To what extent is Henrick Ibsen's A Doll's House a true tragedy when compared to classic Shakespearean tragedies like Hamlet, etc?
Erik Bøghin said: “it is beyond memory since a play so simple in its action and so everyday in its dress made such an impression of artistic mastery. ... Not a single declamatory phrase, no high dramatics, no drop of blood, not even a tear ... never for a moment was the dagger of tragedy raised.”
Let us remind ourselves of Aristotle's definition of a tragedy, which I think your question is referring to. He argued that tragic dramas should be focused on a single protagonist, or hero. This protagonist should be:
[a] character between ... extremes--[one] who is not eminently good and just, yet whose misfortune is brought about not by vice or depravity, but by some error or frailty. He must be one who is highly renowned and prosperous--a personage like Oedipus ... or other illustrious [persons]. (Poetics 13)
Often this frailty takes the form of arrogance. Now, if we examine A Doll's House considering these categories, we can see that it doesn't have much correlation with Aristotle's definition of a tragedy. It does indeed focus on one character, but as we get to know Nora more as the play progresses, we see that her tragic frailties are the result of other people keeping her in a childlike state. In fact, I would want to question whether we can actually consider this play a tragedy at all.
Maybe this is a controversial view, but what we actually see during the course of the play is that Nora finds herself and matures. Her shocking decision to leave her husband and children at the end of the play has actually been viewed as a triumph by many critics through the years. Normally, in tragedies beginning with the Renaissance, the protagonist dies as a result of their tragic frailty and this brings the play to a close. With Nora, the play ends with her slamming the front door shut as she goes out to begin a new life, with all the possibilities that this can bring her. I think it is hard to view this in tragic terms, though her exit can be seen as a form of exile, which was an option for Aristotelian tragic protagonists.