In this thesis, I ask about the political determinants of educational inequalities, and posit that as school quality differs, the competition for school places poses a problem to the social right of equal educational opportunities at the compulsory education level. What are the policy options to equalise access to quality education? When are these reformed? These questions motivated the design of a typology of Student Sorting Institutions with which we can meaningfully compare formal institutional arrangements that interfere in the competition for quality school places. A critical review of sociology of stratification and economics of education literature suggests classifying Student Sorting Institutions along two dimensions: whether they grant school choice to parents, and whether the allocation process permits academic selection. Building on recent insights of the field of political economy of education, the thesis explains institutional reform with an interest-based approach. Policymakers encounter a trilemma between high choice, low selection and enhancing school quality in disadvantaged neighbourhoods: the high choice/low selection option of regulating school choice particularly benefits students that want to opt out of disadvantaged neighbourhood schools, hence risking increasing segregation of such schools. The winners of each institutional arrangement vary according to income and education. How the trilemma is solved depends on parties in government who cater to their electorates' interests. These then change with educational expansion. The high political cost and uncertain benefit structure of such institutions favour the status quo. With the use of new insights in the methodology of process tracing, I show that the theory empirically accounts for variation of reform trajectories in France, Sweden, and the UK (England for school policy) from the 1980s to the 2000s. In contrast, I argue that my findings shed doubt on the explanatory role of neoliberal ideas and path-dependent feedback effects to account for these reform trajectories.