Counting single transferable votes
There are many different methods of counting for the process of the transferable Einzelstimmgebung.
- 3.1 Reallocation of surplus 3.1.1 Random selection
- 3.2.1 Hare method
- 3.2.2 Method Cincinnati
- 3.2.3 Clarke method
- 3.2.4 Gregory method / Senate Rules
- 3.3.1 Meek method
- 3.3.2 Warren method
Voting
Each voter ranks candidates in order of preference.
Determination of the rate
The ratio is the number of votes required for a candidate to be elected. Since it is an absolute limit and not by a percentage value, it is sometimes also called hurdle. It is calculated from the numbers of valid votes and dispensed -to-fill seats. There are two different calculation methods common to one by Hare and by droop.
In the Hare quota at least one candidate is elected with less than a full quota with high probability even if each voter indicates a preference for all candidates.
If each voter indicates a full list of preferences, guaranteed the Droop quota that each selected candidate will reach the quota and not just chosen because it is the last remaining candidate after weaker candidates are eliminated. Therefore, the Droop quota is preferably chosen. It is the smallest number that ensures that no other candidate can meet the quota as soon as many candidates each have a quota votes as there are seats to be filled.
The excess parts of a candidate to be transmitted to other candidates corresponding to the next available preferences. In Meek's method, the rate must be recalculated during the count.
Hare quota
When Thomas Hare invented his version of the transferable Einzelstimmgebung, he imagined the use of a simple ratio, which under the name Hare quota has therefore become known:
It requires that at the end of all votes cast are equally divided between the selected candidates. The only difference between the votes given for each candidate would be based on the distribution of voters between constituencies - Hare's original proposal provided only a single nationwide constituency - and the number of incomplete votes, ie the people who have not included all the candidates in their ranking, which means that some candidates would be selected as the last remaining with less than the quota.
In the special case of only one to be awarded the seat all the preferences have to be evaluated, by the weakest candidate is eliminated in each round and its votes are distributed, until only one remains.
Droop quota
Today it is mostly the Droop quota is used. It is usually specified as follows:
In contrast to the Hare quota, this does not require that all preferences contribute to the election of a candidate. There it is sufficient that enough voices come together, that no other befindlicher still in the race candidate can win. This voices remain within the scope of almost an entire unallocated quota, but it is said that this ratio simplifies dialing and counting of these votes would not change the final result.
In the special case of only one seat to be awarded this, ranging 50 % 1 vote.
Counting of votes
Allocation ( process A): The Erstpräferenzen be counted. If one or more candidates receive more votes than the quota is, they are declared elected. Once a candidate is selected, he can no more votes obtained (see, however, a modernization below).
The surplus votes of the successful candidates will be allotted to the candidates who have obtained on the ballot of the selected candidates to the next higher court. For the transfer of surplus votes, there are various methods ( see below).
A procedure is repeated until there are no more candidates who have reached the quota.
Elimination ( process B): The candidate with the least support is eliminated, his votes are transferred to those candidates who were eliminated on the ballot at the next highest placed. Once a candidate is eliminated, it can not receive any further votes.
After each pass of process B, begins now if candidates are elected, again: A. This continues until all candidates are either elected or eliminated. Process B can not be resumed, as long as there is still an elected candidate whose surplus votes have yet to be transferred.
Reallocation of the surplus
The votes received by a candidate elected in excess of quota, make a surplus. In order that as few votes are wasted, they are transferred to the most varieties on the remaining unelected candidates. This is done according to the next indicated preference.
There are different methods to decide which you want to transfer the votes of the candidates. Some are usually not applied only to the initial surplus, if an unelected candidate exceeds the quota for the first time. Others are applied to subsequent surpluses, if an elected candidate receives more votes transferred.
Random selection
Some of the methods for the distribution of the surplus are based on select votes by accident. Ensuring the randomness happens in various ways. In many cases, to take into account all voices are easily mixed by hand.
In Cambridge, a constituency is counted in each case; this creates an artificial order of the votes. To prevent all be selected to be transferred votes from the same constituency, each te ballot is selected, the break is to be selected.
