# Article “Liberal political equality does not imply proportional representation” in Social Choice and Welfare

In their article ‘Liberal political equality implies proportional representation’, which was published in *Social Choice and Welfare* 33(4):617–627 in 2009, Eliora van der Hout and Anthony J. McGann claim that any seat-allocation rule that satisfies certain ‘Liberal axioms’ produces results essentially equivalent to proportional representation. We show that their claim and its proof are wanting. Firstly, the Liberal axioms are only defined for seat-allocation rules that satisfy a further axiom, which we call *Independence of Vote Realization* (*IVR*). Secondly, the proportional rule is the *only* anonymous seat-allocation rule that satisfies *IVR*. Thirdly, the claim’s proof raises the suspicion that reformulating the Liberal axioms in order to save the claim won’t work. Fourthly, we vindicate this suspicion by providing a seat-allocation rule which satisfies reformulated Liberal axioms but which fails to produce results essentially equivalent to proportional representation. Thus, the attention that their claim received in the literature on normative democratic theory notwithstanding, van der Hout and McGann have *not* established that liberal political equality implies proportional representation.

S. Wintein & H.C.K. Heilmann (2022). Liberal political equality does *not* imply proportional representation. *Social Choice and Welfare*.