PROPORTIONAL REPRESENTATION SOCIETY OF AUSTRALIA

Tel. +613 9589 1802

Tel. +614 2917 6725

 

info@prsa.org.au

www.prsa.org.au

2018-08-20


The district magnitude at a PR election should only be an odd number.

 

Click on a blue hyperlink of interest.

 

An Odd Number of Places is Needed - Not an Even Number:
The reason that an electoral district in a proportional representation election should have only an odd number of places to be filled is that only then does an absolute majority of votes - however slight -
for a given grouping of candidates necessarily produce an absolute majority of seats for that grouping.

In contrast, as the Table below shows, with an even number of places a grouping that has gained an absolute majority of votes needs, unfairly, to exceed 50% by
several percentage points to be able to ensure - with district magnitudes that are the most practicable with PR-STV - an absolute majority of seats for that grouping.

 

 

TOTAL NUMBER OF SEATS






"seats"

APPROXIMATE QUOTA FOR FILLING OF EACH SEAT

BARE ABSOLUTE MAJORITY OF SEATS

NO. OF SEATS ONE BELOW AN ABSOLUTE MAJORITY

RATIO
"max"/"min"
This ratio nears 1.00 as "seats" nears infinity.

Number of seats

Minimum vote to  entitle a grouping to a bare absolute majority of seats

Number of seats

Minimum vote to entitle a grouping to just one seat below an absolute majority 

 
"min"

Maximum vote that could give a grouping just one seat below an absolute majority



 
"max"

2

33.33%

2

66.6% + 2 votes

1

33.3% + 1 vote

66.6% - 1 vote

2.00

3

25.00%

2

50.0% + 2 votes

1

25.0% + 1 vote

50.0% - 1 vote

2.00

4

20.00%

3

60.0% + 3 votes

2

40.0% + 2 votes

60.0% - 2 votes

1.50

5

16.67%

3

50.0% + 3 votes

2

33.3% + 2 votes

50.0% - 2 votes

1.50

6

14.29%

4

57.1% + 4 votes

3

42.9% + 3 votes

57.1% - 3 votes

1.33

7

12.50%

4

50.0% + 4 votes

3

37.5% + 3 votes

50.0% - 3 votes

1.33

8

11.11%

5

55.5% + 5 votes

4

44.4% + 4 votes

55.5% - 4 votes

1.25

9

10.00%

5

50.0% + 5 votes

4

40.0% + 4 votes

50.0% - 4 votes

1.25

10

9.09%

6

54.5% + 6 votes

5

45.5% + 5 votes

54.5% - 5 votes

1.20

11

8.33%

6

50.0% + 6 votes

5

41.7% + 5 votes

50.0% - 5 votes

1.20

12

7.69%

7

53.8% + 7 votes

6

46.2% + 6 votes

53.8% - 6 votes

1.17

13

7.14%

7

50.0% + 7 votes

6

42.9% + 6 votes

50.0% - 6 votes

1.17

14

6.67%

8

53.3% + 8 votes

7

46.7% + 7 votes

53.3% - 7 votes

1.14

15

6.25%

8

50.0% + 8 votes

7

43.8% + 7 votes

50.0% - 7 votes

1.14

16

5.88%

9

52.9% + 9 votes

8

47.1% + 8 votes

52.9% - 8 votes

1.13

17

5.56%

9

50.0% + 9 votes

8

44.4% + 8 votes

50.0% - 8 votes

1.13


Groupings: A grouping can be a formally organized political party, or it can be a group of like-minded candidates that have no formal or organized connection, but are perceived by the voters and commentators as being sufficiently similar in their past voting record if they are standing for re-election or in their promises if they are new candidates. A number of complete and utter independents can also be listed as a grouping in that capacity, in distinction to candidates that are more easily categorized. Groupings, not always recognized, exist at elections in all but unsophisticated and the least organized bodies.

 

An Even Number of Places Fails to Ensure a Majority Predominates: If the absolute majority is not large enough to produce an absolute majority of an even number of seats, the grouping gaining such an absolute majority of votes will only gain half the number of seats available, and the grouping, or groupings, that together gain only a minority of the seats, will gain the other half of the seats, which is less than satisfactory. It can also lead to stalemates. An early official awareness of the unfairly created stalemate problem appeared in Section 6 of Tasmania's Report on General Election 1912. Examples of entrenchment to avoid an even number of places are:

 

·     Section 4 (1) (a) of the Proportional Representation (Hare-Clark) Entrenchment Act 1994 of the Australian Capital Territory entrenches the requirement that an odd number of members of the Legislative Assembly shall be elected from each electorate, and

 

·     Section 16.2.5 of the Constitution of the Republic of Ireland requires the use of the system of proportional representation using the single transferable vote, and Section 16.2.6 requires that no constituency shall elect fewer than three members, which at least avoids the worst case of an odd number, where only 2 members are to be elected.

 

Definitive Report on the Problem: The late Dr George Howatt's 1958 classic thirty-page report to the Parliament of Tasmania on the defects of the original six-member electoral districts used in Tasmania's Hare-Clark system was a superb analysis of the problem, and its key recommendation was implemented when, before the 1959 Assembly elections, each of the five six-member Assembly electoral districts was changed to a seven-member district. Tasmanian Assembly districts were changed to five-member districts before the 1998 elections.

 

Municipal Councils: Municipalities with one or more electoral districts having an even number of seats can, with Victoria's change to proportional representation for such districts, demonstrate the problem there, and Victoria's ad hoc restructuring of electoral districts can institute this problem, if the need for an odd number to be elected is not understood. See also Proportional Representation for Municipal Councils.


Origin of the Senate Problem: The Table above illustrates the problem with even numbers of places to be filled. See paragraph, in A Brief History of PR, on how having and even number of places to be filled has affected Senate outcomes since the number of senators to be elected in each State at a periodic election was first set at an even number, from 1984.

 

The Federal Parliament should have recognized the significance of that Tasmanian finding, although it did take Tasmania over fifty years to decide to resolve the problem. See a paragraph reporting the confession by Dr Richard Klugman, the Inaugural Chairman, in 1983, of the Federal Parliament's Joint Select Committee on Electoral Matters, at the end of an account of the 50th Anniversary Celebration of the Senate's Use of Proportional Representation.

 

The likely persistence of the Parliament's decision that there be two senators for each of Australia’s internal territories is a result of the deliberate “stalemate” effect of such an arrangement where representation is provided, but it is likely that such representation will not result in any net effect on the balance of the overall Senate vote, except in the unlikely circumstance in a particular terrritory that a given grouping of candidates receives more than 66.6% of the vote.

 

Prevent the above problem by ensuring that the number to be elected by proportional representation is set at an ODD NUMBER.

 

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