(spoilers extended) Ned = Richard III?
Richard III: The Kinslayer
When King Edward IV of England died prematurely his heir was too young to sit the throne.
He entrusted his brother, Richard Duke of Gloucester to serve as Lord Protector. Richard was asked to rule the realm and keep his nephew safe until he came of age and could rule by himself.
Richard had other ideas. The power and wealth was too great a prize to let slip through his grasp. He seized the heir(s) and locked them in the tower of London. He accused them of being illegitimate.
His nephews (the heirs) were never seen again and, Richard crowned himself King Richard III. His palace coup succeeds (for a while).
How does this relate to Ned Stark?
Ned's name (Eddard) is surprisingly like Richard's. He's also surrounded by people named "Rich" (his father and his son Rickard/Rickon).
But more importantly, Ned's story is the same as Richard's (with a some important differences).
King Robert dies prematurely (from a hunting accident). His **heir (**Joffrey) is too young to sit the throne.
Ned and Robert are friends (they call each other "Brother"). King Edward and Richard were actual brothers.
Edward named Richard Lord Protector on his deathbed, in order to protect his children. Robert names Ned Lord Protector to protect his children.
Richard named Edward's sons as illegitimate (they probably weren't). Ned named Joffrey and Robert's children by Cersei as illegitimate. The key difference is that Ned was right. Cersei confessed as much to him. This really separates Richard and Ned Stark from a motive perspective. While Richard sought wealth and power, Ned was doing what he thought was right.
Ned tries to seize the heir and fails. Ned's palace coup fails miserably, unlike Richard III.
My comparison of Ned to Richard III is not to say he was evil like Richard III. That'd be ridiculous. We get Richard's point of view in Shakespeare's Richard III play and he is rotten to his core. He lies and manipulates. He murders children! His own nephews!
That is not Ned! Ned tries really hard to do the right thing in his point of view chapters. Specifically, and this puts miles between Richard and Ned essentially making them mirror opposites, is that Ned ABHORS the murder of children. Ned will not abide it! But child murder are Richard III's methods. He doesn't abhor it, at least not enough to not do it for personal gain.
Is Ned Stark Richard III? No! But their lives seem to parallel each other. Ned's story is unmistakably inspired by Richard III's life. Their stories are similar but not the same, they "Rhyme" with each other.
Ned's defining features, the abhorrence of child murder mirror the infamous Richard III's ambition which drove him slay children (his own nephews). You could say this difference between these two men CONFIRMS the relationship of these stories. And directly calls back to Richard III. The text begs us to think about what kind of man slays children? The answer is the infamous Richard III, whose story has so much in common with Ned's (above).
Ironically, because they are mirror opposites (see their stance on child murder), their different circumstances (Richard III's nephews were legitimate, Robert's children were not) actually leads them to the same decision: naming the King's heirs as bastards. Ned does it because he thought it was right. Richard III did it for personal gain.
Ned isn't bad like Richard III. But Ned's life is a deconstruction of Richard III's.
Through Ned, GRRM asks (about Richard III);
-What if Richard III was a decent man (Like Ned)?
-What if Richard wasn't the King's actual brother, but a close friend (Ned is like a brother)?
-What if the King's sons truly were bastards (As we see Ned discover)?