On update monotone, continuous, and consistent collective evaluation rules
- PDF / 3,118,517 Bytes
- 18 Pages / 439.37 x 666.142 pts Page_size
- 31 Downloads / 161 Views
On update monotone, continuous, and consistent collective evaluation rules Edurne Falcó1 · Madhuparna Karmokar2 · Souvik Roy2 · Ton Storcken3 Received: 27 March 2019 / Accepted: 15 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We consider collective evaluation problems, where individual grades given to candidates are combined to obtain a collective grade for each of these candidates. In this paper, we prove the following two results: (1) a collective evaluation rule is update monotone and continuous if and only if it is a min-max rule, and (2) a collective evaluation rule is update monotone and consistent if and only if it is an extreme minmax rule.
1 Introduction We consider (collective) evaluation problems where agents grade candidates based on their level of excellence, and where these individual judgments are to be aggregated to obtain a collective grade for each of these candidates. In education environments, this is daily practice. Here students are graded for different subjects and a final overall grade determines the performance of the students compared to each other. Other examples of these are, for instance, the so-called majority aggregation rules as proposed by Balinski and Laraki (2011) and Balinski and Laraki (2014) or the linguistic decision rules described in García-Lapresta (2006). The fundamental
* Souvik Roy [email protected] Edurne Falcó [email protected] Madhuparna Karmokar [email protected] Ton Storcken [email protected] 1
Virena Navarra S.L., Navarra, Spain
2
Economic Research Unit, Indian Statistical Institute, Kolkata, India
3
Department of Quantitative Economics, University of Maastricht, Maastricht, The Netherlands
13
Vol.:(0123456789)
E. Falcó et al.
problem is to find rules with desirable properties that take all the individual grades as inputs and produce a collective evaluation as output. On the one hand, grades may express an evaluation result on a more or less absolute scale. Examples of such problems include those where agents have to evaluate competitors based on their performances using a predefined grade scale, like for instance in music contests, teaching environments, or certain sport disciplines, such as e.g. gymnastics, or figure skating. On the other hand, these grades can be interpreted as individual quality assessments enabling agents to order a relatively large group of candidates. At job vacancies, grades or quality expressions may support committee members in ordering larger amounts of applicants. Decision-making based on qualitative information has a wide range of practical applications like online auctions, personnel evaluation, and supply chain management. We use linguistic/qualitative grading scales to allow explicitly for individual interpretations of these. Strictly speaking a grade A+ in history given by teacher i is not comparable to a grade B− in geography given by teacher j. Linguistic qualifications like ‘good’ or ‘perfect’ leave this individual interpretation more open t
Data Loading...
