What counts as equitable? Incidence, spatial allocation and accessibility outcomes of a supply-side transit subsidy

Whether a public transport subsidy benefits the poor is usually settled by who is allocated more per trip. That angle shows only part of the picture. We put four questions to one instrument, combining operator expenditure, smartcard validations and vehicle GPS for the bus system of Belo Horizonte, Brazil, subsidized since 2022. First, who receives it, in monetary terms as the literature does, at finer resolution, costing each vehicle segment and dividing it among those aboard. Among riders the transfer is progressive, against prior Global South evidence, the poorest quintile receiving 1.68 times the richest. Second, how the fare distributes costs. That quintile also pays most, on incomes 8.7 times smaller, and 45.8% of riders pay more in fares than they cost. Third, where the money accumulates in the city. It is progressive by income, per rider and per place, because those most expensive to carry live in the poor bus-dependent periphery, yet regressive where disadvantage is accessibility, because an untargeted per-vehicle-kilometer payment follows demand, and enough riders there outweigh their lower cost each. Fourth, whether the access it buys is equitable, against four normative lenses across wide ranges of cumulative and gravity-based specifications. Utilitarian and sufficientarian verdicts hold almost throughout. Egalitarian and Rawlsian verdicts depend on the indicator, its parameter, and whether gains are absolute or relative. The equity of a supply-side subsidy is not one question with one answer. Answering one and stopping is not wrong but partial, and partiality is indistinguishable from selection unless alternatives are reported.