Proportional representation with single-member constituencies

Following the reforms of the nineteenth century, the British electoral system has, throughout living memory, been based overwhelmingly on single-member constituencies, and the consequent identification between each MP and his constituents is widely valued. It is also often argued that proportional representation must dilute or destroy this connexion. In the present note I describe a method of achieving proportional representation while leaving the relationship between electors and members of parliament virtually unchanged. It may be regarded as an adaptation of the "modified list method" described in paper KJ 12/4 of the Keith Joseph Papers. To flesh out the algorithm I describe the effect of applying it to the 2005 election results.

Description of the scheme

  • A general election is conducted as at present, with candidates' parties printed on the ballot papers (as at present).
  • When the votes have all been counted, the entitlement of each party to seats in the House of Commons is calculated, and rounded down to the next integer to give the party's "quota".
  • Each candidate is assessed for "eligibility"; a candidate is eligible for election if either he is the front-runner in the constituency or he has received at least 20% of the votes cast in that constituency. Any candidate who is the only eligible candidate in his constituency is forthwith elected.
  • Candidates are now elected one by one according to an algorithm which proceeds on the following lines. At each stage, those parties which have not yet reached their quotas are reviewed, and one of them is selected as the next party to get an MP. Then the eligible candidates from that party, standing in constituencies which do not yet have MPs, are surveyed, and one of them is chosen. He becomes an MP and the process is repeated. The choice of candidate at this stage is designed to pick a front-runner if possible, and otherwise someone as close behind the front-runner as possible.
  • During this process, it may well happen that a party has no eligible candidate standing in any unrepresented constituency. (In the 2005 election, indeed, the UKIP had a quota of 14 MPs, but did not have a single candidate who received 20% of the vote in his constituency; while the Green party had a quota of 6, but only one eligible candidate.) In this case, such a party is passed over from then on.
  • The main part of the algorithm ends when each party has been removed from the list, either because it has reached its quota or because it has no eligible candidate in any remaining unrepresented constituencies. There will normally be a number of constituencies still unrepresented at this stage; in these constituencies the front-runners are taken as the MPs.
  • Fuller details.

    Notes Many obvious questions are left open by the outline above; I try to deal with some of them.

  • Bye-elections continue to be held under the present rules, that front-runner wins.
  • An independent candidate is regarded as the sole candidate of his "party". His quota is almost certain to be zero; but he has a chance of election in the final phase of the process. In fact the two independent candidates elected in the 2005 election would both have been elected under the scheme here.
  • As it will no longer be possible for returning officers to be confident that counting errors cannot be sufficient to upset results, it will be necessary to re-formulate the rules governing recounts and disputed ballots.
  • Similarly, the rules concerning delayed ballots (as in Staffordshire South in 2005) would have to make it clear when the general election results are to wait for all constituencies to vote, and when delayed results are to be treated as bye-elections.
  • It might be appropriate to re-examine the conventions concerning the Speaker's constituency.

    The 2001 and 2005 elections A feature of the scheme here is that it invites speculation on its detailed consequences of applied to past elections. While it is unlikely that either the parties or the voters would have behaved in quite the same way under a different system (for instance, there are no longer the same incentives for "tactical voting"), it is nevertheless possible to test a number of hypotheses against tolerably realistic data. I have therefore prepared an analysis of the results of applying this scheme to the 2001 and 2005 UK general election results.

    Party VotesProportionate MPs elected:
    entitlement to seats current rulesscheme here
    2001
    Lab 10724953268.0412331
    Con8357615208.9166208
    LibDem4814321120.35285
    SNP46431411.6511
    UKIP3905639.800
    UUP2168395.466
    Plaid Cymru1958934.944
    DUP1819994.555
    Sinn Fein1759334.444
    SDLP1698654.233
    Green1664774.200
    SSP725161.800
    SocAll575531.400
    SocLab572881.400
    BNP471291.200
    R.T.Taylor284870.711
    Speaker160530.411
    2005
    Lab9546969227.0355272
    Con8772598208.6197208
    LibDem5981874142.362130
    UKIP60329814.300
    SNP4122679.868
    Green2577586.101
    DUP2418565.898
    BNP1927464.600
    Plaid Cymru1748384.234
    Sinn Fein1745304.255
    UUP1274143.013
    SDLP1256263.032
    Respect680941.611
    SSP435141.000
    P.Law205050.511
    R.T.Taylor187390.411
    Speaker151530.411

    You can also see what would have happened in individual constituencies in 2005.

    Satisfied voters One statistic which may be felt relevant concerns the number of "satisfied" voters, that is, voters who find themselves represented by someone they voted for. This number is necessarily largest if MPs are elected according to the present system. However the difference is not necessarily great. In the two elections examined here the percentages of satisfied voters were/would have been

    Yearcurrent rulesscheme here
    200150.849.5
    200547.646.1

    Independent candidates Many PR schemes make it impossible for truly independent candidates to be elected. Their apologists brush over this point with the observation that there has not been a significant number of independents elected to any modern British parliament. My own view is that the political value of independents is out of all proportion to their numbers, and I am glad to observe that in both the elections studied here the independents who were successful under the current rules would also have been successful under the scheme proposed.

    Marginal constituencies It looks to me as though the new scheme would render more constituencies "marginal", in the local sense that a fairly small change in the local vote would change the MP in that particular constituency. In support of this I remark that of the 574 constituencies which had the same name in 2001 and 2005, 51 changed party under the current rules and 90 would have changed if both elections had taken place under the proposed scheme.

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    24 May 2005