Summarized distributions of mass: a statistical approach to consumers' consumption spaces

This paper focuses on logical aspects of decisions being made by the consumer under conditions of uncertainty and certainty. A finite number of alternatives is considered. They are mutually exclusive propositions identifying all quantitative states of nature of a contingent consumption plan. Each proposition of it is expressed by a real number. This study distinguishes it from its temporary truth value depending on the state of information and knowledge of the consumer. Given two sets of quantitative states of nature of two contingent consumption plans separately considered, it is possible to assign the arithmetic product of the two corresponding real numbers to each state of nature of a joint contingent consumption plan characterized by a conjoint distribution of mass. This article considers a conjoint distribution of mass because the consumption space of the consumer is generated by all coherent summaries of it. Each point of her consumption space is connected with a weighted average of states of nature of two contingent consumption plans jointly studied. The consumer chooses a point of it representing that bundle of goods actually demanded by her inside of her consumption space. It is possible to show that it is nothing but a bilinear and disaggregate measure. This research decomposes it into two real numbers, where each real number is a linear measure. In this paper, different measures are innovatively obtained. They can be disaggregate or aggregate mea- sures, where the latter are independent of the notion of ordered pair of contingent consumption plans.