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Poster for the European Parliament election 2004 in Italy, showing party lists. Party-list proportional representation (list-PR) is a system of proportional representation based on preregistered political parties, with each party being allocated a certain number of seats roughly proportional to their share of the vote.
However, a greater concern for social choice theorists, and the primary cause behind its abandonment in many countries, is the tendency of such rules to produce erratic or irrational behaviors called apportionment paradoxes: Increasing the number of seats in a legislature can decrease a party's apportionment of seats, called the Alabama paradox.
For these elections, all European Union (EU) countries also must use a proportional electoral system (enabling political proportional representation): When n% of the electorate support a particular political party or set of candidates as their favourite, then roughly n% of seats are allotted to that party or those candidates. [10]
The amount of information necessary for such tallies is expressed as an order function of the number of candidates N. Slower-growing functions such as O(N) or O(N 2) make for easier counting, while faster-growing functions such as O(N!) might make it more difficult to do the same.
In this example, 230,000 voters decide the disposition of 8 seats among 4 parties. Since 8 seats are to be allocated, each party's total votes are divided by 1, then by 3, and 5 (and then, if necessary, by 7, 9, 11, 13, and so on by using the formula above) every time the number of votes is the biggest for the current round of calculation.
Any number in one range of quotas will accomplish this, with the highest number in the range always being the same as the lowest number used by the D'Hondt method to award a seat (if it is used rather than the Jefferson method), and the lowest number in the range being the smallest number larger than the next number which would award a seat in ...
Many systems use the Droop quota, which is even smaller than the Hare for the same number of seats, as it produces more proportional results. Because of this quota-based fairness, under STV it is extremely rare for a party to take a majority of the seats in a district without the support of a majority of the district's voters.
This is distinct from other mixed electoral systems that use parallel voting (superposition) or compensatory voting. For example, the rural-urban proportional (RUP) proposal for British Columbia involved the use of a fully proportional system of list-PR or STV in urban regions, combined with MMP in rural regions. [3]