Axiomatization of divisor methods and weakly degressive proportionality

We suggest a new approach to narrowing the field in elections, based on the ‘deservingness’ of candidates to be contenders in a runoff, or to be declared one of several winners. Instead of specifying some minimum percentage (e.g., 50) that the leading candidate must surpass to avoid a runoff (usually between the top two candidates), we propose that the number of contenders depends on the distribution of votes among all candidates. Divisor methods of apportionment proposed by Jefferson and Webster, among others, provide measures of deservingness, but they can prescribe a runoff even when one candidate receives more than 50 percent of the vote. We propose a new measure of derservingness, called the Next-Two rule, which compares the performance of candidates to the two that immediately follow them. It identifies as contenders candidates who are bunched together near the top. We apply the Next-Two rule to several empirical examples.

Download Full-text

Determining Total Favoring Apportionments Using the General Linear Divisor Method

Economica ◽

10.53486/econ.2021.115.109 ◽

2021 ◽

Author(s):

Ion Bolun ◽

Keyword(s):

General Linear ◽

Divisor Methods ◽

Divisor Method

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.

Download Full-text

Some Properties of Divisor Methods for Legislative Apportionment and Proportional Representation

American Political Science Review ◽

10.1017/s0003055400188410 ◽

1982 ◽

Vol 76 (3) ◽

pp. 575-584 ◽

Cited By ~ 2

Author(s):

Cyril Carter

Keyword(s):

Probability Distribution ◽

Lower Bounds ◽

Proportional Representation ◽

Upper And Lower Bounds ◽

Rigorous Analysis ◽

Political Choice ◽

Divisor Methods ◽

Divisor Method

Some rather elegant properties of linear divisor methods are derived and used to establish upper and lower bounds on the possible variation between apportionment and exact quota entitlement. A probability distribution is derived for this variation, and it is shown that the probability of the variation exceeding one seat is very small with the major fractions linear divisor method.A less rigorous analysis of the nonlinear equal proportions method shows that in practice it is very similar to the major fractions method, but with a very slight bias in favor of small parties (or states). It is concluded that there is no “best” apportionment method, but a knowledge of the properties of the various methods enables a political choice of the most appropriate method.

Download Full-text