Relationships between Borda voting and Zermelo ranking

There are many situations wherein a group of individuals (e.g., voters, experts, sports writers) must produce an ordered list of 'best' alternatives selected from a given group of alternatives (e.g., candidates, proposals, sports teams). Two long established mechanisms that have been used for this task are 'Zermelo's Ranking Method' (1929) and 'Borda's Voting Scheme' (1781). The main purpose of this paper is to point out that they are, under certain common circumstances, identical. We then show that Zermelo's Method can be used in situations that Borda's Method is not designed to handle.