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Archive for March 10th, 2009

Multi-seat Madness

Tuesday, March 10th, 2009

Just to demonstrate a problem that can occur with fptp elections in multi-seat districts, the result of the 2008 municipal election in the Tredegar Central & West ward (a four seater) of Blaenau Gwent CBC:

  1. S.Thomas, Lab, 808
  2. H.L.Trollope, Lab, 740
  3. N.Hobbs, Lab, 712
  4. D.I.Morris, Lab, 691
  5. G.Bowen-Knight, Plaid, 587
  6. G.Walters, PV, 544
  7. W.Kenvin,LDem, 539
  8. D.Wilcox, PV, 516

It is obvious that the voters of Tredegar preferred all four Labour candidates to all four non-Labour candidates. And, on one level, that’s all that matters. But election junkies are usually more interested in partisan support than ‘owt else, election junkies like statistics and election junkies like percentages. So, what were the party totals for Tredegar Central & West? If we just add up everything we get:

  1. Labour, 57.4%
  2. PV, 20.6%
  3. Plaid, 11.5%
  4. LDem, 10.5%

The problems here are obvious. Only one party ran a full slate; two of the parties ran just one candidate. And each voter has four votes; as a result more votes were cast in this election than registered voters in the ward (and this with the usual awful turnout of a local election). One common solution to this problem is just to take an average of the votes for each party, thus:

  1. Labour, 30.8%
  2. Plaid, 24.5%
  3. LDem, 22.5%
  4. PV, 22.1%

While this method might make sense if all parties ran full slates, when one party runs four candidates and no other runs more than two, the percentages start to have little in common with the actual election result. Another common method is just to use the top candidate of each party; this method has the same problem with results like this as just doing an average and throws in a different problem (that of personal votes). A further, desperate, alternative would be to average the results of the Labour and non-Labour candidates, thus:

  1. Labour, 57.5%
  2. Non-Labour,  42.5%

The problems here are obvious as well. When given the choice, some voters always split their tickets and quite a few will only vote for a single candidate (especially if their chosen party has just one candidate). And so on.
In other words, there appears to be no easy solution to this problem, and where does that leave map-makers? A possible answer would be to abandon (more or less) winning-party maps and just map party support instead… comparing the vote of each party to the number of voters in each ward and not to the votes of other parties in the same ward. More on that at a decent hour.