Suppose person A finds person B attractive/unattractive. Is person B more or less likely likely to find person A attractive/unattractive? In other words is there a statistical correlation between how person A perceives B, and how B perceives A? Evolutionarily I can imagine that a correlation would be somewhat beneficial.
Well, I guess if you find someone attractive, you are more likely to treat them positively, which can make you seem more attractive to them. So in that instance if Person B treats Person A particularly well, that raises the chances of person A finding Person B attractive.
However, if you consider the full alphabet of attractiveness, with Person A being the most attractive person in the world, and persons B - Z being of decreasing attractiveness, then I don’t think it’s likely that Person A is going to be attracted to the entire alphabet of people simply because they all find Person A attractive.
True, although I am mostly interested in whether there have been any studies that remove that bias, for instance by showing pictures to a group of strangers who then rate each other’s attractiveness.
Yet there very well may be a statistical correlation. For example, suppose person A is very attractive, and averages an attractiveness rating of ‘9.2’ when rated by strangers. It is possible that when person A finds stranger B of higher-than-average attractiveness, then stranger B tends to rate A somewhat above 9.2, on average, say 9.3.
I can’t find any studies to back me up, but there will certainly be cultural biases that result in people finding others like themselves more attractive. White Europeans will on average find other white Europeans more attactive than a Sub-Saharan African, and vice versa. I don’t find the Jersey Shore girls at all attractive, and I’m sure the opinion would be mutual. But the Jersey boys probably find the girls attractive, and vice versa.
The studies will depend on whether or not you are talking to the person, in some instances. It has been shown that the more dilated the pupil, the more interesting someone looks to you. That’s why romantic restaurants are all lit like caves. Everybody’s eyes dilate, and everybody looks like they are interested in their partner. Which makes them more attractive to them. It’s a vicious circle. 
I’ve observed both. Since the possible positive correlation has already been explained, I’ll explain a possible negative one: Person B may come on too strongly, and scare off Person A. And this can happen even if Person A was initially attracted to Person B.
I’ve been both person A and person B in that situation. But I’ve also been both in the positive situation. In particular, I was person A in the positive situation, with a woman who came on stronger than other woman I’ve ever met. But, she kept this up for so long that it wound up being too much, as I was not that attracted to her.
The funny thing was that she often talked about guys she didn’t like who were obviously attracted to her, and that, while she thought it was cute, it made them less attractive.
Personal viewpoint, I’ve fancied women quite strongly but when I’ve found out that they didn’t fancy me my attraction to them died virtually instantly.
Its not rationalisation or the like, I’ve genuinly lost interest.
I’ve also experienced the same loss of lust when very goodlooking females have turned out to have personalities that weren’t for me.