Measuring individuals' preferences for goods and services has recently obtained considerable attention in both public and private contexts. Individuals' judgments are used for many different purposes, including setting social policies and forecating the acceptance of a new product in the market. While preference modeling is a long-studying problem, modern applications, related to the web, make it an actual topic.
Respondents are called to express their preferences among a set of alternatives and collected data can be represented in various kinds of matrices. This thesis is focused on some popular methods to estimate either scores or ranks of a set of alternatives by analyzing a generalized tournament matrix. The proposed methods are compared via simulation and some special situations are investigated to detect their reliability. Our aim is to compare methods that assume parametric hypotheses on data distribution with methods that do not require such hypotheses. When respondents do not compare directly two alternatives, the matrix representing their preferences may show one or more missing values. We propose a method to estimate the missing entries of a generalized tournament matrix based on the minimization of the sum of its singular values, i.e. the nuclear norm. We perform some simulation studies to investigate the nuclear norm minimization effectiveness
