Electoral_Systems
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3. Pick the highest quotient in the list (including the quotients obtained by dividing the votes by 1). The highest quotient is “400” in the Party D column. We therefore award one seat to Party D.
4. Pick the next highest quotient in the list. The next highest quotient is “300” in the Party C column. We therefore award one seat to Party C.
5. Pick the next highest quotient in the list. The next highest quotient is “200” in the Party D column. We therefore award another seat to Party D. We have successfully filled all the seats available in this constituency.
The final results of the election are therefore:
Party C  1 seat  (or 33% of the total available seats)
Party D  2 seats  (or 66% of the total available seats)
Notice why we call this system “proportional representation:” Under a plurality system, Party D would have received 100% of the seats because that party received a plurality (40%) of the vote--even though 60% of voters voted against Party D by choosing other parties. Under PR, however, we are able to represent some of the interests of the other voters. Party D’s representation in parliament is reduced to 66% of seats, while Party C’s is increased to 33% of seats. The system yields a result that is clearly not perfectly proportional. But the distribution more closely approximates the actual percentage of votes that each party received than would a plurality or majority system.
The d’Hondt method is only one way of allocating seats in party list systems. Other methods include the Saint-Lague method where the divisor is the set of odd numbers (1, 3, 5, 7, 9, . . ., n) and the modified Saint-Lague method used in Denmark, Norway and Sweden, where the divisor is 1.4 plus the set of odd numbers (1.4, 3, 5, 7, 9, . . . , n). Other methods divide the votes by a mathematically derived quota, such as the Droop quota or the Hare quota (see below) 
One other feature of party list systems is called the vote threshold. Party list systems normally establish by law an arbitrary percentage of the vote that parties have to pass before they can be considered in the allocation of seats. The figure ranges from 0.67% in the Netherlands to 5% in Germany and Russia, or even more. Any party that does not reach the threshold is excluded from the calculation of seats. The vote threshold simplifies the process of seat allocation and discourages fringe parties (those that are likely to gain very few votes) from competing in the elections. Obviously, the higher the vote threshold, the fewer the parties that will be represented in parliament.
Single transferable vote (STV)
STV is another important form of proportional representation. In various forms, it is used widely in many countries, although only Ireland, Australia, and Malta have used it in major national elections. Other countries have used it in local elections, and even some communities in the United States (such as Cambridge, MA) use it today. Many student organizations in Europe also use this system for election to university student associations, because it yields an even more proportional result than party list systems, and certainly more proportional than plurality or majority voting. 
STV was originally developed by Thomas Hare (1806-1891), a British politician whose writings greatly influenced the views of the philosopher John Stuart Mill. Under STV, voters vote for individuals, not for parties as in the party list system. The key feature of STV is that individual voters rank candidates according to their 1st, 2nd, 3rd, . . ., nth choices. Rather than simply voting for a single candidate, voters have the opportunity to express a range of preferences for several candidates on the ballot. Like party list systems, though, STV depends on having multi-member constituencies.
The complicated part of STV is tabulating the seats to be awarded after the votes have been cast. As with party list systems, there are a number of mathematical formulas that one can use to accomplish this task. One of the most widely used methods is known as the Droop quota, named for the nineteenth-century thinker and mathematician H. R. Droop. The Droop quota is used to determine the minimal number of votes that an individual candidate must get in order to be awarded a seat. It is calculated using the formula:
 [V/(S+1)] +1
where V is the total number of valid votes cast in the constituency, and S is the total number seats up for election in the constituency. Hence, if we have 1,000 votes cast for 3 seats, the Droop quota is [ 1,000 / (3 + 1) ] + 1 = 251. That means that any candidate who is able to get at least 251 votes will be assured of winning a seat. Once the Droop quota has been calculated and all the votes collected, we still have to allocate the seats. 
In this example, assume that we have 5 candidates (A, B, C, D, E) for 3 seats. In accordance with STV, individual voters have ranked each of these candidates (1 to 5, with one being the first-choice candidate) on their ballots. The allocation of seats then proceeds according to the following steps--but remember that there are a variety of STV methods in use. We will try to keep things very simple here:
1. Pull each ballot out of the ballot box one at a time and place them in piles according to the first-choice candidate marked on the ballot (e.g., if a ballot indicates candidate C as the first choice, place it in a pile marked “C”).
2. As soon as one pile of ballots reaches 251, that candidate is awarded a seat. Let us assume that candidate C was the first to reach the Droop quota of 251 first-choice ballots.
3. Continue drawing ballots out of the ballot box and placing them in piles according to the first-choice candidate marked on the ballot. But since C has already been elected, place any ballots that indicate candidate C as first choice in the pile of the candidate indicated on that ballot as the voter’s second choice. For example, if you pull out a ballot that indicates candidate C as first choice and candidate A as second choice, place the ballot in the pile for candidate A, since candidate C has already been awarded a seat. In this way candidate C’s surplus votes (i.e., the votes beyond those needed to win a seat under the Droop quota) are “transferred” to the next-choice candidate--hence the name “single transferable vote.”
4. Continue with Step 3 until another candidate reaches the 251 mark. Then, continue carrying out Step 3 until you fill all the available seats. For example, let us assume that we have already elected candidate C on first-choice ballots alone, and that by combining second-choice ballots from candidate C with further first-choice ballots from the box, we have also been able to award a seat to candidate A. How do we fill the third seat? We continue in a similar manner as before. Any ballots that list candidate C as the first-choice will be transferred to the second-choice candidate; if the second-choice candidate turns out to be candidate A (who has also already been elected), then we will transfer them to the third-choice candidate. Similarly, all first-choice ballots for candidate A will be transferred to the second-choice candidate indicated on the ballot; if the second-choice candidate turns out to be candidate C (who has already been elected), the ballot is transferred to the third-choice candidate. And so on.
5. But what happens if, after distributing all first-choice ballots, no further candidates have reached the Droop quota and we still have empty seats to fill? In this case, simply eliminate the candidate with the lowest number of first-choice ballots and transfer those votes to the second-choice candidates. Repeat this step as many times as necessary (always eliminating the lowest vote-getter)  in order to reach the number of votes mandated by the Droop quota.
As with party list systems, there are a variety of ways of conducting an STV election. For example, instead of using the Droop quota, we might use the Hare quota (V / S) or the Imperial quota [V / (S + 2)]. A country’s choice of which system to use depends on its history and the degree to which policymakers value genuinely proportional representation.
STV can clearly be rather confusing. Some voters may feel that a plurality system is somehow more “natural,” or that STV and other forms of PR are simply “tinkering with the numbers.” But PR in general, and STV in particular, can yield results that are more truly representative of the choices of individual voters. There is a strong movement for PR in the United Kingdom, with some political leaders arguing that STV should replace the current plurality system for electing parliamentarians to the House of Commons. There is a similar movement in the United States, although since few Americans could even explain how the Electoral College works, they are probably not going to learn STV any time soon.