In this paper 16 different voting procedures for one-seat elections are analysed: the rules of Borda, Condorcet, Black, Copeland, Simpson, Hare, Coombs, Baldwin, Nanson and the plurality, anti-plurality, majority, approval and runoff rules. The 2 criteria we use as a measure for the validity of the voting procedures are Condorcet efficiency (the number of times a voting procedure selects the Condorcet winner) and Borda efficiency (the number of times a voting procedure selects the Borda winner). Computer simulations calculate efficiencies for the 16 voting procedures. We find that the Borda rule is about 85% Condorcet efficient while some voting procedures are always 100 % Condorcet efficient (Black, Copeland, Simpson, Baldwin, Nanson). Another rule is only 100 % Condorcet efficient with single peaked profiles (Coombs). This can be proven theoretically. Another feature from single peaked profiles seems to be that some voting procedures select the same winner (Simpson, Baldwin, and Nanson). This result may be interesting for future research. Considering Borda efficiencies we see that the Black rule scores well, followed by the rules of Copeland, Nanson and Baldwin. Taking both Condorcet and Borda efficiencies into account, we can state that the Black rule is superior. Then come the rules of Copeland, Simpson, Nanson and Baldwin.
