The invention relates to a method for preparing an anionic polyelectrolyte comprising up to 95 mol % of monomer units from 2-methyl 2-[(1-oxo 2-propenyl) amino] 1-propanesulfonic acid that is totally salified in the form of sodium salt, up to 90 mol % of at least one neutral monomer, and optionally up to 10 mol % of at least one monomer of formula (I), where: R1 is a hydrogen atom or a methyl radical, R is an alkyl radical, and n is a number greater than or equal to 1 and less than or equal to 50, said method including: a step a) of preparing a reaction mixture containing, in a solvent (S), 2-methyl 2-[(1-oxo 2-propenyl) amino] 1-propanesulfonic acid, the neutral monomer(s), the neutralizing agent, and optionally, the monomer(s) of Formula (I), said solvent (S) being either: - a ketone from Formula (II), where R3 and R4 are a methyl radical, an ethyl radical, an isopropyl radical, or an isobutyl radical; or – a mixture consisting of, for 100 mol %: - water in a proportion greater than or equal to 0 mol % and less than or equal to 25 mol %; and – a ketone from Formula (II) in a proportion greater than or equal to 75 mol % and less than 100 mol %. The method also includes a step b) of polymerizing said reaction mixture. The polyelectrolyte can be used as a thickening and/or stabilizing and/or emulsifying agent for a cosmetic, dermopharmaceutical, or pharmaceutical topical composition. The invention also relates to a composition containing same.