The consistency of statistical estimates of thurstone-mosteller

The traditional method of analysis procedures of collective choice involves three different approaches: investigation operator voting against the characteristic conditions, investigation the properties of the function of choice, analysis on the possibility of manipulating (verification the stability of the voting process under the influence of negative impacts from voters or organizer). Research team of the department ITMU VSUET proposed and implemented a fourth approach, which is to research the probabilistic characteristics the results of the procedures (value of the displacement valuation of estimate the usefulness of specific alternative to its true value, the standard deviation of evaluating of estimate the usefulness of alternative from its true value, the probability of correct ranking of alternatives at the output the procedure of choice, etc.). This article is dedicated to the analysis of the consistency of estimates the usefulness to compare alternatives, obtained at the output of the traditional procedure Thurstone-Mosteller and its generalizations, created by the authors of. In the general, the term of consistency of estimator of statistical estimation assumes tending to zero error of estimation by increasing the sample size. However, depending on the interpretation of "calculation errors" in science are the following main types of consistency: the weak consistency of statistical estimation, based on the notion of convergence in probability of the random quantity; the strong consistency, based on the concept of convergence with probability to one; the consistency of statistical estimation in the mean square. The variance of this assessment tends to zero. This article provides a proof of the theorem, according to which the assumptions rather general nature of estimates the usefulness being ranked alternatives obtained using the procedure Thurstone-Mosteller satisfied the consistency of statistical estimation in the mean square. In this case, of the consistency of statistical estimation in the mean square follows the weak consistency of statistical estimation of estimates the usefulness alternatives of original sample.