Transfer only the initial surplus
Suppose that Andrea has 190 votes at a certain point of counting and the ratio is 200 Now Andrea receives 30 votes by Bernd transferred ( after Bernd is either elected or eliminated ). The results for Andrea total of 220 votes, ie a surplus of 20 votes to be transmitted. But which 20 votes are to be transferred?
Hare method
From the 30 votes that were transferred from Bernd, 20 votes are drawn by random selection. 20, each of these parts is transferred to the next available preference indicated by Andrea on the ballot. In a count of paper ballots by hand, this method is the easiest to be implemented; it was in 1857 Thomas Hare's original proposal. It is used in the Republic of Ireland (except in senatorial elections).
However, there is no guarantee that the subsequent preferences of the 30 transmitted by Bernd voices are similar to those of the other 190 voices that Andrea had first obtained. Therefore, this method is potentially unfair and opens the possibility of tactical voting. In addition, exhausted ballots are excluded. Thus, if more than 10 of the 30 votes by Andrea no further preference is specified, no 20 voices can be selected for transmission, so some voices need to be wasted.
Cincinnati method
20 votes are drawn randomly selected from all 220 votes. This method is used, Cambridge. ( Where every 11th vote ( 220-200 ) / 220 = 1/11 would ) be taken for transmission. This method is representative more likely than Hare's method and less prone to too many exhausted votes. However, there is still an element of chance. This can be crucial in a tight election, who will win. It should also be ensured in the event of a recount of the votes that doing exactly the same random selection will be used. (That is, the recount is only there to check errors in the original count, and not to make a new random selection. )
If a candidate alone with the Erstpräferenzen exceeds the quota, there are between Hare's method and the Cincinnati method no difference, because all the voices of the candidates are in the " last remaining stack ", is from which the Hare surplus pulled.
Clarke method
All 220 ballots are distributed according to the next preference specified in separate piles. From each batch the same proportion of votes is drawn randomly selected and assigned to the candidates concerned.
If we assume in the example that on 40 ballots by Andrea no further preference is indicated, the proportion. For example, if 54 specify by Andreas 220 votes as the next preference Bernd, 90 Christian and 36 Doris, then 6, 10 and 4 votes of the corresponding three stacks are withdrawn and transferred to the respective candidates.
This method is used in Australia. For non- integer votes is completed in Australia: When an allocation of 52: 88: 40 (ie, 5.8: 9.8: 4.4 ) would the transmission ratio 5: 9: 4 will be made so that only 18 instead of 20 votes are transferred. The number of such " lost" votes is always less than the number of remaining candidates; in practice this is a very small part, because the number of parts is much greater than the number of candidates.
The Clarke method reduces the problem of coincidence of the Cincinnati method, but does not eliminate it.
Gregory method / Senate Rules
Another method is known both as Senate rules ( according to their use for the largest number of seats in elections to the Irish Senate ), as well as Gregory method ( after its inventor JB Gregory ). This eliminates any chance and spent virtually Clarke's method also in all subsequent transfers to. Instead of transferring a portion of the votes with full value, all votes shall be transferred with a part of their value. The share in question is the same as in the Clarke method, ie in the example.
It should be noted that a part of the total of 220 votes may already be assembled for Andrea from proportionate votes from previous transmissions; e.g. Bernd was perhaps chosen with 250 votes, 150 with Andrea as the next preference, so that the transfer of 30 votes was actually 150 votes with a value of each. In this case, these 150 votes would now be transferred with a combined share of value again. In practice, the transmitted value of a voice would normally be specified not as a vulgar fraction, but as a decimal fraction with two or three decimal places. To simplify the counting of the votes, you can give the original cast a numerical value of 100 or 1000 in order to then work with integers can.
Combined fractions to calculate is labor intensive. Therefore, this method is used in Ireland only for the Senate, in which only about 1,500 counselors are eligible to vote. However, this method is used since 1973 in all STV elections in Northern Ireland; it can accommodate up to 7 transfers ( in Local Councils with 8 seats ) instead, and up to 700,000 votes are counted ( in the European elections with 3 seats ).
Transmission and subsequent surpluses
All of the above methods apply only to the transfer of an original surplus when a not initially selected candidate exceeds the quota of votes for the first time during the count. A similar question arises as to where votes are to be transferred and the specified next preference is for a candidate already selected. The usual practice has always been to ignore this preference and the voices instead on the next not yet selected (and not eliminated ) to transfer candidates. This amounts to Hare method and suffers from all of the shortcomings of this method.
