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In 2000 and 2002 the first direct elections for mayors were held in England. They were elected using the supplementary vote method. This article summarises the discussion which led to the adoption of this electoral system, analyses some of the main arguments used, states some general criteria by which electoral systems can be judged, and evaluates some other possible methods for conducting such elections. It concludes that in the light of at least some general conditions, supplementary vote (SV) is a less desirable way of choosing a mayor than alternative vote (AV) and some other systems. However, it seems as if a simple amendment of the original SV procedure will avoid some of its most apparent problems. [ABSTRACT FROM AUTHOR]