18-09-2010
¿Cuál es el sistema electoral más justo y eficaz en una democracia para elegir los parlamentarios y, por ende, un gobierno?. La repuesta es ninguno porque, como explica detalladamente George Szpiro en su nuevo y ameno libro, Numbers Rule: the Vexing Mathematics of Democracy, from Plato to the Present (“Mandan los números: las molestas matemáticas de la Democracia, de platón a la actualidad”, publicado por Princeton University Press) todos los sistemas tienen sus paradojas, faltas de coherencia y manipulaciones. El único sistema que no los tiene es una dictadura. Como dijo Winston Churchill, “la democracia es el menos malo de los sistemas políticos.”
El sistema electoral británico -con circunscripciones de un escaño que se otorgan al candidato más votado aunque no logre la mayoría de los votos- no es ni mucho menos de los más justos, aunque ha cumplido con su misión de producir gobiernos fuertes de un solo partido con mandatos claros. Pero en mayo de este año se ha dado un vuelco a la situación produciéndose la primera coalición (conservadores y liberales-demócratas) desde los años de la Segunda Guerra Mundial (cuando se constituyó un gobierno de concentración nacional).
En 1997, cuando Tony Blair puso fin a 18 años de poder de los conservadores, los laboristas ganaron 418 de los 650 escaños con el 43,2% del voto popular. Este mayo David Cameron puso fin a 13 años de gobierno laboristas con 306 escaños (el 36,1% del voto), quedándose a 20 escaños de la mayoría absoluta. Los liberales necesitaron una media de casi 120.000 votos por escaño en comparación con los 35.000 votos de los conservadores y los 33.350 de los laboristas. El sistema conocido en ingles como first-past-the-post beneficia a los dos grandes partidos (la mayoría de los candidatos en las circunscripciones son elegidos con menos del 50% de los votos). No sorprende que el “precio” de los liberales para formar gobierno con Cameron sea un referéndum en 2011 sobre un nuevo sistema electoral basado más en los resultados de todos los partidos y menos en la mayoría simple de un partido. No es del todo seguro, sin embargo, que mis compatriotas voten a favor de un nuevo sistema.
Hay argumentos en contra del sistema electoral español, aunque es un sistema proporcional (el D’Hondt ). Este método consiste básicamente en ordenar de mayor a menor los votos obtenidos. Luego se van haciendo sucesivas divisiones entre 1 y el número de escaños de cada circunscripción territorial, para ir asignando los escaños de forma proporcional a los votos.
Este sistema cumplió con las necesidades de la transición a la democracia —promover un bipartidismo fuerte y evitar la excesiva atomización de fuerzas políticas en el Parlamento- y ha dado a España gobiernos estables, no sólo los mayoritarios, sino también los minoritarios. Pero, al pasar los años, ha consolidado algunas injusticias.
Por ejemplo, un escaño en las Cortes en las últimas elecciones generales costó a los Socialistas 66.801 votos; al Partido Popular 66.740 votos; a Izquierda Unida 484.973 y a Unión Progreso y Democracia 306.079. Las provincias pequeñas están sobre representadas: en 2008, Soria con un electorado de 78.531 votantes eligió dos miembros del Congreso (uno por cada 39.265 votantes) mientras Madrid con 4,458,540 votantes eligió 35 diputados (uno por cada 127.387 votantes).
Los 306.128 votantes del Partido Nacional Vasco (seis diputados) van a ser más decisivos en la elaboración de los próximos Presupuestos Generales que los 969.946 de Izquierda Unida (dos diputados). Como bien escribió Víctor Morales en una carta publicada en El País , “¿por qué un votante del PNV tiene ahora capacidad de influir en los Presupuestos y yo no?
Szpiro, un matemático y periodista, sigue la historia fascinante de los personajes que inventaron diferentes sistemas electorales distintos. Uno de ellos fue el monje medieval Ramón Llull (c. 1232-1315), más conocido por ser uno de los creadores del catalán literario que por su pensamiento sobre elecciones. Su novel Libre d’Evast e d’Aloma e de Blanquerna tiene un capitulo — En qual manera Natana fu eleta a abadessa — que desarrolla una interesante método electoral.
