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Abstract:The aim of this paper is to check whether mathematical competences influence some manifestations of bounded rationality. A special example of bounded rationality called "framing effect" is dealt with to analyze empirically the thesis that mathematical competences and cognitive effort may reduce the framing effect. Two kinds of cognitive effort: probabilistic and deductive are analysed. Experiments were conducted using samples of Polish students, both mathematically and business oriented. As an example of a framing situation an example called "Asian disease", (the first analyzed and the most popular example of the framing effect), is considered. The thesis that a mathematical background may diminish the occurrence of the framing effect was partly confirmed.

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.

The aim of this paper is to present the results of experiments relating to voting methods based on the bounded rationality theory. The research demonstrated that a positive nudge changes the voting results. The study focused on three methods of voting: the Borda Count method, the Condorcet winner method and the anti-manipulation method. In a laboratory experiment, the subjects were asked to select the best musician. They were to manipulate their voting so that a predetermined winner is chosen. In the first voting, the subjects did not receive any a priori information, while in the second voting, some a priori information was provided, i.e. the true, objective ranking of the musicians. What followed was another voting. It was initially assumed that the participants would manipulate their voting the same way as in the first voting. The results, however, were different. The obtained second ranking of musicians was closest to the true, objective ranking, thus proving that the manipulation effect was neutralised by the a priori positive information about the true, objective order.