The Accuracy of Collective Decision Rules in a Noisy and Corrupt Environment

How do noise and bribery affect the accuracy of collective decision rules? This paper presents simulation results that measure the accuracy of ten well known collective decision rules under noise and bribery. When noise is low these rules can be divided into accurate ("good") and inaccurate ("bad") groups. The bad rules' accuracy improves, sometimes significantly, when noise increases while the good rules' performance steadily worsens with noise. Also, when noise increases the accuracy of the good rules deteriorates at different rates. Bribery delays the effects of noise: accuracy improvement and deterioration due to noise emerge only at higher noise levels with bribery than without it. In some cases at high noise levels there is only a negligible difference between the accuracy of good and bad collective decision rules. Let us assume that a committee has to rank candidates. Suppose that there exists an objective ranking of the candidates but because of human error (later: system noise or noise) committee members' perceptions about the objective ranking are inevitably imperfect and different. In order to generate a collective ranking first committee members individually rank candidates, then the committee aggregates the individual rankings according to a method earlier agreed upon. Several collective decision rules are available to the committee to come up with a collective preference. Suppose that the committee is aware of the fact that the method chosen for preference aggregation may affect the accuracy of the collective rankings and that candidates may try to manipulate committee members to get a better ranking. What is the most accurate and least manipulable method of preference aggregation in a noisy setting? This paper compares how ten well known collective decision rules perform under noise and in the presence of bribery. Consider the task of distributing organs among patients waiting for organ transplant. A fair distribution should be based on, among other things, medical urgency. There must exist an objective ranking of patients considering their medical condition, even if it is not entirely clear to physicians. Sometimes this ranking can be reproduced using objective criteria e.g. blood test results. In other cases the ranking of patients is a result of committee decisions that include judgment calls like in the case of heart transplants. When human error cannot be excluded committee rankings will not perfectly reproduce the objective ranking of patients, i.e. committee members' rankings will be noisy. In addition, if it is known that the …