I was thus surprised to discover that Mayors are elected via the supplementary vote system. (politics.stackexchange.com)
The Greater London Authority Act (for London) and the Local Government Act 2000 (for the rest of England and Wales) prescribed the use of the supplementary vote system (effectively a weak two - party biased version of the alternative vote / instant run off) for local elected executives. (politics.stackexchange.com)
The supplementary voting system, a shorter form of the alternative vote system, gives voters the opportunity to mark their first and second choice. (centreforcities.org)