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Proportional
Representation Society of Australia Inc. |
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Tel. +614 2917 6725 |
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The district magnitude at
a PR election should be an odd number only. Click on a
blue hyperlink of interest. |
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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. |
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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. |
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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 |
Maximum
vote that could give a grouping just one seat below
an absolute majority
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2 |
33.33% |
2 |
66.6% + 2
votes |
1 |
33.3% + 1 vote |
66.6% - 1
vote |
2.00 |
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3 |
25.00% |
2 |
50.0% + 2 votes |
1 |
25.0% + 1
vote |
50.0% - 1 vote
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2.00 |
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4 |
20.00% |
3 |
60.0% + 3
votes |
2 |
40.0% + 2
votes |
60.0% - 2
votes |
1.50 |
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5 |
16.67% |
3 |
50.0% + 3
votes |
2 |
33.3% + 2
votes |
50.0% - 2
votes |
1.50 |
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6 |
14.29% |
4 |
57.1% + 4
votes |
3 |
42.9% + 3
votes |
57.1% - 3
votes |
1.33 |
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7 |
12.50% |
4 |
50.0% + 4
votes |
3 |
37.5% + 3
votes |
50.0% - 3
votes |
1.33 |
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8 |
11.11% |
5 |
55.5% + 5
votes |
4 |
44.4% + 4
votes |
55.5% - 4
votes |
1.25 |
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9 |
10.00% |
5 |
50.0% + 5
votes |
4 |
40.0% + 4
votes |
50.0% - 4 votes |
1.25 |
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10 |
9.09% |
6 |
54.5% + 6
votes |
5 |
45.5% + 5
votes |
54.5% - 5
votes |
1.20 |
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11 |
8.33% |
6 |
50.0% + 6
votes |
5 |
41.7% + 5
votes |
50.0% - 5
votes |
1.20 |
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12 |
7.69% |
7 |
53.8% + 7
votes |
6 |
46.2% + 6
votes |
53.8% - 6
votes |
1.17 |
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13 |
7.14% |
7 |
50.0% + 7 votes |
6 |
42.9% + 6
votes |
50.0% - 6
votes |
1.17 |
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14 |
6.67% |
8 |
53.3% + 8
votes |
7 |
46.7% + 7
votes |
53.3% - 7
votes |
1.14 |
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15 |
6.25% |
8 |
50.0% + 8 votes |
7 |
43.8% + 7
votes |
50.0% - 7
votes |
1.14 |
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16 |
5.88% |
9 |
52.9% + 9
votes |
8 |
47.1% + 8
votes |
52.9% - 8
votes |
1.13 |
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17 |
5.56% |
9 |
50.0% + 9 votes |
8 |
44.4% + 8
votes |
50.0% - 8
votes |
1.13 |
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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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