Earlier today Cllr Dr Rodney Berman, leader of the Welsh Local Government Association’s Liberal Democrat Group, issued the following press release. Me thinks the Local Government Boundary Commission may have a little explaining to do…
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A failure to understand how to compare different ratios has led to the Local Government Boundary Commission for Wales wrongly proposing cuts to the number of councillors in at least two Welsh local authorities to date. And in doing so, the Commission appears to have wasted valuable time and public money producing draft proposals that may have to be ruled out as invalid, with more such proposals currently in preparation.
The Commission was given guidance by the Minister for Local Government, Brian Gibbons, that in reviewing the electoral arrangements of all Welsh counties it should aim “to achieve electoral divisions with a councillor to electorate ratio no lower than 1:1750″.
However, a failure to understand when a ratio is lower than another ratio (or when it is higher than another ratio) has led the Commission to come up with proposals which go in the opposite direction to that intended by the Minister in terms of the number of councillors the Commission is proposing should be in place in future to serve electors.
In the Commission’s draft proposals for Newport and Denbighshire it has proposed cutting the number of councillors when it should have proposed increasing the number of councillors in order to comply with the direction in the Minister’s guidance. For example in Newport, Commissioners are proposing moving from a current ratio of councillors to electors of 1:2283 to a ratio of 1:2447 on the wrong assumption that 1:2447 is more than 1:2283. In actual fact a ratio of 1:2447 is less than a ration of 1:2283 because it gives you a lesser number of councillors for a given size of electorate.
Commenting on the blunder, the leader of the Welsh Local Government Association’s Liberal Democrat Group, Councillor Rodney Berman, said: “I am aghast that the Local Government Boundary Commission appears to have got its sums badly wrong. By not understanding a particular mathematical concept outlined in the directions they have been given by the Minister, the Commissioners have proposed cutting numbers of councillors in cases where they should be proposing increasing the number of councillors.
“A huge row is now brewing between officials in the Welsh Assembly Government’s local government division and the Commission. Angry letters have been exchanged with the Commission complaining that its independence is being threatened. But no-one seems to have spotted that the Commission has got its maths wrong, and this is a key reason why it has come up with results which are contrary to what the Minister intended.
“What concerns me most is the amount of time and money that could have been wasted as a result of this blunder. Boundary reviews that have been published, or are still in preparation, may now turn out to be invalid and the Commission may have to go back to the drawing board. This could mean the Commission is unable to complete its task of reviewing electoral division boundaries in all 22 Welsh local authorities in time
for the next round of local elections in Wales in 2012.”
ENDS
Notes:
1. Councillor Rodney Berman has tested his understanding of how ratios should be compared by consulting with experts at Cardiff University. His assumption that the Commission has misunderstood when a ratio should be regarded as more than or less than another ratio has been confirmed as correct by more than one professor at Cardiff University.
2. An example of where the Local Government Boundary Commission has misunderstood when a ratio is more or less than another ratio can be found in paragraph 5.6 of the report outlining proposals for Newport where it is stated that “there are currently two electoral divisions, Stow Hill and Langstone that have councillor to electorate ratios that are below 1:1750″. The current councillor to electorate ratio in Stow Hill is 1:1587 whilst the current councillor to electorate ration in Langstone is 1:1718. Both those ratios are in fact above a ratio of 1:1750, not below it. This mistake is repeated throughout all the reports that the Commission has so far produced.
3. A letter sent by an official in WAG’s local government division is attached along with the reply sent by the Secretary of the Commission.
E-mail sent by Rodney Berman to Cardiff University:
I have what you might view as a slightly strange request. I am hoping that you can point me in the direction of a mathematician who can give me a definitive view on how you determine if a particular ratio is less than or more than another ratio.
The question has arisen in regard to boundary reviews currently being undertaken by the Local Government Boundary Commission for Wales.
There has been a bit of disquiet about the way the Commission has interpreted guidance from the Minister for Local Government in the first three reviews it has published (covering Newport, Neath Port Talbot and Denbighshire). Part of the guidance is that they should aim to achieve a councillor to elector ratio of no less than 1:1750. The question is how you interpret what is a lesser ratio and what is a higher ratio. I think the Commission has got it the wrong way round, but I need the opinion of a mathematician to either confirm that, or else tell me I’ve got it wrong.
As an example, in my view a ratio of councillors to electors of 1:3000 is more than a ratio of 1:4000 (on the basis that for an electorate of a fixed size you would have more councillors with a ratio of 1:3000 than you would with a ratio of 1:4000). From the reports that the Local Government Boundary Commission for Wales has produced to date, it would seem that they believe the opposite. They believe that a ratio of 1:3000 is less than a ratio of 1:4000. The question is have they got it wrong, or have I got it wrong?
An argument is now brewing because in these first three boundary reviews, the Commission has proposed a reduction in the total number of councillors for each of those three counties and a letter expressing concern at this has been sent to the Commission in response by officials in WAG’s local government division. If I am right, then the Commission has perhaps wrongly gone down the road of a reduction in the number of councillors because they have incorrectly interpreted what constitutes a ratio being less than or more than another ratio.
I don’t know if any of this makes sense to you. However, would you be able to assist in identifying someone in your mathematics department who could advise me as to whether or not I am right?
The Commission is currently working its way through boundary reviews of all 22 Welsh local authorities and so it is important that this is got to the bottom of before they continue in their ongoing work. If at all possible, therefore, an early response to this request would be appreciated.
Reply from Professor of Medical Statistics:
Oh dear.
Yes, a ratio of 1:3000 is larger than 1:4000 If you had 12,000 electors then a ratio of 1:3000 would mean 4 councillors while one of 1:4000 would mean 3 councillors. It is a bit confusing as obviously 3000 is less than 4000 – but those are what you divide by. I suspect the confusion is common Hope this clarifies it.
Reply from Professor of Mathematics:
when ordering ratios, technically one converts to a fraction (or decimal) and then orders. Please see the examples below (purposefully laboured to demonstrate the point!) . In summary I agree with Rodney.
e.g. consider two ratios 1:5 and 1:10
1:5 = 1/5 = 0.2
1:10 = 1/10 = 0.1
Since 0.2 > 0.1 it follows that 1:5 > 1:10
Therefore with respect to the problem at hand, to achieve a ratio of no less than 1:1750 (the ‘no less’ is equivalent to requiring a ratio ‘greater than or equal to’ 1:1750) this would require that every councillor would be needed for <= 1750 population. e.g. one councillor to 1,000 population = 1/1000 = 0.001 which is more than 1/1750 = 0.00057 i.e. 1:1000 > 1:1750. So in Rodney’s example, 1:3000 is MORE than a ratio of 1:4000 as Rodney suggests.
I hope this helps.
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