### Star ratings re-revisited

I did, very briefly, consider a completely different rating system for my reviews, instead of just awarding 0 to 5 shiny gold stars.

I considered rating books out of ten on several axes - for example, entertainment, literary merit, imagination, consistency. I would then combine them by treating those scores as the co-ordinates of a point in an N-dimensional space, the overall rating being the distance of that point from the origin, or equivalently, they are components of a velocity vector in an N-dimensional space. Let me give a couple of examples:

The Quantum Thief might score 8/10 for entertainment, 10/10 for literary merit, 9/10 for imagination, and 10/10 for consistency. The score, then, is sqrt(8^{2}+10^{2}+9^{2}+10^{2}) = 18.6. A perfect score on those axes would be sqrt(4*10^{2}) = 20. So to normalise to a score out of ten we divide by 2, giving 9.3/10. I actually gave it 5/5.

A Mighty Fortress, on the other hand, might get 5/10 for entertainment, 2/10 for literary merit, 2/10 for imagination, and 8/10 for consistency, for a score of 9.8, which normalises to 4.9/10. I actually gave it 2/5.

There are at least three obvious reasons why I didn't go with this.

- Maximum marks on one axis gets you half way to perfection with four axes, even closer with fewer. I don't want to give undue weight to good marks in any one axis. We could perhaps solve this by making it harder to attain maximum velocity in any direction the closer you get to the maximum. The physicists in the audience may now run away screaming;
- different type of book require different axes. eg fiction vs textbook vs biography;
- it over-complicates things, and is just a poor attempt to hide how subjective reviews are. Note that in the numbers above, I fudged the individual axis scores for both books so they'd mostly agree with the scores I actually gave :-)