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Axiomatization of divisor methods and weakly degressive proportionality

100%
Dniestrzański P.
Didactics of Mathematics
|
2017
|
issue 14(18)
19-26
EN
The paper analyzes the differences between weakly degressive proportionality and proportional allocations represented by divisor methods. The analysis is accomplished by the axiomatization of divisor methods in line with Balinski and Young.
2

Degressively proportional functions using the example of seat distribution in the European Parliament

100%
Dniestrzański P.
Didactics of Mathematics
|
2012
|
issue 9(13)
35-42
EN
This article presents an example of the current problem from the borders of economics and politics, which can be used in mathematics courses for economics majors. This problem is the distribution of seats in the European Parliament among the member states of the European Union, and the principle of degressive proportionality formulated for this purpose in the legislation.
3

Systems of linear equations and reduced matrix in a linear algebra course for economics studies

100%
Dniestrzański P.
Didactics of Mathematics
|
2012
|
issue 9(13)
43-54
EN
The article presents two elements of the concept of a linear algebra lecture for economics studies. It attempts to demonstrate the significant role of ordering of the lectured content – with a focus on starting the lecture with systems of linear equations, and shows the considerable benefits of introducing the concept of the reduced row echelon form of matrix as one of the most useful concepts of linear algebra.
4
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Kompromis z Cambridge - pomiędzy równością a proporcjonalnością

100%
Dniestrzański P.
Studia Ekonomiczne
|
2014
|
vol. 203
50-60
EN
The problem of allocating seats in the European Parliament among EU member states is still open. The principle of degressive proportionality which is incorporated into the Lisbon Treaty offers so much room to maneuver, that it decides on how the composition of the European Parliament during subsequent terms only to a certain extent. This paper examines the principle of degressive proportionality, showing how from the mathematical point of view it is located between equal and proportional division. The paper suggests, furthermore, a way of measuring to what extent the division of seats is equal and to which proportional. The analysis carried out in the context of the Cambridge Compromise, where a group of mathematicians (invited by Parliament) has submitted a proposal for a long-term solution to the problem of allocation of mandates.
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