Abstract
We propose a modification of the standard Borda count which significantly reduces the level of manipulation demonstrated in experiments and observed in actual voting. The method may be applied in voting systems in which the Borda count is usually adopted, e.g. musical competitions, elections in educational institutions and professional and technical societies, sports awards, and even some political elections. We first analyze the actual voting results in the 2016 Henryk Wieniawski International Violin Competition. We show that some jurors are suspected of having exploited a weakness in the standard Borda count method to manipulate the final results. We then consider modifications of the Borda count with a view to designing a method more resistant to manipulation. We show that discarding all the scores of the 20% of jurors who deviate most from the jury average gives a ranking that agrees with public opinion and general expert consensus. Modifications of the Borda count were then experimentally tested against their resistance to manipulability. The results clearly show that excluding jurors has very good statistical properties to recover the objective order of the contestants. Most importantly, however, it dramatically reduces the level of manipulation demonstrated by subjects playing the role of jurors. Finally, we present the mathematical properties of the method proposed. We show that the new method is a compromise between the Majority Criterion and the standard Borda count in that it offers more “consensus-based” rankings than the former while being less vulnerable to manipulation than the latter.
Highlights
Scoring and voting systems are described in the literature on social choice theory
There is a wealth of literature on voting methodology, it is generally concerned with political elections (e.g. Austen-Smith and Banks 2002)
Glejser and Heyndels (2001) find strong evidence of biases in the scoring process in all the piano and violin categories of the Queen Elisabeth Competition from 1956 to 1999: musicians who perform later in the final week obtain higher scores, women receive lower scores than men, performing a popular concerto leads to a lower score, and, prior to 1990, finalists from the Soviet Union received higher-than-average scores
Summary
Scoring and voting systems are described in the literature on social choice theory (review in Arrow et al 2002; Nurmi 1987). This theory covers areas such as Arrow’s (1963) impossibility theorem, voting systems analysis, the structure of the (collective) social choice function, individual rights theory, and justice theory. There is, a paucity of literature on scoring and voting systems in music competitions, and what little there is mainly deals with the factors that influence the final scores, e.g. order of appearance, the sex and country of origin of the performer, and the pieces that he or she performs. The effect of position in a sequence of performances and the halo effect are likewise significant
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