Digital Educational Systems (DES) enable millions of individuals to learn or to acquire new skills. Their promises vary from one platform to another: some grant genuine degrees, others pledge rapid progress, drawing for this purpose on a range of techniques, from the recommendation of learning resources through complex models to a plain course textbook uploaded onto a learning management system. In this article, we argue that categorizing DES along two dimensions allows to map differences in the way these DES structurally conceptualise the learning process. These underlying dimensions are at once dimensions of the student model and mechanisms built in the DES's designs; we identify them as agency and legitimacy. Indeed, DES are, on the one hand, anchored in an institutionalised regime that grants them legitimacy and, in turn, legitimises the learning undertaken on these platforms; on the other hand, they make design choices as to the share of decision left to the learner in the learning process. We map a curated sample of common DES onto a plane composed of these two dimensions translated into indicators. This allows us to highlight underpopulated regions of the plane and to envisage how a DES might regulate these two dimensions algorithmically, in the interest of learning.

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