threshold pr

threshold proportional representation

a.k.a

proportional representation by majority threshold and transferable vote

is it
on recent UK General Election results
of reader's opinions
stuff that goes nowhere else

what

threshold pr

why

The current scheme is that each constituency is considered in isolation and is won by the candidate with the most votes, end of story. It turns out this doesn't represent voters' views proportionally, also it seems unfair to win a seat by a handful of votes, which can happen. However, the usual problems with pr schemes are that they give very small, unworkablee, government majorities (the difference in votes between the two major parties is often small) and they need lists of extra candidates who get artificially elected as adjustments to make the seat numbers up.

what

The threshold pr scheme:
  1. has the same candidature and voting system as currently, it's the counting that's different.
  2. a majority (percentage difference between 1st and 2nd places) threshold is decided which must be met to win a seat, on the basis that it shouldn't be possible to win a seat by 1 vote or anything like it; the examples below suggest 20% would be about right.
  3. those that already pass the majority threshold are won outright by their 1st place candidates;
  4. those that don't pass the majority threshold go into the transfer phase:
    1. starting with the seat with the greatest majority not yet won
    2. take the 1st place candidate; work out how many extra votes would be needed to meet the majority threshold
    3. transfer votes from candidates for the same party starting with the seat with the least majority, on the basis that that seat is the least decided about who they want and so will be the least annoyed about having the result affected by this scheme; if the transfer would leave that seat with no candidate with any votes then go on to the next least. The effect of this is to move votes for the major parties away from marginal seats leaving the minority parties to contest them between themselves.
  5. if any seats are left with not enough transferable votes to meet the majority threshold then they are winnable by a simple majorty.
  6. extra rules for specific cases:
    1. 1st place candidates without a party, i.e. independents, can win by a simple majority.
    2. candidates who lose their deposit (fewer than 5% of the votes in the constituency) can't have votes transferred to them nor win by a simple majority in the last phase, but their votes can be transferred to other candidates in the same party.
    3. a voter should be able to say that their vote isn't transferable.

pros

  1. depending on the choice of majority threshold value the proportion of votes to seats won is closer than with simple majority counting.
  2. there is no sense of arbitrariness from the possibility of someone winning by a handful of votes.
  3. all candidates represent a particular seat, unlike most pr schemes which involve lists of extras decided centrally. We don't like it when a candidate doesn't come from their constituency, let alone when they've been parachuted in from Westminster, still less having lists of party hacks to make up the numbers.
  4. the government majority (number of seats more than all non-government seats) is reduced but still, mostly, effective. Other pr schemes can produce wafer-thin majorities leaving a third, possibly extreme, party holding the balance of power.
  5. national but minority parties have a good chance of gaining representation, improving the colourfulness of Parliament and encouraging disaffected voters to turn out.
  6. there is the possibility, in the event of a hung Parliament, of changing the majority threshold value after the first count so that the government majority is increased to some workable number, thus avoiding the effort and cost of a second election. The Act could say "the majority threshold shall be N% except in the case of a Government majority of fewer than M when the threshold shall be adjusted accordingly" or similar.

cons

  1. the proportion of votes to seats is not perfect. The scheme is a compromise between improving the pr and avoiding the usual problems with pr schemes.
  2. some marginal constituencies will likely end up wth MPs regarded as fringe. It will be up to the minority parties to show they are not fringe nutters.
  3. not everyone's vote will be counted in the constituency they voted in.
  4. it's more complex to think about than simple majority counting, particularly as it is essentially a compromise between competing problems.
  5. if the turn-out improves significantly then it's likely the overall pattern of voting will be changed, to what we don't know.
  6. the election night count can't be completed until all the seats are in. However, good estimates can be made and it might make it less unexciting.

effects

threshold pr
Here are re-runs of the last few UK General Elections with what would have happened under threshold pr with various majority thresholds. In general the higher the threshold the lower the government majority and the more seats go to minority parties, in fact the transition is really smooth. The regional parties tend not to be much affected since their vote is very concentrated geographically.

