I think a few things can be achieved with a photo, it all depends on the desired outcome of the person that posts the photo. As it is, the information in our profiles are very limited, also the psychological test seems novel to me. You can not come to any realistic conclusion relating to any individuals' personality only by asking a few questions.

So for instance, and I hope the translator doesn't mess this up, If I decided that I don't want anything serious, I only want a very beautiful young girl to have some fun. I would go to the nearest Porsche, Ferrari etc. etc. dealer, book a test drive, drive with that car to a big nice house and have someone take a picture of me inside the car in front of the house and post the picture on my profile stating " me in front of my house" Lots of attention guaranteed! You could then pick and choose the nicest girl and invite her to some place cheap like Turkey or Egypt, under the auspices of the first meeting on "Neutral territory" theory. Have your fun and that would be that!

If however you really want to find a partner for life, the photo can play a critical role. I think it should be an attempt to reflect something of your character. Obviously this could only be achieved to a limited degree, but the photo is the one thing that is the determining factor when the other person has to decide whether or not to make contact or reply to a first letter.