflict between two members the third one can act as arbiter; even if any of the two members in conflict does not agree with the final resolution to the conflict, he may find himself too weak to challenge the other two members of the triumvirate put together.
That is not to say that a triumvirate is any kind of a magic solution; while certainly better than duumvirates they are rather scarce. With time, any two members of the triumvirate may ally themselves and conspire to remove the other one, leading to a duumvirate or even single ruler.
In most of these apparitions of triumvirates, I think it is worth looking closely at the particular circumstances that led to them (what did each member of the triumvirate apport to the group) than to try to establish a general rule. The notable exception could be Fascist Italy, that due to its "hobby" of trying to mimic the Roman Empire could have done so just as an imitation of the famous (and failed) Roman triumvirates.