cite case law. Is there a difference between jurisdiction? Does size and type of group matter? Statutory vs private boards makes a difference?
A "group" is a rather Ill-defined concept.
If the group is a familial or social group then their decisions are not legally binding so it doesn't matter.
If the group is the creature of a contract then the contract will tell you. If the contract is silent then a decision would amount to a renegotiation of the contract and would have to be unanimous.
If the group is a creature of statute (e.g. company boards, incorporated associations etc.) then the statute will tell you. The statute may tell you that the group can create its own rules. There may also be different levels of majority specified (simple, 2/3, 3/4 etc.) and also if it is a majority of the whole or just those in attendance.
So, yes, jurisdiction matters; yes, size matters and yes; type matters,