Proportional Voting

"Proportional Representation" systems attempt to allocate seats as closely as possible to the proportion of votes won by each party. By definition, this requires more than one vacancy, so multi-member constituencies are necessary. This means that each political party can preselect as many candidates as there are seats available within each electorate.

Proportional representation systems can be broadly grouped into two categories: “List” systems and “Single Transferable Vote” (STV) systems. List systems can allow the elector to choose between entire groups of candidates, whereas STV only allows choice between individual candidates. The example below just employs a Single Transferable Vote process.

Advantages:

Proportional representation systems were developed primarily to provide representation for minority opinions, thereby overcoming the main weakness of majoritorian systems. Another related advantage of proportional voting, is that few votes are wasted. If a voter wished to vote for a particular candidate but the candidate was either so popular as to have no need for his vote or so unpopular as to have no chance of election, then the vote was not wasted but used to elect the voters' second choice candidate.

Unlike preferential voting which requires support from the majority of the party members, proportional voting requires a much smaller threshold of support. If a party has several factions, proportional voting will produce a power sharing arrangement, whereas the preferential voting system would keep the largest faction in control of all positions. Proportional representation arguably prevents a particular faction or group from obtaining a disproportionately large number of available positions.

Sometimes geography may influence the choice of a proportional system. Proportional systems can ensure balance between regions of a country or an electorate.

Disadvantages:

The foremost problem with proportional voting is its complexity – especially in counting and scrutiny procedures. Unlike proportional voting, where every ballot paper carries a numerical value of 1, a preferential ballot paper can shatter among several candidates (for instance one candidate receives 0.7% of a vote, another obtains 0.2% and a third gets 0.1% of the same ballot paper). In such a complex system, even scrutineers can become confused and uncertain if the correct calculation methods are being used. Counting and declaring a result can be delayed significantly. Party members may find it hard to understanding and accept the cumbersome process. These problems all undermine the perceived legitimacy of the system.

Since proportional voting can encourage the proliferation of minor factions on a party ticket, this can result in party instability. If a minority faction obtains a position, then they can cause public bickering and a semblance of disunity among the preselected party candidates. Where minor factions gain a balance of power, then the party campaign can be effectively run by the dictates of an unpopular minority. The resulting behind-the-scenes manoeuvring and bargaining can lead to situations where the party follows policies that bear only a slight resemblance to its core beliefs. Minor factions can thus hold major parties to ransom in recompense for their support.

Choice of a “Quota”

To match the proportion of seats with the proportion of votes, experts have devised numerous complex computational formulas. These formulas usually calculate a “quota” - the number of votes required to obtain a seat.
The simplest method of determining a quota is to divide the number of valid votes by the number of seats to be allocated. This method is often referred to as the Hare quota.

Three alternatives to the Hare quota exist; The Hagenbach-Bischoff quota, in which the number of votes is divided by the number of seats plus one; the Droop quota, in which the number of votes is divided by the number of seats plus one and adding one to the quotient; and the Imperiali quota, in which the number of votes is divided by the number of seats plus two.

In the following examples 60000 valid votes are cast and 5 seats are to be allocated.

Quotas

"Hare" =   
Votes       = 60 000          = 12 000
                   Seats               5 

"Hagenbach-Bischoff" = 
Votes             =   60 000     = 10 000
                                          Seats + 1                  6 

"Droop"   = 
Votes          + 1        = 60 000    + 1            = 10 001
                      Seats + 1                           6 

"Imperiali"  = 
Votes                = 60 000      = 8 571
                         Seats + 2                   7 

Lower quotas result in more seats being allocated on the basis of candidates receiving a full quota and less being allocated by remainders.

Thresholds

If there is a desire to give make it easier for candidates from smaller factions to be elected, then a threshold can be also used, to require that each candidate achieve a set percentage of the vote before they can be eligible to be elected. For instance, any candidate attaining less than 5% of votes could be immediately eliminated.


Method

A. Under the system of proportional representation, the voter indicates preferences for nominees by using the numbers 1, 2, 3 etc. A candidate is elected when they poll a number of votes equal to or greater than a “quota”. A quota is best calculated using the following “Droop” formula:

Quota =
Total number of formal votes    + 1 (subtracting any fractional remainder)
              Number to be elected + 1

Candidates receiving a number of first preference votes greater than or equal to a quota are declared elected.

B. If no candidate receives a number of first preference votes greater than or equal to a quota then the candidate with the fewest votes is excluded from the count. All of the ballot papers held by an excluded candidate are distributed to the candidates remaining in the count according to the next available preference expressed on those ballot papers.

