User:RodCrosby/QPR2

Quota proportional representation squared (QPR2), also known simply as PR squared or PR^2, is an electoral system designed to produce semi-proportional election results across a region by electing two representatives in each of the region’s districts. The 1st seat in every district is awarded to the party or candidate which receives the most votes, similar to first-past-the-post voting (FPTP). The 2nd seat is awarded to one of the remaining district parties or candidates so that squared proportionality is achieved across the region, using a calculation that aims to award parties their seats in the districts where they had their strongest performances, relative to the Droop quota.

Origin

The first suggestion for squaring votes before assigning seats in proportion to these squares appears to have been made by Julian Wiseman in 1998, proposing a version of the system to elect the UK Westminster parliament. In May 2010, Rod Stringer offered improvements that would make the system more practical and politically acceptable,and this version of the system was later simplified.

Objectives and rationale

Stringer believes that a combination of political vested interest and inability to agree on one of the various true proportional systems means that it is unlikely that the UK will ever abandon FPTP for Westminster.

PR squared is a system that is a relatively small change from the perspective of voters and the major parties, has some benefits for almost all parties, and accordingly may stand a higher chance of achieving consensus for its adoption. While not closely proportional, PR squared can be shown to be about half as disproportional as FPTP, according to certain common measures, in particular treating third and fourth parties which compete UK-wide more fairly.

The prospect of majority government on a minority of votes remains quite possible, and in large part PR squared is advocated for pragmatic reasons.

QPR2 described

Constituency structure

The current single-member seats would be amalgamated into ideally units of two, although accommodation could be made to retain three island seats as single-member and, exceptionally, a few three-member seats could also exist, mostly in the cities or where a county currently has an odd number of seats. This constituency structure would mimic the constituency structure that in fact existed from 1265 to 1885 and did not finally disappear in some places in the UK until 1950.

Ballot structure

Major parties would most likely run two candidates in each constituency, although it is not a requirement. If two, candidates for a party could run together as primary and secondary in an effectively closed list, similarly as in the Dual member proportional system, or they could run separately. Parties might choose the later option in an open seat or in a hopeless seat, to effectively combine a primary with the general election.

It is recommended that voters employ a preferential 1,2,3, etc vote, for reasons discussed below, although an "X" would also be deemed a valid vote.

The ballot size would not be materially increased over that of the current FPTP ballot.

National vote count

Counting would proceed in a constituency similarly to FPTP, except where candidates from the same party were running separately, in which case they would first have their combined vote total aggregated and assigned to their party. The party vote totals and those for any individual independent candidates in the constituency would then be forwarded to the national counting centre, one for each of the four UK constituent nations.

Upon receipt, these totals would be aggregated party-wise and the squares of the totals computed, ultimately producing,in each nation, party percentages relative to the sum of these squares. The normal vote percentages would naturally also be calculated and published, just as now.

National seat computation

In each nation, the squared percentages calculated above would be applied to the national seat total to estimate the number of seats won by each party. Largest remainder would be used to assign fractional seats. Note that the ultimate result may vary slightly from these figures, for reasons outlined later.

For example, the first "target" computation for a simple one nation house of 650 could be:

• Party A votes 40%, seats 56.1%, n=364.9, rounded n=365
• Party B votes 30%, seats 31.6%, n=205.3, rounded n=205
• Party C votes 15%, seats 7.9%, n=51.3, rounded n=51
• Party D votes 10%, seats 3.5%, n=22.8, rounded n=23
• Party E votes 5%, seats 0.9%, n=5.7, rounded n=6

An alternative example election result:

• Party A votes 35%, seats 46.4%, n=301.8, rounded n=302
• Party B votes 30%, seats 34.1%, n=221.8, rounded n=222
• Party C votes 20%, seats 15.2%, n=98.6, rounded n=98
• Party D votes 8%, seats 2.4%, n=15.8, rounded n=16
• Party E votes 7%, seats 1.9%, n=12.1, rounded n=12

First members elected

Again, similarly to FPTP, the candidate who tops the poll will be declared elected by the local returning officer. In the case of two running on a closed list the primary candidate will be elected. Additionally, any other candidate (or list) that exceeds the Droop quota will also be declared elected. In a few cases, mostly inner-city Labour seats, a party may obtain two Droop quotas - more than 66.67% - in which case both candidates of that party are elected, and the seat closed. A little over half the MPs should be elected in this manner, and election night coverage by TV networks would initially not look too different to what it does under FPTP.

