Muggles' Guide to Harry Potter/Major Events/Head Boy

Overview
Head Boys and Head Girls are not, strictly speaking, magical. They are an integral part of the power structure of any school run on the English model; a Head Boy typically is the senior of the male Prefects, as the Head Girl is the senior of the female Prefects. Typically they have a few additional privileges, and in return are responsible for assigning duties to other prefects and seeing that they are carried out.

Event Details
In Harry Potter and the Prisoner of Azkaban, Percy Weasley has just been made Head Boy, and his pomposity has increased incredibly. The only thing that makes him tolerable at all is that the twins are perpetually puncturing his ego, or at least trying to; their continual japing makes him a figure of fun rather than a simple bore.

Hagrid has mentioned to Harry, in Harry Potter and the Philosopher's Stone, that Harry's father and mother were Head Boy and Head Girl while they were at Hogwarts.

While there must be a Head Boy and a Head Girl in each year Harry attends Hogwarts, the only one we ever hear of is Percy.

Notable Consequences
Generally speaking, consequences will be few, as the Head Boy and Head Girl will invariably be in their last year at Hogwarts. It is true that Percy, as Head Boy, became even more pompous and stuffy than he had been as a Prefect.

Analysis
There is a minor contradiction here. Hagrid says in Harry Potter and the Philosopher's Stone, as mentioned above, that Harry's father was Head Boy. Yet, in Harry Potter and the Order of the Phoenix, Sirius Black states that Remus Lupin was a Prefect; both Sirius and James were spending too much time in detention to be considered for that post. Later, Lupin and Sirius did say that James had improved by his seventh year; so we have four possibilities.
 * 1) With some other prefect's departure before 7th Year, it may have been necessary to appoint a new prefect, and that job, with the Head Boy promotion, might have fallen to James. This is somewhat unlikely as James had not previously been Prefect; as Lupin had, it seems more likely that Lupin would be Head Boy, although Lupin being a Werewolf, and the Werewolf potion having not been invented yet, could have precluded him from being appointed to this position.
 * 2) Hagrid might have over-inflated ideas about James' student office, or might be improving on the truth, either to make Harry more aware of his fame, or just on general principles.
 * 3) James' character, which granted seems unsuitable for the Head Boy office, might not have been totally firmed up that early in the series, and the author might have chosen to have him be Head Boy to build up his apparent status in the Wizarding world.
 * 4) We are told that James was an excellent Quidditch player during his time at school, so it is possible he became captain in his later years. Since Quidditch captains have almost the same privileges as Prefects, it is possible he was been made Head Boy on the strength of his Quidditch captaincy in his seventh year. Or, the most likely,
 * 5) Head Boys and Girls do not have to be chosen from Prefects and are simply chosen by the headmaster.

Of the first four options, the third seems most likely; however, the second and fourth make more sense in the context of the story.

As we can see from Percy, by comparison with Fred and George, the students chosen for prefect and head boy positions are not necessarily the most powerful wizards in residence. Thus, if James Potter was not head boy, it is unlikely that it bears any reflection on his Wizarding ability.

Questions

 * 1) How likely is it that both Head Boy and Head Girl would be in the same house?

Greater Picture
It is possible that Hermione would have been made Head Girl had she returned to Hogwarts for her seventh year, and if Hogwarts had remained a place that she could go to. However, she chooses instead to accompany Harry to help him deal with Lord Voldemort. Also, with the school largely under Death Eater control at that point, it is unlikely that Gryffindor House would have been honoured with the position, no matter how worthy Hermione was. In fact, being Muggle-born, Hermione would not be allowed to return to the school for her seventh year; instead, she would have been arrested and convicted of stealing a wand, and sentenced to a Dementor-guarded prison.