I am currently putting the finishing touches on an essay entitled "Cartesian Egalitarianism: From Poullain de la Barre to Rancière," which will be published in a forthcoming issue of Phaenex (their site).
We do not typically consider Descartes an egalitarian. He is more often interpreted, in the post-Heideggerian tradition of philosophy, as an epochal figure of the modern destiny of metaphysics. On this account, Descartes introduces the metaphysical ground of technicity by dividing all beings between thinking subjects and objects of a calculable objective world. Or, following Antonio Negri, he is considered an architect of a “reasonable ideology” that expresses the class compromise constitutive of the formation of bourgeois class power after the 1620s: whereas Descartes formulates his philosophy as the production of human significance (and practical utility) in its separation from the world, the bourgeoisie affirms its position in civil society at the same time it accepts a temporary class compromise with absolutism (Negri, Political Descartes, 295-296).
I argue that Descartes's legacy cannot be reduced to either of these interpretations, that there is something more to his philosophy.
As of late, both Alain Badiou and Slavoj Zizek have laid claim to the legacy of the Cartesian subject, but their appropriation is largely programmatic (Zizek, in fact, is more interested in the Kantian/Hegelian subject; and Badiou the use of mathematics to reconceptualize ontology).
With Rancière (just as, I would argue, François Poullain de la Barre and Simone de Beauvoir), the discussion of the Cartesian subject has a specific content: equality. Cartesian egalitarianism pursues the consequences of Descartes's supposition, found in the Discourse on Method, that reason is equally distributed to all human beings (looking, of course, past the ironic posturing of the first sentence):
Good sense (bon sens) is the best distributed (partagée) thing in the world: for everyone thinks himself so well endowed with it that even those who are the hardest to please in everything else do not usually desire more of it than they possess. In this it is unlikely that everyone is mistaken. It indicates rather that the power of judging well and of distinguishing the true from the false—which is what we properly call ‘good sense’ or ‘reason’—is naturally equal in all men, and consequently that the diversity of our opinions does not arise because some of us are more reasonable than others but solely because we direct our thoughts along different paths and do not attend to the same things. (AT, VI: 1-2)
This claim, that good sense or reason is equal in all human beings, is fundamental to later Cartesian egalitarians, beginning with Poullain de la Barre. Here's Rancière's gloss of the way that Poullain and Jacotot take up this passage: “there are not several manners of being intelligent, no distribution between two forms of intelligence, and then between two forms of humanity. The equality of intelligences is first the equality of intelligence itself in all of its operations” ("L’actualité du Maître ignorant,” 412-413).
As I said, I'm still putting the finishing touches on the essay, so I can't get into all the details here (or else why would you read the article when it is finally published?). I can provide what I take to be the conditions necessary to count a thinker as a Cartesian egalitarian, as I've given them in the abstract (slightly edited here):
I present an overview of what I call “Cartesian egalitarianism,” a current of political thought that runs from François Poullain de la Barre, through Simone de Beauvoir, to Jacques Rancière. The impetus for this egalitarianism, I argue, is derived from Descartes’s supposition that “good sense” or “reason” is equally distributed among all people. Although Descartes himself limits the egalitarian import of this supposition [restricting the import to the evaluation of epistemological and metaphysical claims], I claim that we can nevertheless identify three features of this subsequent tradition or tendency. First, Cartesian egalitarians think political agency as a practice of subjectivity. Second, they share the supposition that there is an equality of intelligences and abilities shared by all human beings. Third, these thinkers conceptualize politics as a processing of a wrong, meaning that politics initiates new practices through which those who were previously oppressed assert themselves as self-determining political subjects.