In the case where two party candidates are running separately, and their combined party vote either wins a plurality over all other party votes, or it exceeds the quota, a further STV-style count must be employed later, once the full complexion of the constituency is discerned, to distinguish the winning candidate(s). Such instances should be comparatively rare since, in viable seats,_, most parties would usually adopt the closed "tandem" list variant of presenting candidates.

e.g.

• Party A (Smith [primary], Jones [secondary])

as opposed to what could be termed the "unicycles" approach

• Party A (Jones)
• Party A (Smith)

Subsequent members elected

The novel part of the process really begins here. At the national count centre, the ordinary party vote percentages in each constituency for the first and second ranked parties are then normalised relative to the Droop quota, disregarding any integer part. For example, if Party A obtained 45% and Party B obtained 25%, these would translate to approximately 0.35 and 0.75 "remainder" quotas respectively. Normalised remainder quotas, instead of raw remainder votes, are employed to control for constituency size and/or turnout effects.

The national count centre and TV networks would rank these remainders separately for each party from highest to lowest, including the constituency name, as results become available. As election night develops, these rankings become indicative of those parties which will win the available second seats, and where they will likely win them. As fresh results arrive, they will be "slotted" into the correct order, so the table rankings will continuously change, attracting interest from viewers and commentators.

e.g.

Party D - Seats available: 8

Constituency	Remainder Quota
Blankshire West	0.91
Oldtown North	0.83
Bracketshire South	0.71
Newtown East	0.62
...	...
...	...

In simple terms, the number of seats already won by each party on the first count is deducted from their national seat allocation and the n best remainder quotas for each party are assigned to the relevant constituencies as the second seats. Some parties may end up winning both seats as a result, while strong second places will also be rewarded.

Adjustments

It may be that a local independent or micro-party, with no prospect of national seat allocation, makes a breakthrough to quota or plurality in a particular constituency, and hence wins a seat. This is an admirable feature, not a bug, of the system, although its incidence may only be marginally higher than under FPTP.

In such case, the parties' national seat allocation would require to be re-computed, after deducting a seat from the national total initially available. Such adjustments would be automatically calculated by national counting centre and TV network computers.

National thresholds?

The system, by virtue of the mathematics of squaring, will generate nominal "natural thresholds" for each of the four nations. The actual figures will vary slightly, depending on the precise distribution of votes for the parties, but they are approximately:

• England 2.5%
• Scotland 7%
• Wales 8%
• Northern Ireland 10.5%

Especially for the smaller countries, these may seem high, until it is recognised the thresholds are not absolutely "hard", nor indeed guaranteed. The additional features of the system afford an alternative route to winning a seat or seats, by virtue of topping a local poll or obtaining a quota. In this respect, the system makes it marginally easier for an independent compared to FPTP. 33.34% compared to perhaps 35-40% under FPTP.

Conversely, a national party in England on 5% could still win no seats if its vote was so uniformly distributed that it obtained no constituency second places.

Why ranked ballots?

While not absolutely essential, they would have utility as follows:

• in a handful of cases where a winning party's candidates ran separately in a constituency, it may be more appropriate to employ a kind of STV to identify the winning candidate instead of the alternative, a kind of SNTV.
• the ranked ballots could be subsequently recounted to compute a nationwide two-party preferred vote, as occurs in Australia. In a UK context that may be of value in the event of a hung parliament.

Possible additional features

Addressing lack of candidates

For all serious parties, maximising their national vote share is imperative under this system. But on occasion, for a variety of reasons, a party may not be able to field a full slate in every constituency, thereby seriously handicapping itself. In such cases, a party-only box could be permitted on the ballot in a candidate-less constituency. While not benefiting the party locally, it would still garner "votes" that would contribute to its national seat-total, helping to elect candidates elsewhere. Of course, the usual rules on lost deposits would apply to such "empty" boxes, to deter national no-hopers from running an "empty" box in every constituency.

