Blackwell's bookshop and the art of deception UPDATE

UPDATE

Just had a very apologetic phone call from manager of Blackwell Art and Poster Shop at 27 Broad Street, Oxford, OX1 3BS and had my £2 refunded. They were in the wrong, I was in the right but they are very honourable people and have put things right and if you are ever in Oxford you should visit their splendid shop.

Dear Sir / Madam

I visited your store in Oxford yesterday and bought about £40 of goods. I came away feeling I had been cheated out of £2 – a relatively small sum I concede, but I’m not the sort of person who simply lets such things go.

Let me explain the problem as follows (using prices rounded up do the nearest pound for simplicity):

If I had gone into your shop and bought 3 prints at £4 each under the “3 for 2” offer I would have paid £8, saving £4.

If I had then gone back into your shop five minutes later and bought another 3 prints at £6 each under the “3 for 2” offer I would have paid £12, saving £6.

So far so good. I would, by this time, have saved £10.

What I did yesterday, however, was (ignoring my other purchases) to buy exactly the same items as above under exactly the same offer, but all in one go. I only saved £8 - £2 less than I should have saved.

The reason (explained when I complained) is that the computer grouped my purchases thus: (£4+£4+£6) + (£6+£6+£4) and I saved 2 x £4. I was told that this policy was explicitly stated on the offer signs which explained that the cheapest item goes free.

I find your policy here misleading to the point of dishonesty. Either your computer should employ a more sophisticated (and fairer) algorithm or you should inform you customers in advance that they would be better off making separate purchases if making multiple “3 for 2” buys.

I suppose I could have taken this further within the shop, but I was too taken aback to complain further at the time. (Your staff were perfectly civil but quite convinced they were in the right.)

Upon further reflection, I feel as though I have been cheated out of £2 and I should like to have this money returned.

I look forward to hearing from you.

Yours faithfully

Mike Ward


PS Blackwell Art and Poster Shop at 27 Broad Street, Oxford, OX1 3BS is a simply wonderful shop which I frequent and which I would encourage you all to visit. They should, however, refrain from these (I assume unintentionally) misleading promotions!

AV - not my first preference

The best electoral system, without doubt, is STV in multi-member constituencies. Since AV is all that's on offer in the coming referendum and since (at least in some scenarios) it's an improvement on FPTP I shall, albeit with a heavy heart, probably vote in favour. I worry that a "no" vote will be taken as a "no" to any attempt at electoral reform. (There's a reasonably good guide to the different systems here: http://blogs.lse.ac.uk/politicsandpolicy/the-lses-simple-guide-to-voting-systems/)

Having said all that. there some serious flaws in the proposed AV system and I wish to focus here on one of them.....

Most critiques of AV focus on its main drawback, which is that it is not a proportional system. There is no guarantee that it will not produce barmy national results (such as the party with fewer votes winning the national election) just as the current FPTP system sometimes does (twice in my own short lifetime!).

I've constructed an highly contrived but simple example which shows one way in which AV can go wrong even within a single constituency:

Let us assume we have a very small constituency with 9 voters and 3 candidates: the usual Labour, LibDem, and Tory. Let us further assume that the preferences of these 9 voters are as follows:

*	Lib	Lab	Con
voter1	1	3	2
voter2	1	3	2
voter3	2	1	3
voter4	2	1	3
voter5	2	1	3
voter6	2	1	3
voter7	2	3	1
voter8	2	3	1
voter9	2	3	1

Where "1" = first choice, "2" = second choice, and "3 .... okay you get the idea. ;-)

The problem with the current system (FPTP) is clear: Labour wins with 44% of first preferences even though the other 56% didn't have Labour as their first choice and both the Labour and Conservative voters could clearly live with a Liberal victory.

So what does AV give us?

There would need to be 2 rounds:

In the first round, the results would be: Labour 44%, Lib 22%, and Con 33%. Since the LibDems come out last, they would be eliminated and the second preferences of those who voted for the unsuccessful LibDem candidate would be taken into account. This would give final totals of: Lab 44% and Con 56% - a Conservative victory.

This is a rather unsatisfactory result since, just looking at the figures in the above table, I think most fair minded people would conclude that the Liberal candidate was the best compromise given the range of preferences expressed.

The problem here, with the straight AV system, is that it gives second (and lower) preferences (once they are counted) the same weight as first preferences. Straight AV also ignores the second preferences of those who vote for the most successful candidate in the first round.

Why not simply weight each preference (in the counting system behind the scenes I mean - I'm not advocating a more complicated voting system)?

If a first choice got 3 points, a second choice got 2 points and a third choice got 1 point, the results in the above table would give: Lib 37%, Lab 31%, Con 31%. A LibDem victory.

This would be almost as easy to count as FPTP (only a single round required) and (in this example at least) produces a result which accords with our intuitions of "fairness" and the "best compromise".

I have made this example as small as possible and chosen the figures carefully to illustrate the point, but the example is not particularly far-fetched and could (in its fundamental features)easily be repeated in a real election on a larger scale.