2005

party votes votes % seats seats % tpr 10%
seats
tpr 10%
seats %
tpr 15%
seats
tpr 15%
seats %
tpr 20%
seats
tpr 20%
seats %
tpr 25%
seats
tpr 25%
seats %
tpr 30%
seats
tpr 30%
seats %
Labour 9,552,436 35.2% 355 55.0% 349 54.0% 343 53.1% 338 52.3% 327 50.6% 319 49.4%
majority 64 52 40 30 8 -8
Conservative 8,784,915 32.4% 198 30.7% 204 31.6% 207 32.0% 200 31.0% 194 30.0% 187 28.9%
Liberal Democrats 5,985,454 22.0% 62 9.6% 62 9.6% 63 9.8% 72 11.1% 90 10.4% 101 15.6%
UKIP 605,973 2.2% 0 0.0% 0 0.0% 0 0.0% 0 0.0% 0 0.0% 1 0.2%
Scottish Nationalists 412,267 1.5% 6 0.9% 5 0.8% 6 0.9% 7 1.1% 7 1.1% 7 1.1%
Green 283,414 1.0% 0 0.0% 0 0.0% 0 0.0% 2 0.3% 2 0.3% 2 0.3%
Democratic Unionists 241,856 0.9% 9 1.4% 9 1.4% 9 1.4% 9 1.4% 9 1.4% 9 1.4%
Plaid Cymru 174,838 0.6% 3 0.5% 4 0.6% 5 0.8% 5 0.8% 4 0.6% 7 1.1%
Sinn Fein 174,530 0.6% 5 0.8% 5 0.8% 5 0.8% 5 0.8% 5 0.8% 4 0.6%
SDLP 125,626 0.5% 3 0.5% 3 0.5% 3 0.5% 3 0.5% 2 0.3% 2 0.3%
Ulster Unionists 127,414 0.5% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 2 0.3% 3 0.5%
Independent 122,416 0.5% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
Respect 68,094 0.3% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
KHHC 18,739 0.1% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
Speaker 15,153 0.1% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%

2001

party votes votes % seats seats % tpr 10%
seats
tpr 10%
seats %
tpr 15%
seats
tpr 15%
seats %
tpr 20%
seats
tpr 20%
seats %
tpr 25%
seats
tpr 25%
seats %
tpr 30%
seats
tpr 30%
seats %
Labour 10,724,953 40.7% 412 62.5% 410 62.2% 406 61.6% 400 60.7% 392 59.5% 383 58.1%
majority 165 161 153 141 125 107
Conservative 8,357,615 31.7% 166 25.2% 166 25.2% 166 25.2% 164 24.9% 161 24.4% 158 24.0%
Liberal Democrats 4,814,321 18.3% 52 7.9% 53 8.0% 57 8.6% 65 9.9% 75 11.4% 88 13.4%
Scottish Nationalists 464,314 1.8% 5 0.8% 6 0.9% 6 0.9% 6 0.9% 6 0.9% 6 0.9%
Ulster Unionists 216,839 0.8% 6 0.9% 6 0.9% 6 0.9% 6 0.9% 5 0.8% 5 0.8%
Plaid Cymru 195,893 0.7% 4 0.6% 4 0.6% 4 0.6% 4 0.6% 5 0.8% 4 0.6%
Democratic Unionists 181,999 0.7% 5 0.8% 5 0.8% 5 0.8% 5 0.8% 5 0.8% 5 0.8%
Sinn Fein 175,933 0.7% 4 0.6% 4 0.6% 4 0.6% 4 0.6% 4 0.6% 3 0.5%
SDLP 169,865 0.6% 3 0.5% 3 0.5% 3 0.5% 3 0.5% 3 0.5% 3 0.5%
Alliance Party of NI 28,999 0.1% 0 0.0% 0 0.0% 0 0.0% 0 0.0% 1 0.2% 1 0.2%
KHHC 28,487 0.1% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
Speaker 16,053 0.1% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%

