Borda's voting paradox: Theoretical likelihood and electoral occurrences

Abstract

Voting procedures, which playa major role in the decision making subsystems of group and societal level systems, generate interesting paradoxes. Some have been intensively studied in recent years. The possibility that the alternative chosen by simple plurality voting may not be preferred to the defeated alternatives by a majority of the voters has, however, been neglected since its discovery by Borda in the 18th Century. The Borda effect has important implications for democratic theory and practice. With the use of survey data regarding voters' preference rankings, occurrences of the Borda effect were sought in the results of a British General Election. Fifteen instances were found out of 261 three-cornered contests. Fourteen of these resulted in a Conservative win. although in each case a majority of the voters preferred the Labor or the Liberal candidate. The frequency of the Borda effect turned out to be lower than would have been anticipated with equally likely preference rankings, but the phenomenon resulted in a systematic bias in the electoral outcomes.