C. If an elected candidates has more votes than the quota, all their ballot papers are transferred to the remaining candidates at a reduced value. The questions of which votes actually elect the first elected candidate and which votes are surplus (and hence distributed) is resolved by determining the proportions favouring other candidates. A fraction of each vote stays with the first elected candidate and the remaining fraction is distributed on to other candidates. To do this, the ballot papers of each elected candidate are re-examined (commencing with the candidate with the largest surplus) and the total number of second or next available preferences for each unelected candidate is multiplied by that elected candidate’s “transfer value”. The resultant decimal numbers are added to the progressive total of each respective continuing candidate.

D. Where a transfer of ballot papers raises the number of votes obtained by a candidate up to a quota, the candidate is declared elected. No more ballot papers are transferred to that elected candidate at any succeeding count.

E. In the transfer of an elected candidate’s surplus votes, only those ballot papers received in the preceding transfer from a previously elected or excluded candidate are distributed to unelected candidates.

F. When all surpluses have been transferred, and vacancies remain to be filled, exclusions begin. If an excluded candidate has received any “surplus” votes” these ballot papers are transferred at the transfer value they were received at. Exclusions continue until a candidate eventually obtains a number of votes equal to or greater than the quota, and is therefore elected.

G. The process of distributing surpluses and excluding candidates continues as necessary, until either all vacancies are filled or the number of candidates in the count is equal to the number of vacancies remaining to be filled. In the latter case, the remaining candidates are declared elected.

H. Where, at any stage in the count, a ballot paper contains no preference for any one candidate remaining in the count, then that ballot paper is deemed “exhausted” and is set aside as being finally dealt with.

Definitions

1. "Candidate" – shall be taken to include any nominee for preselection.
"Continuing candidate" - any candidate not elected or excluded at any given time.
"Count" - all the operations involved in counting the first preferences recorded for candidates, or, all the operations involved in the transfer of the surplus of an elected candidate, or all the operations involved in the transfer of votes of an excluded candidate.
"Exhausted paper" - a ballot paper on which no second or subsequent preference is recorded for a continuing candidate, and any paper on which it is not possible to determine for which of the continuing candidates the next available preference of the voter is recorded.
"None of the above" - the expression is to be treated as if this represents the name of one or more candidates.
"Original vote" - in regard to any candidate means a vote derived from a ballot paper on which a first preference is recorded for that candidate.
"Surplus" - the value of votes credited to any candidate (including original and transferred vote values),  minus the quota.
"Transferable paper" - a ballot paper on which following a first preference, a second or subsequent preference is recorded for a continuing candidate.
"Transferred vote" - in regard to any candidate means a vote derived from a ballot paper on which a second or subsequent preference is recorded for that candidate.

Calculation of the Quota

2. On completion of the time allowed for voting, the returning officer shall examine the ballot papers and sort them into parcels according to the first preferences recorded for each candidate, rejecting any that are informal. A ballot paper is informal on which:
(a) the figure 1 standing alone indicating a first preference is not placed against the name of a candidate or is placed against the name of more than one candidate; or
(b) the figure 1 together with another figure is placed against the name of a candidate; or
(c) it cannot be determined for which candidate the first preference is recorded.

3. The Returning Officer shall then count the number of papers in each parcel and shall credit each candidate with the number of valid papers on which a first preference has been recorded for such candidate, and a corresponding value, and he shall ascertain the total sum of valid votes cast for all candidates by recording the numbers in a form substantially similar to Table 1.  For this and subsequent purposes each original ballot paper shall be deemed to have a value of 1.0000, but the Returning Officer shall be permitted to calculate further decimal places where this is necessary.

4. The Returning Officer shall then divide the total value of formal ballot papers (including those marked “None of the Above”) by a number exceeding by one the number of vacancies to be filled.  The result, increased by 1 (any fractional remainder being disregarded), shall be the value of votes sufficient to secure the election of a candidate.  This value is herein called the ‘quota’.

Illustration:

  Quota =  Total formal votes               + 1  (excluding any remainder)
               Number to be elected + 1

Election of Candidates

5. If at the end of any count, or at the end of the transfer of a parcel or sub-parcel of an excluded candidate’s votes, the value of votes credited to a candidate is greater than or equal to the quota, that candidate shall thereon be elected. Where the votes of a candidate are exactly equal to the quota, those votes shall be set aside as finally dealt with. Elected candidates shall not receive further transfers of preferences.

6. The order of priority of election shall be that of the order in which they are elected, and if at the end of any count two or more candidates are elected, the order of priority shall be the order of magnitude of the value of votes then credited to such candidates, commencing with the greatest.