No hay espacio aquí para explicarlo en detalle. El ejemplo es la elección de abadesas en los conventos. Consiste básicamente en que cada una de las nueve monjas de una lista electoral para ser abadesa compite con cada una de ellas en series de dos y cada victoria acumula puntos. Cada candidata de las nueve tiene que presentarse ocho veces. La ganadora es la monja que consigue más puntos. En este caso el máximo número de puntos es ocho. Llull creía que su sistema representaba la voluntad de Dios, pero es poco práctico para elecciones generales con centenares de candidatos y millones de votantes.
Otras personas estudiadas en el libro de Szpiro son Platón, Plinio el joven, el Marques de Condorcet (quien demostró que la mayoría en el voto en una elección podría tener un resultado que no diera un claro ganador), Thomas Jefferson, Alexander Hamilton y Kenneth Arrow (Premio Nobel de Economía en 1972).
En suma, el sistema electoral perfecto está aún por inventarse. ¡Que los políticos tomen nota!
1) What was the problem with elections?
2) What is the mathematical explanation?
3) Which other mathematicians have studied these kind of problems?
3) Other Comoments?
I have some problems to understand some concepts but I will try to ask the questions.
1. That the politicians that are more famouse can have more botes that politicians that are know in a few part of the society.
2. That’re impossible to take in acount all the votes
3. Platón, Plinio el joven, el Marques de Condorcet, Ramon Llull are some of the “scientifics” that have studied this problem
At the start I say that I have problems to understand the text, so I think that the questions are correct but I can’t afirmate 100%
The problem with the election systems is that there isn’t any system with no manipulations or paradoxes, so we can’t have a perfect way to elect our president. The only one that hasn’t got any of these problems is a dictatorship, and considering them, democracy is the best one.
We could say that the main problem is about proportionality. The number of votes and seats (I think that’s “escaño”) hasn’t got the same proportion in all the political parties, so some of them need few votes to get more seats.
Long time ago, Ramon Llull tried to create a new method by making to compete the candidates between them in groups of 2, and whoever wins scores points. The candidate with the most points at the end of all the competitions would be the one elected. This method could work with small numbers, but now that would be impossible.
I think the solution would be making all the seats cost the same votes, but I don’t really know the consequences of that and I don’t know how the law D’Hondt works, so I don’t have a valid opinion in here. What I do know is that now it’s very unfair for the smaller political parties.
The problem it’s that there so many manipulations or paradoxes, so there isn’t a way to elect what we want.
Ther’re different types of votes and seats, so some of them need few votes to seats, and it’s impossible to take account of all the votes.
Platón, Plinio el joven, el Marques de Condorcet, Ramon Llull are some of the people that have studied this.
The solution would be to that seats cost the same number of votes.
1) The problem with the elctions is that depending on the place you’re or if in that place that you are there is a lot or few people, your vote is more important or count more or less. This is not logic, but I don’t understand so much how works politics and the new’s title is very clar because the maths un that case woks wrong.
2) The mathematical explanation consists in order of most to least votes obtained. Then they go by successive divisions from 1 to the number of seats of each territorial constituency to be allocated seats in proportion to the votes.
3) The mathematicians that studied this kind of problems are Platon, Plinio, Condorcet, Thomas Jefferson, Alexander Hamilton and Kenneth Arrow. And also, Ramon Llull, a famous catlan writer, studied this kind of problems.
4) I think that this democratic method is not so exact, like all mathematicians like and maybe not all the governments are 100% correct, but in all of these cases is democracy and we cannot discuss it so much because people decide their future governments, so like in the text says, is the less bad politician system.
1. The electoral system isn’t just because depend on how share out the votes one political party can win and other can lose.
2. The mathematical explanation is that you have to distribute votes in representatives and depends on the mathematical formula you choose, you give more power to a one political force or another.
3.The mathematician that studied these kind of problems are Platón, Plinio el joven, el Marques de Condorcet and Ramon Llull.
