Cardinal Sense Research Articles

Blocking Pairs Versus Blocking Students: Stability Comparisons in School Choice

It is known that there are school choice problems without an efficient and stable assignment. We consider comparing assignments in terms of their stability by comparing their sets of blocking (student-school) pairs or comparing their sets of blocking students who are involved in at least one blocking pair. Although there always exists a Pareto improvement over the student-optimal stable (DA) assignment which is minimally unstable among efficient assignments when the stability comparison is based on comparing the sets of blocking pairs in the set-inclusion sense, we show that this is not necessarily true when the stability comparison is based on comparing the sets of blocking pairs in the cardinal sense, or when it is based on comparing sets of blocking students (in the set-inclusion or cardinal sense). Given the latter impossibilities, we characterize the priority profiles where there exists a Pareto improvement over the DA mechanism which is cardinally minimally stable among efficient assignments when counting blocking pairs or counting blocking students. The resulting domain restrictions suggest to take with caution school choice analysis which relies on a particular stability comparison method.

Investigation of the method of decomposition of a complex science-intensive instrument-making device for the formation of a rational strategy for its modernization

The object of research is the life cycle of products (a complex equipment object) of a manufacturing enterprise. Each product has its own life cycle, i.e., time interval, expiration date. In Ukraine, it is a period of 5 years. All the problems of enterprises lie in this fact. The current situation in the country does not allow enterprises to update their production capacity every 5 years, and therefore it is the most problematic place. To solve this problem, a method for decomposing an object of complex equipment (OCE), which allows to determine the necessary, morally outdated component in the OCE, and modernize it to a more modern - innovative. It also allows to extend such stage of the product life cycle as - operation, adding additional functions and (or) capabilities to the product. In this case, of course, there is a risk, which is to correctly identify the necessary element of modernization. For this purpose, a mathematical apparatus is applied in the work, which unlike others, allows to decompose the OCE with the greatest accuracy. The author laid the foundation in the cardinal sense with respect to the ecological component, as well as the duration of the product life cycle, which theoretically can last for infinity and requires a deeper and more detailed study.

Large null sets in metric spaces

It is shown that every locally compact σ-compact metric space endowed with a Borel measure related to the metric by a natural condition contains sets of measure zero which are extremely large in the sense of cardinality, Hausdorff dimension and Baire category classification.

An Application of Independent Families of Sets to the Measure Extension Problem

The method of independent families of sets elaborated by Tarski [Set theory. With an introduction to descriptiveset theory, PWN–Polish Scientific Publishers, 1976] and Kakutani and Oxtoby [Ann. of Math. 52: 580–590, 1950] is applied to the construction of maximal (in the sense of cardinality) families of pairwise orthogonal nonseparable invariant extensions of Haar measures.

Policy appraisal and the structure of protection in a low‐income developing country: Problems of measurement and evaluation in Burundi

The article provides estimates of the structure of nominal and effective tariffs and the tariff equivalents of a set of quantitative import restrictions for Burundi, a low‐income, data‐deficient developing country. It carefully indicates the assumptions and limitations of the analysis. The overall conclusion of the article is that not much significance can be attached to the estimates in a cardinal sense. Nevertheless, recommendations about altering the structure of relative incentives can be justified, where these are directed at increasing transparency and uniformity.

A Note on the Pure Theory of Consumer's Behaviour

FROM its very beginning the theory of consumer's choice has marched steadily towards greater generality, sloughing off at successive stages unnecessarily restrictive conditions. From the time of Gossen to our own day we have seen the removal of (a) the assumption of linearity of marginal utility; (b) the assumption of independence of utilities; (c) the assumption of the measurability of utility in a cardinal sense; and (d) even the assumption of an integrable field of preference elements.. The discrediting of utility as a. psychological concept robbed it of its only possible virtue as an explanation -of human behaviour in other than a circular sense, revealing its emptiness as even a construction. As a result the most modern theory confines itself to an analysis of indifference elements, budgetary equilibrium being defined by equivalence of price ratios to respective indifference slopes. Consistently applied, however, the modern criticism turns back on itself and cuts deeply. For just as we do not claim to know by introspection the behaviour of utility, many will argue we cannot know the behaviour of ratios of marginal utilities or of indifference directions. Why should one believe in the increasing rate of marginal substitution, except in so far as it leads to the type of demand functions in the market which seem plausible ? Even on the advanced front we are confronted with this dilemma -either the argument with respect to indifference varieties is circular or to many people inadmissible (at least without further demonstration). Hence, despite the fact that the notion of utility has been repudiated or ignored by modern theory, it is clear that much of even the most modern analysis shows vestigial traces of the utility concept. Thus, to any person not