Tuesday, April 12, 2011

AV, a case in Statistics.

A paper published in Significance, the statistics journal, collated election returns of the various government election systems. The aim is to show the various real-world properties of these election systems. It came to some unsurprising, and some surprising results.


We can identify how related the returns are to the proporition of the national votes. This identify if elections produce proportional results, something that smaller parties find is a problem with FPTP. The average deviation from the vote share shows an aproximate guage of this, with smaller numbers being better.

* UK, First Past the Post - 29.4
* Australia, Alternative Vote - 27.3
* Republic of Ireland, Single Transferable Vote - 12
* Netherlands, Open List Proportional Representation - 5.22

Naturarly, the Open List PR provides the closest representation. But despite claims that AV is no more proportional than FPTP it does show a slightly closer result. Some individual results under FPTP have been more proportional than AV. However, this only occurs for a third of the sample set. This suggests that AV is naturally more proportional than FPTP with some error overlap.

Probability of Coalition

Using probability statistics, it's possible to estimate the probability of certain events based on previous ones. Identifying the probability that random variations in future results, based on the known standard deviations from the data.

Here we see the probability, considering a rerun of the most recent election, of there being a coalition. For purposes of comparison, the Netherlands result was modelled as a race between the two largest parties and only one other minor party.

* AV Australia 2007 - 93% (Actual result - Single Party majority)
* FPTP UK 2010 - 87% (Actual result - Coalition)
* Ireland 2007 STV - 77% (Actual result - Coalition)
* Netherlands PRO - 48% (Actual result - Coalition)

The result here is a little muddier. If anything, it shows that the political situation is more likely to generate coalitions than the election system. The statistics suggest that AV has a higher probability of coalition, but the actual result in Australia was one that firmly established a single majority. They also show that FPTP can also produce a very high probability of coalition under the right circumstances.

Seat Changes

Another metric to compare elections is the amounts of seats than change hands in an election. This is somewhat a contentious statistic however, since the differing politics of the countries may produce more difference than the election system used. Numbers indicate more seats changed in the average election.

* FPTP - 17.3
* STV - 17.4
* AV - 19
* PRO - 21

As we can see, the surprising result is that AV does seem to make it slightly easier to unseat incumbents. Being only behind Party List based elections, while STV and FPTP are statistically tied for last.

Even assuming that the differences are more based on differing politics amongst the country; at the very least this indicates there is no incumbency advantage generated by AV, and it will not be harder to vote out unpopular governments.


The conclusions taken from this paper for comparison between FPTP and AV seem to be that AV does produce slightly more proportional results, that there is no clear link to coalitions being more likely, and that it may be easier to vote out unpopular governments under AV.


  1. The polls seem to have swung quite hard against AV now - looks like Cameron may have escaped one hell of a time with his party.

    My guess is that many Labour voters are more willing to blame the junior partner for the sins of the coalition ("they should know better, wheras Tories are Tories") and this is impacting upon the 'Yes' vote.

    On a related note, it will be interesting to see how your Westminster voting intention model looks like - are you planning on posting an update soon? The polls are all over the place at the moment, with Ipsos-Mori today putting the Tories neck and neck with Labour, but others pointing the other way.

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