My Take
It's interesting that so many people "believe" or at least "espouse" the adage, "beauty is in the eye of the beholder". For what follows that statement, is the assumption that everyone *understands* what beauty is, such that they are not "wrong" if they perceive something to be beautiful. If one were to think a mangled deer at the side of a freeway was "beautiful", should that assessment be considered accurate? Clearly, beauty is NOT in the eye of the beholder...
What surprises me about this thread isn't the "incompleteness" of so many posts, but that not a single person has introduced the concept of "rating" human visual beauty from 0-10. Since this thread is quite generally about *measuring* beauty, even if one is of the belief that such an endeavor is for naught, the most common definiton of beauty is human visual beauty. And the most commong measure of that specific beauty IS a point scale. :-) Some prefer a minimum value of 1, which is fine. I myself prefer the 0-10 scale as it provides an integer value for the "middle" beauty value of "average" - neither beautiful nor "ugly". Which leads me to another aspect of the measuring of beauty. Many people will quickly give the value of 10 to someone they find quite beautiful, and 0 (or 1) to a person if they are "mostly" ugly. It seems that people often err towards an extreme, when making "objective" evaluations of beauty. They don't put forth enough effort to be accurate, even more so when evaluation is "difficult" because the object being evaluated is nearer the middle of the continuum. That said...
Another mistake that people often make is to anthropocentrize universals, like beauty. Many people think of beauty *primarily* as human visual beauty. That shows how many people really don't understand what beauty is at all. In the "set" of all that is beautiful, the visual beauty of the human being is but a single member. Beauty is far more than a visual influence. As I like to do, when I want to understand something better, I include in my research the dictionary definition when applicable. Here's what I get from Dictionary.com:
"1. The quality that gives pleasure to the mind or senses and is associated with such properties as harmony of form or color, excellence of artistry, truthfulness, and originality."
There are five senses with which people can evaluate beauty, yet as I said before, most people only "understand" the visual sense of the concept. And then there's the mind itself, which can evaluate "hidden" aspects of beauty. (like Euler's identity) But I'd like to focus on visual beauty for a moment. As others in this thread have said, SYMMETRY is a major factor. A few here have mentioned PHI, or the golden ratio, as another factor. What should be noted is that symmetry is a form of self-similarity and the golden ratio does influence self-similarity.
I'd like to get back to the "scale" that people often use to measure human visual beauty. Almost exclusively, people implement a linear scale for evaluation, where 10 is the "maximum" amount of beauty possible. Sure, some like to use "11" in "special" cases, but let's ignore that anomaly. Theoretically, the "maximum" measurement of beauty should be very rare, if not "unattainable". However, there's a different scale which I find can be more "useful" - the exponential scale. Whereas "average" beauty is but the "mid-point" between the two extremes of "maximum beauty" and "maximum ugliness", and hence would be a "5" on the 0-10 scale, on the exponential scale, "average" beauty is more akin to "beauty to the zeroth power". Something which is "ugly" can then be described as "beauty to the negative first power", and something "beautiful" would be "beauty to the first power". As ugliness increases, so does the negative exponent - likewise, as beauty increases, so does the positive exponent. If, in one's evaluation, they determine the beauty of a thing to be an "order of magnitude" greater than merely "beautiful", they could describe that thing as "beautiful squared" - etc. (yes, I really like math) Of course, any rating system is only good if a "rater" is trying to be consistently accurate.
The point of my post is twofold. Firstly, to highlight the adequacy and/or inadequacy of "rating scales" as they pertain to beauty. Secondly, to say that beauty IS something which CAN be measured - and not everyone is "qualified" to measure it accurately. Just as it is true that not everyone knows how to calculate a derivative or integral, or knows how to prepare Peking duck, there certainly are people who don't know how to measure beauty. What they state is then mere opinion and CAN be "incorrect"...
I look forward to your feedback and the ensuing discourse. (and forgive the edits, I didn't like what I said in a couple places)