Something from the WFA with regard to a comment made by Jonathan about if the 2005 election had been run under AV.
To start here's the cut-down version of the FPTP results (colours assigned to show up on my default background, for use later)
|Monster Raving Loony||303|
In this instance we see that Health Concern have won with 40% ((18,739/46,987)*100) of the vote however under AV they didn't reach 50% so a second round takes place.
To shorten the process we can take the extremes - if every Monster second placed Health Concern they still wouldn't reach 50% (18,739+303 < 23,493.5).
If every Monster only used one preference the new total still wouldn't leave Health Concern with 50%.
((46,987-303)/2 > 18,739)
If every Monster second placed UKIP they wouldn't beat the Liberals. (1,074+303 < 2,666)
If we do the same for every Monster+UKIP votes (303+1,074=1,377) Health Concern still wouldn't reach 50% either way (18,739+1,377 < 23,493.5) and ((46,987-1,377)/2 > 18,739)
If added to the Liberal vote wouldn't topple the Labour vote (2,666+1,377 < 10,716) So plodding through the rounds in this instance we'll always end up eliminating the bottom three candidates and reassigning their votes.
As such I will now refer to the combined Monster+UKIP+Liberal vote as "The Block" comprising of the total 4,043 votes.
If everyone in The Block voted for Health Concern (18,739+4,043 < 23,493.5) or no-one in The Block made a second preference vote ((46,987-4,043)/2 > 18,739) Health Concern still wouldn't reach 50% of the vote so we're always going to have to go another round.
Our final extreme measure - everyone in The Block second places either the Conservatives or Labour. If they choose Labour the total beats the Conservatives (10,716+4,043 > 13,489) and we're left with a stand-off between Labour and Health Concern with the Conservative votes to reassign.
For Health Concern to lose there needs to be 3,981 more Conservative voters placing Labour above Health Concern. If every Conservative voter used their full preferences that's means for Health Concern to lose by just 1 vote the Conservative votes would be split 4,754 (35%) and 8,735 (65%).
Alternatively if everyone in The Block votes Conservative they still don't beat Health Concern (13,489+4,043 < 18,739) and we're left with a stand-off between Health Concern and the Conservatives with the Labour votes left to distribute.
For Health Concern to lose there needs to be 1,208 more Labour voters placing Conservative above Health Concern. If every Labour voter used their full preferences that's means for Health Concern to lose by 1 vote the Labour votes would be split 4,754 (44%) and 5,962 (56%).
So in both cases the only way Health Concern could lose is if the majority of Labour/Conservative voters voted for each other instead of choosing Health Concern. The likelihood of that is unknown, but I'm willing to bet it's small.
So Health Concern would still win, but at least this time we know that the majority really did prefer them.