4. For example, In Catalonia the two most important political parties are CIU and PSOE and IIf you want to cast to other political party it’s hardly ever impossible to win because of the electoral system that favors the most important forces.
I have already read the new, but I have problems to understand it. So I will try to answer the questions as well as I could.
1) I think that the problem with the elections is that every kind of system has got paradoxes, inconsistencies and manipulations.
How ever, I think I’m illusory because really belive that, actually, the elections, aren’t manipulates by anyone.
2) There isn’t any electoral system reliable, because anyone has found it.
3) Other people that has studiet this problem are: George Szpiro, Ramon Llul, Platón.
I think, that if that new is true: Are we in a decmocracy?
Because if we go to vote, and our vote is not counting at all, we have a problem…
I don’t know If I have understand the new well.
ELISENDAA!;)
I ‘ve to say that the true is that this new it’s a messy, and personaly I didn’t like it very much, because I don’t like these topics such as politics. But, well as it was for homework, here you have my answers:
1) The problem of the elections was that the wins the most voted candidate even he hasn’t won the majority of votes, and so as my clasmates have said there are manipulations on this elections we’re suposed to be the ones who choose.
2) The mathematical explanations is maybe the percentages and amount of votes that are not taken into account in this elections, I supose, because I do’nt understand it very much.
3) The philosophical ideas of Plato had many social implications, particularly concerning the ideal state or government.
Under the patronage of the Generalitat of Catalonia and the government’s initial collaboration of the Balearic Islands, created the Institut Ramon Llull (2002), in order to promote the outreach of the Catalan language and culture.
4) This comment is maybe more about politics than maths, but I think we shouldn’t vote if finally our votes are not used at all. And the politicians do what they want using briberies and so on. But my opinion in here it maybehas not have a lot do, because I don’t understant about this topics, but I don’t really want it
1) The problem with the systems of the elections is that there’s no system that it’s perfect, I mean, any system is exact and this is a terrible mistake, especially for the mathematics, being that mathematician always have tried to be exact. So there’s no elections that haven’t been manipulated, we could say that they are unfair.
2) The actual system’s method consists in order, from the greatest to the least the votes obtained. Afterwards we divide 1 and the number of each territorial constituency seats successively, to assign the seats in a proportional way to the votes.
3) Other mathematician that studied this kind of electorals’ systems were Platón, Plinio el joven, el Marques de Condorcet Thomas Jefferson, Alexander Hamilton & Kenneth Arrow.
4) In my opinion if we tried to find a good electoral system we could find out one, but I also supose that politicians are not very interested in discover one …Why do I say this? Because probably beeing a little bit less exact some candidates wouldn’t have as many votes as now, so they don’t take seriously this problem of the elections.
Ariadna Corredera 3rA
First of all I add that i don’t like this news becuase for me the politics things are boring because they always are angry and they’re always discussing. But well I will do…
1) The new said that there is a problem to count the votes of our opinion because it says that is not the 100%.But I prefer the democraty instead of the dictatorship.
2) The problem of maths ,it’s that is no certainly nad it’s not 100% because it can be a 80% o like this but you don’t have all the opinion that you said in the paper.
3)Platón, Plinio el joven, el Marques de Condorcet, Ramon Llull are some of the people that have studied this.
They studied this :Plinio el joven, Platón, Ramon Lull ans more people.
4) My comment is the same like Elisenda because if it’s a democracy it can’t be and 80% of our opinion it will be all the opinion .And with all the votes we can make our government.
The problem with the elections system is that, any system isn’t 100% just and without paradoxes and manipulations, only the dictatorship is totally reliable and I think our system is much better, even if has some paradoxes, that a dictatorship.
The mathematical explanations is related with the proportionality, the biggest political parties has more advantage that minorities parties.
Some mathematicians have studied these kind of problems for exemple: Ramon Llull (he development an own electoral method), Szpiro, Platón, Plinio, the Marquis of Condorcet, Thomas Jefferson, Alexander Hamilton and Kenneth Arrow (the winner of the Nobel Prize in Economics in 1972).
I think the solution would be that all parties might be required votes to win a seat.