Ricardo Martínez (Departmento de Teoría e Historia Económica, Universidad de Granada), Joaquín Sánchez and Natividad Llorca (Operations Research Center, University Miguel Hernández of Elche)
Abstract: In this paper we study how to assess the performance of a group of individuals according to their achievements in several attributes or categories by means of a scoring system. Such an assessment is the composition of two steps. First, each individual obtains a partial score in each category (that may potentially depend on her opponents’ performance). And second, those partial scores are combined into a global assessment. The partial score in each attribute is upper bounded by an exogenous threshold or cap. Each problem is determined by four elements: a set of agents (or tenders), a set of attributes to be evaluated, a matrix of achievements that specified the score each agent has obtained in each attribute, and a vector of caps. By means of the axiomatic methodology, we identify the families of assessment functions that satisfy some natural requirements (anonymity, continuity, monotonicity, null contribution, additivity, and separability). Our findings state that these families are weighted averages of the attribute assessments. Finally, as an illustration, we analyze a public tender whose purpose was to carry out an accounts auditing of a public company. As a practical implication of our theoretical results, we show that truncation presents significant advantages with respect to other methods. Particularly, it avoids the exclusion paradox.