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A lifetime of observing interpersonal relationships with a sometimes weirdly clinical bent has led to the following observations about the properties of different group sizes:
2 people is obviously the smallest number of people that can have interpersonal interactions.
3 people is the smallest number of people that can vote in any meaningful sense. It is also the smallest number of people in which someone can act as an arbiter of the disagreements of two opposing tendencies.
4 people is the smallest number of people that can be split into two groups or factions, both containing multiple factions. It is also the smallest number of people in which a meaningful vote with two options can be tied.
5 people is the smallest number of people which can be split into two multi-person factions, one of which being larger than the other. This is a bit of a mouthful but it is also the smallest number of people that can have a faction that contains within it two sub-factions, one of which is larger than the other.
By the time we get to 6, we’re almost out of interesting properties, but it is interesting to note that 6 is the smallest number of people which can contain two opposed factions large enough to have an internal factional majority/minority and thus votes.