In principle it would be possible to use one of the other methods. Suppose that the already chosen Andrea gets 20 transfers from newly elected Bernd addition to the rate of 200 previously withheld: In the Cincinnati approach, you'd mix all 220 voices of Andrea and select randomly selected 20 votes for transmission. The problem is that some of these 20 votes again include retransmissions by Andrea Bernd and thus generate a recursion. This is unclean. In the case of Senate rules, it would be an infinite recursion, since at each step all the votes are transferred and smaller fractions arise.
Meek method
1969 Designed Brian L. Meek, a counting method, which is based on the Gregory method (Senate Rules). As there voices fractions are transferred. However, candidates who have already chosen not skipped in further counting, but can get through transfers more votes. However, the thereby occurring again surplus must be redistributed so that each person elected not ultimately has more votes than the quota is. This happens because the fraction, the one candidate from each received voice (and also from any votes received fraction ) reserves, is reduced. This fraction is referred to Keep holding value. It is every time the candidate receives votes transferred again, further reduced. The holding value of the candidates will each time be reduced so that they have just a whole odd voices again.
Since an infinite recursion caused by transmissions and retransmissions of ( lower in each subsequent round ) votes fractions, used Meeks method an iterative approximation method, which continues the transfers to the part transferred share of the vote is vanishingly small, such as a millionth. This process would involve a manual counting extremely complex, since all the ballots re-evaluated in each passage and transfers must be completed.
Therefore, the Meek method requires a count of the votes by computer, even if the vote is on paper. However, once calculated, keep what proportion of the respective candidates by every voice, the results can also be checked using paper ballots. (One can think of it as a system of equations with many variables imagine. Calculation of variables is expensive. But if they are calculated, the accuracy can be relatively easily checked by the variables used in the equations. )
A candidate who has not yet reached the quota, but is still in the race, always has the value 1 Keep His votes are fully counted until now. Exceeds the candidate in the course of counting the quota, the holding value drops to less than 1
If a candidate does not have enough votes and is therefore deleted, its holding value is set to 0. Accordingly, the corresponding voice will be fully transferred to the next preference. If a candidate is deleted, the count will behave as if he had never started (except that no other previously painted candidate can be revived ).
In general, the share of voice, which is not retained is transmitted.
If a candidate is selected, so all votes cast for him votes are weighted by the holding value, and the balance of the votes value is proportionally distributed to the following preferences, each of which also only keeps the portion corresponding to their holding value and the remainder again forwards them to the next preference.
If votes can not be transferred because no further preferences are specified, the rate is recalculated. Meek's method is the only one in which the quota is changed in the middle in the process. The rate is calculated as follows
It is thus a variation of the Droop quota. Recalculating a result, that of the holding value ( the "weight" ) of each candidate is changed.
This process is repeated until the value of all the votes of the candidates elected is almost the same rate ( within a very small range, ie from 0.99999 to 1.00001 of a share ).
When Meek method, all surpluses are transferred simultaneously, rather than in a specific order. The surpluses originate with the corresponding percentage of all ballots received not only by the in the previous transmission.
The Meek method shall be that of STV method that best embodies the principles of STV. It is currently being used in some local elections in New Zealand.
Warren method
Warren's method is similar to Meeks method. Here, however, the retained fractions of votes are not multiplied, but added together.
Example
Suppose we perform an STV election as possible, using the Droop quota, have two vacant seats and four candidates: Andrea, Bernd, Christian and Doris. Suppose further that 57 voters participate, which indicate in their ballots the following preference ranking, the many other possible sequences do not occur.
The droop rate or hurdle is:
The Hare quota fraud:
In the first round Andrea receives 40 votes and 17 Doris Andrea is selected and has 20 excess votes. This surplus votes are allocated pro rata to their second preferences. So go 12 of transferred votes to Christian and 8 to Bernd.
Since none of the remaining candidates reach the quota, Bernd, the candidate with the fewest votes is eliminated. All of his votes have Christian as a runner- preference and are now transferred to Christian. Christian gets so 20 votes and is elected; he occupied the second seat