How is Theseus characterized in Shakespeare's A Midsummer Night's Dream?

Shakespeare characterized Theseus as one of the few
rationally-minded characters in the play.

We first observe his
rationalism in the opening scene when Egeus petitions Theseus to have his daughter
punished for continuing to refuse to marry Demetrius. According to the "ancient
privilege of Athens" a father may have a disobedient daughter put to death or sent to a
convent. Interestingly, while sending Hermia to a convent is still an option, he only
petitions Theseus for her death, as we see in his
lines:

As she
is mine, I may dispose of her;
Which shall be either to this
gentleman
Or to her death, according to our law.
(I.i.43-45)

Theseus first
demonstrates his ability to think reasonably and rationally when he changes Egeus's
petition to once again include the more humane option of sending her to a convent.
Theseus knows he must uphold the ancient law of Athens, even if he thinks it is unjust
to force Hermia to marry Demetrius. He reminds Hermia that she is expected to treat her
father as her god and obey his every will. When Hermia asks what could happen to her,
unlike her father, Theseus includes the option of sending her to a convent in the
prospective punishment, as we see in his lines, "Either to die the death, or to abjure /
For ever the society of men" (67-68). Since Theseus leaves the more humane option in the
punishment, we see that he is being more rational and level-headed than her
father.

A second place in which we see Theseus acting as the voice of
reason is when he decrees that Hermia will be permitted to marry Lysander, and Demetrius
will be permitted to marry Helena. When Egeus and Theseus see the four lovers in the
woods, Egeus, typical of his character, wants to insist on Hermia's and Lysander's
punishment for stealing away into the woods in order to defeat himself and Demetrius.
However, after Demetrius explains that he is now in love with Helena, whom he was
engaged to before, like a sensible, rational leader, Theseus overrules Egeus and decrees
that the couples shall be married as is.