McDonald’s poster, headlined ’40,312 POSSIBLE COMBINATIONS’

Beneath the headline was a table citing eight food items.

My original complaint was that this was mathematically incorrect and therefore misleading. The vast majority of consumers would not be mathematicians, and that the advertisement contravened code 7.1.

Following the adjudication where the complaint was not upheld, I wrote to the ASA explaining the mathematics of my complaint, why the adjudication was incorrect and that the original advertisement and subsequent adjudication contravened codes 6.1 and 7.1. The reply (dated 8^th May 2002) does not explain why the ASA have viewed it acceptable that the advertiser can change its basis of calculation for the purposes of adjudication, nor has it addressed the flaws in the original mathematics that I explained in my letter.

A substantial flaw in the ASA Council’s adjudication. The flaws are as follows:

• The adjudication does not note that ‘permutation’ (factorial) mathematics is an incorrect method for calculating ‘combinations’ (the word used in the poster) and therefore leads to a mathematically incorrect answer. Thus the advertisement is misleading and, particularly given the use of advanced mathematical concepts, contravenes codes 6.1 and 7.1. Therefore, the complaint should be upheld and the advertisement withdrawn.

• The rationale in the adjudication not to uphold the complaint is to accept a different method of calculation from the advertiser, this time using ‘combination’ mathematics but for 16 items – whereas only 8 items are cited in the advertisement. Therefore, on this basis, the advertisement is still misleading, and the complaint should be upheld and the advertisement withdrawn.

The ASA has not addressed the original complaint of misleading advertising, and furthermore accepts an explanation that continues to mislead.

‘Combinations’ is a specific mathematical concept, and is the word used in the advertisement in conjunction with a mathematical calculation. Possible combinations are the number of different ways in which people can ‘mix and match’ items (including not ordering any of them).

If there are eight items, as stated in the advertisement, the formula for the number of possible combinations is 2^8 = 256. ‘256 possible combinations’ is what should have been stated on the poster.

Combination mathematics would not take account of the possibility of purchasing more than one of the same item in a combination (e.g. two or three portions of fries), as the possibilities would be limitless and it would be pointless to try to calculate this.

In the poster, McDonald’s employed factorial mathematics and calculated the number of ‘permutations’ (arrangements), which is mathematically a different concept to that of ‘combinations’. The number of permutations presumes that there is a difference in the order of choices, for example, that fries and a coke is different to a coke and fries – which is clearly not the case. What McDonald’s have cited on the poster is that consumers can ask for 8 items in 40,312 variations of sequence. This is not what the advertisement said, and is not ‘possible combinations’. Furthermore, the 40,312 calculation is in itself incorrect – the number of permutations for 8 items is actually 40,320. In the adjudication, the advertiser admitted that it had used factorial maths to calculate permutations – therefore the complaint should be upheld, and the advertising should be withdrawn.

In the adjudication, the advertiser offered to use ‘combination’ mathematics stating that if flavour variants are taken into account then there are actually 16 items, not 8 as originally stated. On this basis, McDonald’s then calculated the possible ‘combinations’ of 16 items by the formula 2^16 = 65,536. This was accepted by the ASA, on the grounds that the resultant total was larger than 40,312.

There are several flaws with this approach:

• First, the advertisement showed 8 items only – if the advertiser meant to calculate ‘possible combinations’ of 16 items, then 16 items should have been included in the advertisement. Therefore, the adjudication has accepted what is still misleading advertising.

• Secondly, it could be argued that flavour variants are a form of ‘duplicate’ item, and behaviourally do not make sense as ‘possible combinations’. The advertiser as much admitted this in the adjudication.

• Thirdly, it appears that the advertiser has been allowed to change its mind on the method of calculation to prevent a valid complaint from being upheld.