Abstract
Aspects of total favouring of large or small beneficiaries in proportional apportionments of entities using linear divisor methods (LDM) are discussed in the paper. In this aim, the requirements of apportionments compliance with linear divisor methods’ solution were defined and the conditions of LDM apportionments compliance with the requirements of total favouring large or small beneficiaries were determined. Subsequently, the A1 algorithm for determining the LDM apportionments which totally favour beneficiaries was elaborated. Using A1, calculations for three examples were performed, obtaining: a d’Hondt method’s apportionment which totally favours large beneficiaries, a Sainte-Laguë method’s apportionment which totally favours large beneficiaries and a Dependent linear divisor method’s apportionment which totally favors small beneficiaries. Obtained results confirm the opportunity of using the algorithm A1 for the determining of LDM apportionments which totally favour large beneficiaries or, on the contrary, the small ones.
Highlights
Metoda d'Hondt [6] îi favorizează pe beneficiarii mari [1, 4, 7, 8], iar metoda Huntington-Hill [9] îi favorizează pe cei mici [4, 10]
For linear divisor methods with c ≥ 1, requirement (5) of apportionment {xi, 1, } total favouring of large beneficiaries can be replaced by: max max iar cerinţa (5) de favorizare totală de către repartizarea {xi, 1, } a beneficiarilor mici poate fi înlocuită cu: and requirement (6) of apportionment {xi, 1, } total favouring of small beneficiaries can be replaced by: max max
One can say that at c > 0 no one of linear divisor methods is always compliant with the requirement (1) of total favouring of large beneficiaries and with the requirement (2) of total favouring of small beneficiaries
Summary
Metoda d'Hondt [6] îi favorizează pe beneficiarii mari (cu valoarea Vi mai mare) [1, 4, 7, 8], iar metoda Huntington-Hill [9] îi favorizează pe cei mici (cu valoare Vi mai mică) [4, 10]. Dar care dintre cele două favorizează beneficiarii într-o măsură mai mare? Marshall, Olkin și Pukelsheim [11, p.1] au plasat cinci metode PRP „în ordinea în care se ştie că favorizează partidele mai mari faţă de partidele mai mici”. O altă, „de favorizare totală”, bazată pe definiţia favorizării beneficiarilor mari sau a celor mici printr-o metodă de repartizare propusă de către Balinski şi Young [1], a fost examinată de către autor în articolul [15]. Unele aspecte ale determinării repartizărilor metodei Divizor liniar general (GLD), ce îi favorizează total pe beneficiarii mari sau pe cei mici, sunt examinate în această lucrare
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