Transfer of Surpluses

7. If at the end of any count the value of votes credited to a candidate is greater than the quota, only those votes in the parcel or sub-parcel last received by the elected candidate shall be distributed, at a reduced value, to the continuing candidates for whom the next available preferences have been recorded on the ballot papers.

8. If more than one candidate has a surplus, the larger surplus shall be dealt with first.  Where two or more surpluses are equal, the surplus of the candidate with the highest value of votes at the most recent count at which the candidates have an unequal value of votes shall be dealt with first, and if they have the same value at all counts the Returning Officer shall determine by lot which one he shall deal with first.

9. If the votes credited to an elected candidate consist solely of original votes only, the Returning Officer shall identify transferable papers by examining all the papers contained in the parcel of the elected candidate whose surplus is to be transferred.

10. If the votes credited to an elected candidate consist of transferred and original votes, or transferred votes only, the returning officer shall identify transferable papers by examining only the papers contained in the last sub-parcel received by the elected candidate whose surplus is to be transferred.

11. A surplus shall be transferred in the following manner and recorded in a form substantially similar to Table 2.
(a) The Returning Officer shall:
             (i) sort the transferable papers into sub-parcels according
                  to the next available preferences recorded thereon;
             (ii) make a separate sub-parcel of the exhausted papers; and
             (iii) ascertain the value of papers in each sub-parcel.
(b) To calculate the transfer value, the surplus shall be divided by the total number of transferable votes obtained in the last parcel or sub-parcel received by that candidate, and the resulting fraction is the ‘transfer value’.
(c) Each parcel of transferable votes shall be transferred to the next continuing candidate at that transfer value.
(d) Each continuing candidate shall be credited with the value of the votes so transferred to him.

Exclusion of Candidates

12. If vacancies remain to be filled after all surpluses from elected candidates have been distributed, the process of excluding the lowest-scoring candidate begins. If at the end of any count, no candidate has a surplus and one or more vacancies exist to be filled, the Returning Officer shall exclude the candidate lowest on the poll.

13. If, when a candidate is to be excluded, two or more candidates have the same value of votes and are lowest on the poll, the candidate with the lowest value of votes at the earliest count at which the candidates have an unequal value of votes, shall be excluded, and if they have the same value at all counts, the Returning Officer shall determine by lot which is to be excluded.

14. On the exclusion of any candidate, the Returning Officer shall, except as provided below, examine all the papers credited to that candidate, shall sort the transferable papers into sub-parcels according to the next available preference recorded thereon, and shall transfer each sub-parcel to the candidates for whom that preference is recorded, and shall set aside the exhausted papers.

15. When the votes of an excluded candidate are transferred, the parcel containing original votes, if any, shall be transferred first, at the full value of 1.0000, followed by the transfer of sub-parcels of transferred votes in the order in which and at the value at which they were received. All transfers of votes from excluded candidates shall be recorded in a form substantially similar to Table 3.

16. If at the end of any count, or at the end of the transfer of a parcel or sub-parcel of an excluded candidates’ votes, the number of elected candidates is equal to the number of vacancies to be filled, no further transfer of votes shall be made.

17. If on the exclusion of a candidate or candidates the number of the then continuing candidates is equal to the number of vacancies remaining unfilled, the continuing candidates shall be elected, and no further transfer of votes shall be made.

Sorting of Vote Parcels


18. When a transfer is made, each sub-parcel of papers transferred shall be placed on the top of the parcel, if any, of the papers of the candidate to whom the transfer is made, and that candidate shall be credited with the value of the papers transferred to him.

19. Exhausted papers at the end of any count shall be set aside as a separate sub-parcel together with all parcels of exhausted papers already set aside.

20. Papers bearing a preference for ‘None of the above’ shall be treated as if ‘None of the above’ were a continuing candidate.  For each quota received by ‘None of the above’ the total number of candidates to be elected by this method shall be reduced by one, but the quota shall not be reduced.

Recounts

21. Any scrutineer may, at the end of any count, request the Returning Officer to re-examine and recount all or any of the papers dealt with during that count, and the Returning Officer shall forthwith re-examine and recount such papers. However, the returning officer is not obliged to recount the same papers more than once. The Returning Officer shall, if necessary, recalculate the values of all, or any, of the papers dealt with during the recount.  No alteration of the dispositions of the papers shall be made at the end of a recount except to correct errors discovered in the recount.

22. The Returning Officer may at his discretion recount papers either once or more often in any case in which he is not satisfied as to the accuracy of any previous counting of the vote.


   Alternative Voting Systems:

          See Choosing a Voting System

Asia Pacific Democrat Youth

Country Profiles

Policy Debates

News & History

Activist Resources

Business Support

About APDY

Email Us

1