Monday, March 28, 2011

A re-examination of the UK AV proposal - a possible flaw in my plan

In trying to resolve my Median Rule in mathematical terms I discovered a specialised case whereby it would fail.

Essentially it is possible, despite skimming off the top 50% candidates, for a situation to arise whereby one of the candidates of the discarded/re-assigned votes can replace one of the others in order of priority and thus rise to be a retained candidate.

It requires the combined total of all the lowest votes to be greater than that of the next highest candidate.

Once again I'll use the Wyre Forest results to demonstrate:

PartyVote%
Conservative18,79336.9
Health Concern16,11531.7
Labour7,29814.3
Liberal Democrat6,04011.9
UKIP1,4982.9
BNP1,1202.2

If we use the systematic method we'd re-assign the BNP votes. However if we make an assumption that all such votes would be given to UKIP the total would be less than that given to the Liberal Democrats. As such it's possible to reassign the votes for both the BNP and UKIP in one round. However if we assumed that all such were re-assigned to the Liberal Democrat candidate the total would exceed that of the Labour vote. In such an instance the next round would see the Labour votes re-assigned and not those of the Liberal Democrats.

In this instance it makes no odds as if we then added all the Labour, UKIP and BNP votes to the Liberal Democrat it would still be lower than that of the Health Concern; so their votes would be re-distributed anyway; with the same result as if we'd applied the Median Rule. However this cannot be guaranteed.

I can see why the systematic method will be used as it requires little thought; the process can still be shortened though.