See also the case of the Speaker below.

The Speaker

The case of the Speaker presents a possible difficulty. Representing a two-member seat, if the Speaker, under his former party colours, was one of a pair from the same party, that party could hardly stand down in his favour (as happens under FPTP), losing both an MP and crucial national votes, although standing would risk the Speaker's defeat. A similar self-interested view would undoubtedly be taken by the other parties. Under single-member FPTP in the UK, Opposition parties frequently stand against the Speaker, invariably to no effect. There are several possible solutions.

• adopt the Irish solution, where the Ceann Comhairle is automatically deemed re-elected as a member of the House, reducing the number of electorally-contested seats in his/her multi-member constituency by one. Under PR squared, this would result in a single-member contest between the parties in the Speaker's constituency.

• simply deem the Speaker an ex officio or co-opted Member of the House, without any need to continue to represent a constituency, thereby restoring the former constituency to normal electoral competition. The current Westminster convention seems a bit farcical, considering the last Speaker to be defeated in his constituency was Richard Onslow in 1710, and it's difficult to see how a Speaker can vigorously pursue or defend the interests of their constituents while remaining, as s/he must, completely neutral towards the government of the day.

• adopt an "empty" box mechanism on the ballot paper (see previous section) to permit one or more parties to still win crucial national votes, without risking the defeat of the Speaker.

Three or four member constituencies?

While the basic proposal envisages reorganising into uniformly two-member constituencies, that may be impractical in some respects. Several natural units in the UK, such as cities, councils or counties currently have an odd number of single-member constituencies. To insist on units of two would result in either breaking these natural units or increasing malapportionment.

There is no reason, in principle, why PR^2 could not accommodate a few 3-member seats. The trade-off would be that the quota in such seats would be somewhat lower at 25%, and some third-placed candidates could secure election in a three-seater. Some may find this inequitable; others may shrug it off as just a facet of a flexible system, of scant interest.

A four-member seat would have a quota of 20%, which might be thought too low.

Simulations

Regional

PR squared should also increase the number of voters who have an MP of their first choice party, compared to FPTP. This is due to a combination of the slight increase in the district magnitude, and the quota algorithm assigning seats more efficiently than FPTP in terms of the geography of support.

We see this quite starkly in an example from Wales.

Firstly, the seats under each system.

Wales 2010

	Labour	Conservative	LidDem	Plaid
Votes	36.2%	26.1%	20.1%	11.3%
FPTP seats	26	8	3	3
PR^2 seats	21	11	6	2

Next, how many of a party's voters have an MP from their choice of party.

Wales 2010

Total Voters Represented	Labour	Conservative	LidDem	Plaid
FPTP
42.6%	75.7%	35.2%	17.6%	21.6%
PR^2
72.3%	98.8%	83.0%	54.4%	34.9%

Note that despite Labour obtaining five fewer seats under the PR^2 simulation (21 compared to 26 out of 40), almost all of its voters in Wales (ex Powys) would have had an Labour MP.

In this respect, PR squared seems almost comparable with STV, despite a far smaller district magnitude.

In terms of the overall disproportionality of the example result in Wales, the Loosemore-Hanby Index is reduced from 28.8% to 17.7%.

Comparison with FPTP for Westminster

Under PR squared, it can be shown that a 1% swing between the major parties will result, on average, in about 2% of the seats changing hands, or around 13 seats.

This is very interesting as it is almost identical to the average shift currently seen under FPTP.

By comparison, pure PR systems would only shift about 1% of the seats, or 6 seats.

Perceptions

There is polling evidence that a significant proportion of voters imagine that single-member FPTP actually operates in a similar fashion to PR squared, which of course is not the case. Under FPTP a vast number - sometimes even a majority - of all votes elect no-one and have no impact on the result, whereas with PR squared almost all votes will directly affect the national outcome. But many voters believe that their vote under FPTP, even if objectively ineffective, in some mysterious way somehow still helps elect "the Prime Minister", their preferred "party", or increases its seat total.

It would be fairer to voters to adopt a system that actually gives them what they think they're already getting!