What qualities would make the Hamlet character Horatio a good king of Denmark? Why would he make a better king than Fortinbras?

We really know very little about Fortinbras since he doesn't appear in person until near the end of the play. From what we learn about him through his actions and the reports of others, Fortinbras seems like a rash, impulsive, ambitious, inexperienced young man who is out to make a name for himself. If he became king of Denmark, as seems very likely to happen, he would probably always be involving the nation in military...

We really know very little about Fortinbras since he doesn't appear in person until near the end of the play. From what we learn about him through his actions and the reports of others, Fortinbras seems like a rash, impulsive, ambitious, inexperienced young man who is out to make a name for himself. If he became king of Denmark, as seems very likely to happen, he would probably always be involving the nation in military adventures, much like a young Napoleon Bonaparte. Fortinbras seems very much like young Octavius in Shakespeare's play Julius Caesar. Octavius is also young and inexperienced. He has nothing to recommend him as one of the rulers of Rome except for the fact that Julius Caesar appointed him his heir. Fortinbras is in a similar position. He is the nephew of the reigning king of Norway and heir apparent to that throne. Both Octavius and Fortinbras are young, ambitious, untested, impulsive, and eager to perform great deeds and make names for themselves.

By contrast, Horatio is modest, thoughtful, cautious, and serious. Hamlet speaks very highly of him when he says,

Since my dear soul was mistress of her choice,
And could of men distinguish her election,
Sh'hath seal'd thee for herself. For thou hast been
As one, in suff'ring all, that suffers nothing;
A man that Fortune's buffets and rewards
Hast ta'en with equal thanks; and blest are those
Whose blood and judgment are so well commeddled
That they are not a pipe for Fortune's finger
To sound what stop she please. Give me that man
That is not passion's slave, and I will wear him
In my heart's core, ay, in my heart of heart,
As I do thee (Act III, Scene 2).

I would argue Hamlet would have made a good king because he has intelligence and wisdom. Since Horatio is Hamlet's alter-ego, it follows that Horatio would also govern with wisdom and justice. Horatio is presented to readers and audience members as an admirable character who is kind, compassionate, unselfish, and understanding. If Fortinbras became king of Denmark, he would have a lot to learn. Horatio, on the other hand, could step right into the role and govern the nation with discretion. Hamlet does not think of nominating Horatio to be king, though, because, unlike Fortinbras, Horatio does not have the social status to be considered for such an honor.