The classical definition
Oligarchia — oligos-archē, rule of the few — names the political form in which authority is concentrated in a small group of citizens distinguished by some specific criterion: typically wealth (timocratic / timocratia), descent (aristocratic in the strict sense), or institutional position (restricted assemblies, restricted magistracies). The form sits between absolute monarchy at one end and democracy at the other on the classical constitutional spectrum.
In the working ancient sources oligarchy is not a single constitutional form but a family of forms. Aristotle in Politics IV catalogues at least four working varieties: oligarchies in which property qualifications are low and the magistracies are widely accessible to the qualified; oligarchies in which the qualifications are high and the magistracies are accessible only to the very wealthy; oligarchies in which the body of citizens with full political rights co-opts its successors; oligarchies in which the magistracies are themselves hereditary. The Greek world ran on the working spectrum across these variants.
Oligarchy in the Greek practice
Most Greek city-states most of the time were oligarchies in the working classical sense. The Athenian democratic experiment of the fifth and fourth centuries was — by the standards of the polis network as a whole — the unusual case. Corinth, Thebes (for most of its history), the smaller Doric cities, most of the islands, most of the Anatolian coast operated under property-qualified or institutionally- restricted constitutional forms in which the working political class was some fraction of the adult male citizen body.
Sparta is a separate case — formally a mixed constitution with oligarchic features rather than a straight oligarchy. The Spartan Apella admitted all Spartiate citizens, but the Spartiate citizen body itself was structurally a small fraction of the total Lacedaemonian population, and the Gerousia and Ephorate concentrated effective authority further. The platform reads Sparta as oligarchic in working substance even where the constitutional form is mixed.
The classical critique and defence
The classical sources contain both critique and defence of the form, often in the same author.
Aristotle in Politics IV–V reads oligarchy as typically factional — a form in which the political class prefers its own interest to the common interest, and which therefore generates political conflict (the stasis the Greek world was structurally vulnerable to). The corrupt form is oligarchy proper (the few ruling in their own interest); the good form is aristokratia in the strict sense (the genuinely-best ruling in the common interest), which Aristotle notes is rare in practice.
Plato in the Republic Book VIII reads oligarchy as the political consequence of timocratic decay — the political form that takes over when the spirited warrior class of the timocratic regime gives way to the acquisitive moneyed class, and which itself decays into democracy when the dispossessed populace of the city revolts against the moneyed minority. The Platonic regime cycle is the working ancient case for reading constitutional forms as dynamic rather than static.
The defence of oligarchy in the classical sources is usually comparative — oligarchy as the working alternative to the unruly democracy or the unstable tyranny. The ancient oligarchic apologists (Theramenes at the Athenian oligarchic interludes of 411 and 404; the Spartan apologists generally; the philosophical critique-of-democracy tradition) argue that the form preserves political continuity and competence at the cost of restricting participation, and that the cost is worth paying.
The structural tension with democracy
The Greek world's principal stasis — civil-conflict — pattern across the classical period was the oligarchic / democratic factional struggle. Each polis that swung between the two forms (which was most poleis at some point) recorded the same working pattern: democratic faction in alliance with the propertyless and the working population; oligarchic faction in alliance with the propertied and the conservative political class; periodic constitutional revolutions in one direction or the other; occasional foreign intervention (Sparta backing oligarchies; Athens, when it could, backing democracies). The pattern is constitutive of the polis period.
Thucydides records the stasis on Corcyra in 427 BCE (Book III.70–85) as the working case study — the deformation of political language under conditions of factional civil war, the working dissolution of customary restraints, the generalisation of the conflict across the Greek world during the Peloponnesian War. The passage is the most considered ancient analysis of what democratic-oligarchic stasis does to a polis.
Why the platform reads it
The platform reads oligarchy because it is the working ancient alternative to democracy and because the constitutional dynamic between the two forms — the stasis pattern, the mutual delegitimisation, the recurrent rebalancing — is the working political experience of the classical Greek world. The European republican tradition's reading of mixed constitution (Polybius VI, Cicero's De Re Publica, Madison's Federalist 10 and 51) is in large part a working attempt to design constitutional forms that defuse the democracy / oligarchy stasis the Greek tradition recorded in painful detail. The form does not disappear from the European tradition; it gets renamed and re-engineered.