A ‘good society’ is one which is governed by a number of prized social virtues. Amongst these virtues, surely, must be counted a deference to the values of personal liberty and inter-personal equity. (These, after all, are two of the three values embodied in the French Revolution's stirring exhortation to ‘Liberty, Equality, and Fraternity’!) In urging, or professing, an acceptance of these values, there is the implicit judgment that the acceptance entails no possible problem of internal coherence or logical consistency. In this small essay, it will be shown that the apparently unproblematic judgment just mentioned could prove to be suspect. In particular, the reader is invited to consider that there are plausible, but mutually incompatible, ways in which the principles of ‘liberty’ and ‘equity’ can be formulated. The essay draws on the conventions and methods of a body of knowledge called ‘social choice theory’, which lies at the intersection of philosophy, political science, and economics.