To provide: an electrolyte material having high oxygen permeability as compared with conventional ones; a membrane electrode assembly for a polymer electrolyte fuel cell excellent in power generation characteristics as compared with conventional ones; a liquid composition suitable for forming a catalyst layer for the membrane electrode assembly; and a fluorinated branched polymer useful as e.g. a raw material of the electrolyte material. The electrolyte material comprises a fluoropolymer (H)1 having a structural unit (u1) that has an ionic group and a structural unit (u2) that has an alicyclic structure, wherein the fluoropolymer (H)1 is composed of a branched molecular chain, and has a segment (A)3 comprising a molecular chain having the structural unit (u1) and a segment (B)2 composed of a molecular chain having the structural unit (u2), and the ion exchange capacity of the segment (B)2 is smaller than the ion exchange capacity of the segment (A)3.