I can't quite remember if this manga is a Yaoi or a Shounen Ai, so I apologize if this is in the wrong section. It's basically about a boy who goes to an all boys boarding school, either at the request or in search of his Daddy Long Legs. Upon entering the school, he finds an odd system employed where students play a game by completing tasks (such as burning quiz questions) to increase their rank/points/social standing. Teachers don't interfere with this system. It has a similar atmosphere to Caste Heaven and Shiiku Gakari Rika but it's neither of the above. Apparently, a pair of twins are at the top of the food chain in this school, and if memory serves, the protagonist has remarkable eyes (and is the half brother to these twins). Thank you in advance.

Is it Torikago Syndrome?

Yup, I think that's it! Oh, it was a Shoujo- Thank you!