Cost-benefit analysis is a weighing-scale approach to making business decisions: all the pluses (the benefits) are put on one side of the balance and all the minuses (the costs) are put on the other. Whichever weighs the heavier wins.
However, since the story constantly points out Jon's conflict with his illegitimacy and Ned's strict code of honor, many fans have come up with a theory that actually explains who they think Jon's parents really are. Fans know the theory as R+L=J.. R+L=J would refer to Jon Snow (J) being the child of Rhaegar Targaryen (R) and Ned Stark's sister, Lyanna Stark (L) rather than Jon being the illegitimate child of Ned.
The head of the house is the Lord of Winterfell. Before the Targaryen conquest, the leaders of House Stark ruled over the region as the Kings in the North. Jon Snow is the current King in the North and the Vale, partially due to the allegiance of Petyr Baelish, the Lord Regent of the Vale, to House Stark.