It is difficult to justify the use of arithmetic operations for many data types we collect inresearch. This paper intends to draw researchers’ attention to the importance of derivingmeasurements from input data which are amenable to arithmetic operations and those whichcapture as much information in data as possible. Such measurements can be obtained by theleast squares regression of them on input data, a task which is carried out by quantificationtheory.

A clustering procedure is developed to classify the row vectors of a multivariate data matrixinto clusters with their sizes, that is, the numbers of vectors allocated to clusters, keptfixed at prescribed numbers. For this fixed size clustering, [1] the estimation of centroid vectorsof clusters and [2] the permutation of the rows of a data matrix are alternately iterated,so that the sum of the squared distances between the centroid vectors and permuted rowvectors is minimized. Here, the step [2] can be called least squares permutation in which thepermutation matrix optimally matching a permuted matrix to a target matrix is obtainedwith a simple iterative algorithm. In simulation studies and the application to a real dataset, the fixed size clustering procedure was found to perform sufficiently correct classification,and the least squares permutation was also found to well recover true permutationmatrices, though the procedures often yielded local minima.

In opinion polls and other types of social surveys, decline of response rates has long been aproblem, and has produced a lot of research papers. Many of those papers, however, are notnecessarily careful enough with regard to the distinctions among the types of social surveys;accordingly they tend to miss correct ways to cope with the challenges of each kind of study.

In this paper I will show how we can improve the quality of each type of social surveys, distinguishingsurvey types in terms of purpose and methodology. Section 1 describes the taskwe are facing. I will review the post-war history of the establishment of scientific methodsof public opinion polls in Sec.2, and of the methodologies of public opinion polls in countriesother than Japan in Sec.3. In Sec.4, I review the mathematical definitions of “probability”space which underlies the sampling theory of social survey. Building on that review, inSec.5, I will revisit the terminologies on survey research and attempt to correct them asnecessary. In Sec.6, I present some practical suggestions as to the classification of opinionpolls and sociological survey. Lastly, some comments for future research are provided inSection 7.

The aim of this paper is to identify classes or order of crimes from the view of their severity evaluated by people as well as to examine some different methods of aggregation for those classification and ordering. Here, three types of methods are used to aggregate each individual answer: an ordinary summation method applied to ranking method data, MDPREF as a multidimensional scaling analysis applied to paired comparisons data, and fuzzy relational method applied to paired comparisons data. Applying these three methods for the data obtained from students by questionnaire survey, following outcomes are found. Methodologically, each method reaches almost same order of crimes, but on the way of analysis, provides an important knowledge. Multidimensional analysis guaranteed the one-dimensional scaling, and the fuzzy relational approach provides different partitions according to dominance level. Substantively, although evaluated crime severity is basically as same as severity measured by formal sanction in the criminal law, some important traits are recognized. The most severe crime is murder, and there is no difference among arson, kidnapping and rape. Abortion is evaluated more seriously especially among young women. Rape is evaluated more severely than the consequences stated in legal sanction. This collective consciousness could, in time, result in political or social pressure on the legal process.