My Dad just asked me a logic question and I thought I'd check my answer here.

Scenario:

30 people take an online survey of 44 questions (answering from 0.0 up to 10.0 in 0.1 increments).

If then you take a person (Mr X) and set his answers as a benchmark you will then get a rank order of the other 29 people where no 1 is the closest fit to Mr X and no 29 is the furthest away from Mr X. (If that makes sense).

Ok, now the problem. (This was asked by a user of the software to my Dad and he was having difficulty getting the user to acknowledge what he was saying so he wanted to make sure he was correct).

The person ranked 3rd in the list is Mr Y. If you then take Mr Y and set his answers as the benchmark then where would you expect Mr X to be in rank order?

The user was saying that it was wrong because Mr X was appearing as no 29 in rank order not 3rd. But I said that (if the answers were all fairly close) then there is no guarantee where Mr X will appear in the list.

Is that correct?

I don't quite get the question (the "is this correct" bit), but:

Consider X to be the first person in a list of 30, so you have:

X A B Y C D E ... F

where A,B,C,D,E,F are all other people.

If there's a big gap between Y and C, then with your new baseline you could have:

Y B A X C D E ... F

But if C -> F is small compared to Y -> B you could end up with:

Y C D E ... F B A X

These are your extreme cases - there could be anything in between.

Cool, that makes sense.

The "is this correct" was my statement of there being no guarntee of where X will appear in the list. You have explained it well

You could also swap X and Y for any letters and say the same thing. So there is no correlation between the position of Y when X is the baseline and X when Y is the baseline.

That's what we wanted to check.

Thanks

Just out of pure curiosity, how are you going to rank these records? Total-distance from thetotal of your benchmark, or some other means? I think that could be where most of the interestingness lies with this type of problem.

Not too sure TBH. The system is already complete. This user is a prospective buyer and testing some results.

I know the ranking is done per quetion. i.e. if X answered 5 all the way through then the closest person in the ranking would be the person who ranked closest to 5 for every question. Although having people answer 5 all the way through would be fairly unlikely due to the nature of the interface.