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“Social preference orders” obtained by voting rules may be evaluated in terms of how individual preferences expressed by voters have been properly reflected in the obtained orders. To represent the degree of reflection of the preferences by voter i, Pi, in a given social order, P, we defined the matching score, tipby the number of those pairs of alternatives the orders of which match for Piand P. Then we proposed using the meanand varianceof the tipto evaluate outcomes of voting, i.e., social orders, given a profile of individual preferences expressed by voters. A new rule, Varmin rule, is proposed which yields the order that minimizes the variance of these matching scores. Various social orders obtained by a number of voting rules, such as. Majority, Borda, Double Plurality, and Varmin, were evaluated in terms of means and variances of matching scores through a computer simulation of 15,000 profiles. Results generally indicated as follows: The Majority rule tends to yield rather large variances, although it theoretically yields in largest mean. The Borda rule yielded rather small variances, keeping the means at rather high levels. The Double Plurality rule yielded large variances with unpredictable fluctuations of the means. The Varmin rule yielded too small means, although it theoretically yields the least possible variance. A method to modify social orders to reduce the variances most effectively was proposed (called, “Maximum Covariance Method”), showing that only a small modification of the Majority orders would be sufficient to yield very small variances with only a minor decrease of means.

A distribution of weights in a weighted voting system sometimes yields quite undesirable effects on the outcome of voting, which have not been foreseen until such outcomes actually occur. Examples are the existence of so-called “dummies,” unexpected power of veto, the failure of reflecting the dominance order of weights proportionally on the order of the effective power. The present paper introduce a number of criteria to distinguish such undesirable aspects which potentially exist in some particular configurations of the weight distribution. The criteria were stated in simple relations among weights which can be checked quite easily. Mathematical relations among the criteria were also presented in theorems with their empirical interpretations. Using the proposed criteria, the recent results of the general election for the House of Representatives in Japan was analyzed.

A computer program called POET generated “poems” through a system which incorporated (1) transitional dependencies of words, (2) transformational structures of language, and (3) semantic, or imagery, aspects in the decision about a general theme of a poem. It was assumed that each sentence in a “poem” contains a single “thematic word” as the main subject. Thematic words were selected on the basis of the similarities of words to the major thematic word (which was to be given by the experimenter) in an image space defined according to Osgood’s Semantic Differential Space. The other words in the individual sentences were assumed to be generated on the basis of both transition probabilities of word associations under the given theme and choice probabilities of transformational rules in language habit. Some of the “poems” generated by the system were introduced and discussed in relations to psychological processes of sentence generation.

It was proposed that people could evaluate the other person’s evaluation scheme in terms of the similarity (or dissimilarity) of the other person’s evaluation scheme to their own schemes. The metric for the dissimilarity of evaluation schemes was proposed to be the Minkowski-p metric for the utilities evaluated under different schemes. This model provides a basis for allocating importance to utility functions, where importance is to be interpreted as the similarity of the integrated scheme to the schemes represented by the utility functions. An experiment was done to investigate whether people’s intuitive judgments for the dissimilarity of evaluation schemes could be described by the Minkowski-p) metric; the results generally supported the model and also suggested that the metric would be the “city-block” metric, i.e., p-1 in the Minkowski-p metric.