1997

party votes votes % seats seats % tpr 10%
seats
tpr 10%
seats %
tpr 15%
seats
tpr 15%
seats %
tpr 20%
seats
tpr 20%
seats %
tpr 25%
seats
tpr 25%
seats %
tpr 30%
seats
tpr 30%
seats %
Labour 12,653,431 41.7% 385 59.3% 383 59.0% 380 58.6% 376 57.9% 370 57.0% 364 56.1%
majority 121 117 111 103 91 79
Conservative 9,425,095 30.5% 161 24.8% 160 24.7% 156 24.0% 150 23.1% 145 22.3% 141 21.7%
Liberal Democrats 5,165,578 16.7% 44 6.8% 47 7.2% 54 8.3% 63 9.7% 70 10.8% 79 12.2%
Labour (Co-op) 634,550 2.1% 25 3.9% 25 3.9% 24 3.7% 24 3.7% 24 3.7% 23 3.5%
Scottish Nationalists 608,958 2.0% 6 0.9% 6 0.9% 6 0.9% 6 0.9% 6 0.9% 6 0.9%
Ulster Unionists 235,145 0.8% 9 1.4% 9 1.4% 9 1.4% 8 1.2% 8 1.2% 8 1.2%
SDLP 188,609 0.6% 3 0.5% 3 0.5% 3 0.5% 4 0.6% 4 0.6% 3 0.5%
Plaid Cymru 160,292 0.5% 4 0.6% 4 0.6% 4 0.6% 4 0.6% 4 0.6% 4 0.6%
Sinn Fein 125,568 0.4% 2 0.3% 2 0.3% 2 0.3% 2 0.3% 2 0.3% 3 0.5%
U Democratic Unionists 84,026 0.3% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
Independent 61,996 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
Labour (Independent) 46,520 0.2% 2 0.3% 2 0.3% 2 0.3% 2 0.3% 2 0.3% 2 0.3%
Conservative (Labour) 24,282 0.1% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
Speaker 23,969 0.1% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
Conservative (Independent) 23,570 0.1% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
Conservative (Independent Conservative) 22,888 0.1% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
Independent Conservative 20,279 0.1% 0 0.0% 0 0.0% 0 0.0% 0 0.0% 0 0.0% 1 0.2%
Labour (Independent Labour) 18,525 0.1% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
UKUP 12,817 0.0% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%

1992

party votes votes % seats seats % tpr 10%
seats
tpr 10%
seats %
tpr 15%
seats
tpr 15%
seats %
tpr 20%
seats
tpr 20%
seats %
tpr 25%
seats
tpr 25%
seats %
tpr 30%
seats
tpr 30%
seats %
Conservative 14,093,007 41.9% 335 51.5% 328 50.5% 323 49.7% 318 48.9% 309 47.5% 302 46.5%
majority 20 6 -4 -14 -32 -46
Labour 11,122,445 33.1% 258 39.7% 257 39.5% 256 39.4% 253 38.9% 248 38.2% 244 37.5%
Liberal Democrats 6,010,310 17.9% 20 3.1% 26 4.0% 33 5.1% 40 6.2% 53 8.2% 62 9.5%
Scottish Nationalists 629,564 1.9% 3 0.5% 4 0.6% 3 0.5% 4 0.6% 5 0.8% 6 0.9%
Labour (Co-op) 438,039 1.3% 13 2.0% 14 2.2% 14 2.2% 15 2.3% 15 2.3% 15 2.3%
Ulster Unionists 271,049 0.8% 9 1.4% 9 1.4% 9 1.4% 9 1.4% 9 1.4% 9 1.4%
SDLP 187,012 0.6% 4 0.6% 4 0.6% 3 0.5% 3 0.5% 3 0.5% 3 0.5%
Plaid Cymru 150,032 0.4% 4 0.6% 4 0.6% 4 0.6% 3 0.5% 3 0.5% 4 0.6%
Democratic Unionists 103,039 0.3% 3 0.5% 3 0.5% 3 0.5% 3 0.5% 3 0.5% 3 0.5%
Sinn Fein 78,291 0.2% 0 0.0% 0 0.0% 1 0.2% 1 0.2% 1 0.2% 1 0.2%
Ulster Popular Unionists 19,305 0.1% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2% 1 0.2%

poll

threshold pr


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2006.09.15
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copyright

Patrick Herring, except where otherwise acknowledged eg. in "alt" clauses.