Not sure if this should be GQ or GD, but here goes:
In a dictatorship the Big Guy lays down the law and his followers obey, or else. In a democracy, a standard set of rules for voting on controversies is followed, and the losers more or less gracefully accept the result. But inbetween you have oligarchy: a small group of people dedicated to holding power and usually maintaining some sort of orthodoxy. It can be a political party, a religous hierarchy, or other similar group.
It usually has a leader, but on a “first among equals” basis rather than an absolute dictator. A certain set of core beliefs is sacrosanct, and “heretics” are expelled. But there is some room for questions about policy, tactics, interpretation of the rules, etc. There’s often a minority “reform” faction advocatiing liberalization, or a radical faction pushing a more absolutist agenda. So just how are differences of opinion decided in an oligarchy? At what point does a minority viewpoint risk being declared “treasonous” to the organization?
It depends on the type of oligarchy you mean. Where the oligarchs are really equals, I presume controversies would be decided by a majority of the oligarchs (similar to the way the Supreme Court makes decisions). In Sparta, for example, there were 5 ephors and 30 senators, among other groups. The fact that the number of senators was not odd requires that there be some method of breaking ties, which I do not know. Once a decision was made by a majority, I suspect there would be some means of dealing with dissenters if they caused trouble, such as having the figureheads situated above the oligarchs (like the two kings of Sparta) remove the dissenter.
Some oligarchies have a power structure within the government, as you might expect in a theocracy or even some Communist states. In a theocracy, of course, the religious dogma determines what decisions are acceptable, which is an important way of maintaining order (and gives power to the religious class that interprets and decides upon the religious dogma). Such a government might have a tiered oligarchy, with a single or a few dominant super-high priests, some high priests, and a lot of lower priests.
Even oligarchies are familiar with the idea of majority rule, including the need to accept the decision of the majority. The losing faction might simply go along with the majority and try a different strategy. Oligarchies, especially theocracies, aristocracies, plutocracies and military governments, tend to want to maintain the present order of things above all else, though, so there’s often not much room for reform.
Good first point. Otherwise, then you can have differences of power-base among the respective oligarchs and the factions they represent, so that for instance a faction that has the backing of the main economic movers and shakers, or that has high-prestige figures as supporters, can be more persuasive to their fellow oligarchs to move along.
And it becomes “treasonous” when it threatens the continued existence or the pretense of legitimacy of the oligarchy itself.