A nonexistence of the optimal voting system can be proven in many situations, I wanted to propose a general discussion about choosing the best voting systems for various purposes and countries. Especially regarding the most interesting - parliamentary election: there is a territory divided into districts in which people vote for local candidates (usually representing one of parties), and we want to find seat apportionment to fulfill two priorities: 1) The total number of seats of different parties is proportional to their total number of votes, 2) Locally there are chosen those having majority of votes. Unfortunately these two priorities exclude each other – there are usually used systems based on the first one (proportional representation, e.g. Holland, Portugal, Switzerland, Spain, Poland, Brazil) or the second (e.g. single-member district - USA, Canada). As we would like to fulfill both priorities, there are also mixed systems (e.g. Germany), like: half of the seats are chosen by local majorities, half by proportional representation – what has some technical difficulties to fulfill. There is also being developed more modern biproportional apportionment to fulfill both priorities at once, but it based on approximations. I think that in the age of computers we don’t have to be satisfied by some approximation, as we can find the optimal apportionment – if only we would quantitatively define what do we mean by the best apportionment – define “optimality” function, such that we are searching for an apportionment having its highest value. Then a computer can start with some approximation and search nearby apportionments to find the best one. As it is a difficult computational problem, after voting statistics are announced, they could wait e.g. a day when everybody could search for a better apportionment (with higher “optimality” value) and finally the best found would be set. So the question is how to define this “optimality” function – it should be some average (e.g. weighted arithmetic) of terms corresponding to penalties of both priorities: 1) minus distance of proportion of seats and proportion of votes, e.g. the simples Gallagher index. We could also take a more complex distance to emphasize the fact that accuracy is more essential for small parties (e.g. Kullback-Leibler). 2) e.g. sum over districts of minus “the number of voters choosing a candidate with larger number of votes than the winner for this district” – for single-member districts (can be easily generalized). So it is kind of a number of people having a reason to complain as their candidate got more votes than the winner - it is zero if the one having majority has won. There has remained many questions, like what weights, distance, function in 2), averages should we choose. E.g. arithmetic average is more tolerable for compensating than geometric average (e.g. if 3,0 is better than 1,1 ?). Then, what kind of question should be asked – to motivate voters to come and to properly represent their choices. Maybe a choice of a single candidate, maybe a few, or maybe some preferential system? What would be the best voting systems and why – especially for your countries? What do we mean by the best apportionment – how to define the “optimality” function?
the representative system voting such as you has described evolved in a time when counting massive amounts of votes was tedious at best, and for most people the burden of traveling to and from polling places for every single vote would have been a burden. in the modern world where laptops, android tablets, and cell phones often out number the number of inhabitants of a given country, such representative voting is somewhat antiquated in that a direct vote of the population can taken fairly easily.
I completely agree that now we can and should try to move toward direct democracy ( discussion: http://www.sciforums.com/showthread...-quot-discuss-then-vote-quot-direct-democracy ) - especially on discussion level, however, it will be a long process and still always we will need representatives making some essential decisions, e.g. when there is not enough time, or when a secret information is involved. And direct democracy also means votes - even more of them, and we have votes also in other places - how should we choose, design them?
I'm saying there are 100's of state, and federal agencies that dole out money to the less fortunate in our society. Go back about 50 years and you'd see no programs to help those less fortunate.
