User:RodCrosby/QPR2: Difference between revisions
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'''Quota proportional representation''' '''squared''' ('''QPR2''')
▲'''Quota proportional representation''' '''squared''' ('''QPR2'''), also known simply as '''PR squared''' or '''PR^2''', is an [[electoral system]] designed to produce [[Proportional representation|semi-proportional election results]] across a region by electing two [[Legislator|representatives]] in each of the region’s [[Electoral district|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]].
The system is very similar to "[[PR squared]]", devised by Dr. [[Julian Wiseman]].
==Origin==
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===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 continuously in England from 1265 to 1885 and which did not finally disappear in some places in the UK until 1950.
===Ballot structure===
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For example, the first "target" computation for a simple one nation house of 650 could be:
{| class="wikitable"
* Party A votes 40%, seats 56.1%, n=364.9, rounded n=365▼
|+ Example election
* 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 !! %Votes !! %Seats !! Unrounded Seats !! Rounded Seats
* Party D votes 10%, seats 3.5%, n=22.8, rounded n=23▼
|-
|-
|-
|-
|-
| E || 5% || 0.9% || 5.7 || 6
|}
An alternative example election result:
{| class="wikitable"
* Party A votes 35%, seats 46.4%, n=301.8, rounded n=302▼
|+ Example election
* 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 !! %Votes !! %Seats !! Unrounded Seats !! Rounded Seats
|-
|-
|-
|-
| D || 8% || 2.4% || 15.8 || 16
|-
| E || 7% || 1.9% || 12.1 || 12
|}
===First members elected===
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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, with Party A of course already having won one seat. Normalised remainder quotas, instead of raw remainder votes, are employed to control for constituency electorate 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 their 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.
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===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
In such case, the major 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.
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* 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. Approximately 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 first or second places. But that, of course, is little different to the current system in the UK.
==Why ranked ballots?==
While not absolutely essential, they would have utility as follows:
* in a
* 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.
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===Safe seats are reduced===
While parties may still have their core constituencies, every candidate there and elsewhere might have to compete equally against others from the same party for the privilege of being elected, especially if the parties were to adopt the open list format of running candidates as opposed to the "tandem" closed list format.
Party-wise, the tendency for FPTP to produce clean sweeps in sub-regions would be reduced, meaning hitherto reasonably safe seats would become vulnerable, especially for secondary candidates on "tandem" lists.
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===Overall majority possible===
Under the system, simulations of the elections of 1979, 1983, 1987, 1992, 1997, 2001 and 2019 would have still produced overall majorities,
===No practical possibility of "wrong-winner" election===
No other constituency-based system offers this, including FPTP. Under simulations, PR squared gets the very close election of February 1974 "right", whereas under FPTP, the national vote plurality winners (the Conservatives) were reduced to second place in seats. Similar FPTP "inversions" occurred in 1951 and 1929.
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==Disadvantages==
===Single-member seats abolished===
It is recognised that, in a multi-party democracy, a more proportional and representative electoral system cannot be created from exclusively single-member constituencies, except with huge loss of credibility. (as in Wiseman's original proposal, re-assigning single-member constituency losers as winners)
A minimal increase in district magnitude to two (essentially reverting to the previous long-standing UK configuration) would, under PR-Squared, make huge strides towards representativeness and proportionality, with few minor anomalies undermining its credibility.
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According to simulations (see below) the elections of October 1974, 2005 and 2015 would have produced hung parliaments, in contrast to overall majorities under FPTP. Given the closeness of votes in those three elections, these outcomes do not seem unreasonable.
Of the thirteen elections since February 1974, FPTP produced 10 overall majorities and 3 hung parliaments. Simulations indicate that the outcomes under PR squared would have been 7 and 6 respectively. It's worth noting that, due to long-term changes in the operation of FPTP in the UK, since 2010 the ratio of majority to hung parliaments has been even, and the current (as of 2023) opposition Labour party faces an unprecedented challenge to secure a majority at the next UK election. It seem the UK is having more hung parliaments anyway.
===Not PR===
PR-Squared does not explicitly seek close proportionality, although simulations indicate that it goes a lot further towards that outcome than FPTP.
Moreover, PR-Squared can deliver more proportional outcomes than some supposedly PR systems! For example, the Welsh Additional Member System has produced ''Gallagher Indexes'' of disproportionality in excess of 10% in four out of six elections since 1999. Even higher values can be found in elections to the European Parliament conducted in Ireland under STV. <ref>{{cite web |first=Michael |last=Gallagher |title=Election Indices |url=https://www.tcd.ie/Political_Science/people/michael_gallagher/ElSystems/Docts/ElectionIndices.pdf |date=January 18, 2023}}</ref>
Simulations suggest that PR-Squared would have delivered ''Gallagher Indexes'' of '''''less''''' than 10% in nine out of thirteen elections for the UK parliament since 1974. (and compared to only one under FPTP)
===Declarations===
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If Party D is the smallest national party awarded seats, and the partywise smallest first allocation is adopted, and Party A's 0.65 remainder quota is also somewhere amongst ''its'' best remainders entitled to seats, then Party D will be awarded the seat despite having a slightly ''smaller'' remainder quota than Party A in Newtown East. The next best result of Party A's list of remainders would move up that list, replacing the position of the unsuccessful candidate in Newtown East.
Simulations indicate that whatever method is employed, including Buhagiar's preferred Priority Queue, such anomalies cannot be avoided entirely, and are just subjectively more or less "unfair" to the particular candidates affected. Simulations also suggest that only a handful of allocations would meet such
An alternative resolution of these approximately 20 seat conflicts would be to follow that method recommended for the Dual Member Proportional System. In this case, simply award the seat to the party with the largest remainder quota, and the party denied the seat would utilise its next best reminder quota for its next viable allocation. Under this method the partywise order of allocation is not relevant.
Such rare blemishes could be argued to be far outweighed by the list of overall major improvements offered by PR^2 compared to FPTP.▼
Whichever method is adopted, simulations show that around 97% of the declarations will be straightforward, employing either FPTP or full quota, or best remainder quotas.
▲Such rare blemishes could be argued to be far outweighed by the list of overall major improvements offered by PR^2 compared to FPTP.
===Justifications===
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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 former 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.
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A four-member seat would have a quota of 20%, which might be thought too low.
Alternatively, the "quota" could be fixed at 33.34% irrespective of the number of members to be elected in a constituency.
===Quasi single-member?===
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|+ PR^2 Simulation
|-
!
|-
| 2019 || 364 || 200 || 26 || 40 || 1 || 1|| Con Majority 78
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|+ Wales 2010
|-
! !! Labour !! Conservative !! LibDem!! Plaid Cymru
|-
| '''Votes''' || 36.2% || 26.1% || 20.1% || 11.3%
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|+ Wales 2010
|-
! Total Voters Represented !! Labour !! Conservative !! LibDem !! Plaid Cymru
|-
| '''FPTP'''
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|}
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. Other parties also see dramatic improvements in the representation of their voters.
In this respect, PR squared seems almost comparable with STV, despite a far smaller district magnitude.
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==Links==
== Related Systems==
[[Quadratic voting]]
== References ==
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