Victoriano Ramírez

Parametric methods of apportionment, rounding and production

Abstract The class of “parametric” methods of apportionment, of rounding, or for minimizing the variation of production rates in just-in-time production systems is characterized in several different ways that depend on the underlying qualitative behavior of its solutions.

A bi-proportional method applied to the Spanish Congress

A bi-proportional divisor method is applied to allocate the seats of the 2004 Spanish Congress, thus achieving proportionality relative to the population counts in the fifty-two districts, as well as proportionality relative to the vote counts for the political parties. Also, advantages and disadvantages of the method are discussed.

Parametric vs. divisor methods of apportionment

This paper formulates a new criterion that distinguishes the set of parametric methods within the set of all the divisor methods of apportionment. The criterion—that a method transfer seats as it “should”—asks that as population (or the votes of parties in a PR system) is shifted more and more from one state to another state (from one party to another party) at some point the first state (or party) is apportioned one less seat, the second state (or party) one more seat, and the remaining apportionments are as they were. It goes on to examine several properties of parametric methods.

Degressively Proportional Methods for the Allotment of the European Parliament Seats Amongst the EU Member States

In this work we present several methods for distributing the seats of the European Parliament amongst the States of the European Union, in accordance with the restrictions established in article I-20 of the projected European Constitution. The proposed methods can be applied to the current composition of the EU, but also if there is a change in the number of states or their populations. They are based on adjusting the quotas of every country so that they verify the constitutional restrictions, and so that their rounding to an integer number will constitute an allotment of the seats of the Parliament.

The senatorial election in Spain. Proportional Borda methods for selecting several candidates

Abstract Firstly, in this paper, we analyze how the electors vote in the Senate election in Spain. We show examples in which the election outcome is predictable and not proportional. We also show similar examples for other social choice problems, in which the strategic vote affords a great advantage to those who put it into practice. Secondly, we introduce the definition of a proportional social choice method. We then prove the main result that determines the only Borda type social choice method that has the same proportionality as a given divisor method. We include results with the vote thresholds that guarantee the candidates will be elected under Limited Approval Voting and, finally, compare these thresholds with the proportional Borda Method.

The whole and its parts: On the coherence theorem of Balinski and Young

A new proof of the Coherence Theorem of Balinski and Young is presented. The theorem elucidates the methods used to apportion parliamentary seats among political parties proportionately to their vote counts, or among geographical districts proportionately to their population figures. A proportional apportionment method is coherent when each seat apportionment among all claimants is such that every part of it is a valid solution for the subset of claimants concerned. The Coherence Theorem states that every coherent apportionment method is compatible with a divisor method.

Allotment According to Preferential Vote: Ecuador's Elections

In this paper we show results for some unipersonal and pluripersonal elections in Ecuador and in Spain, observing that the used methods can be replaced by better ones. We present a method for individual elections based on one-on-one comparisons, and preferential voting. This method verifies CONDORCET and PARETO, and it is furthermore better than the Two Round method. For multicandidate elections we give proportional and monotone methods based on preferential vote. We also analyse the electoral system of Ecuador and propose alternatives for it.