So beauty could either be i) absolute in the sense that it is independent of our opinion, ii) absolute in the sense that our brains are all wired the same way and all have a common opinion on the object (a dog could have a different opinion however), or iii) beauty is not absolute at all and is purely a matter of our personal opinions.
I don't think the latter possibility is completely the case. I think we can all agree that the Colosseum is more beautiful than a dog house. There must be something that explains why we all think that way.
When public opinion starts dividing though, we have issues. Between the Eiffel Tower and the Colosseum, I imagine we cannot rank absolutely. I think this is fine. But between Mozart and N'Sync, where public opinion is also divided, is it for different reasons?
This is an issue that has bothered me often. I was reminded of it in the Zidane goal thread in WFF. I have a strong belief that A is better than B. It is so obvious to me that responding that this discussion is just a matter of opinion is ridiculous to me.
In the case of goals, I could rationalize my choice by adding that the difficulty in scoring the goal is an important factor. That seems to take away some matter of opinion.
Are there other such factors that could help us say that something is more beautiful than the other outside of opinion?
Do not mix the things. Even if we have rules for science, there is still people who think they are wrong or given facts to be wrong, etc. So, it won't be something like Beauty that will grant you a system beyond failure.
The definition of Beauty must come in hand, if you use something that only a specialist can qualify, you will find norms, which wont please most people, because after all, they are not specialists. But if you allow beauty be taste, then it is a hell of subjectiveness.
No matter if you can definite what is a beautiful poem or not - a fact that remains is that appreciation of anything is the subjective part of all. And it is not affected only by our bias, but by the momment. You may find Zidane goal so beautiful and tomorrow think it was not...
And even if you have a factor - it is not a degree. It is not mathematical. I can tell you the rythim, the symbolism, the oral power of Yeats poems are what make them beautiful, but I cann't tell you that Leda and the Swan is a 7,2 while The Rose ofthe World is a 5,6. At some point, all is melted and all your knowledge in poetry cann't make the rank.