In Shakespeare's Othello, the reader might well witness "double poetic justice" directed at Othello—with a caveat (see below).
Othello loses Desdemona, his wife, because he does not believe her. While he reassures her father that he did not bewitch her but won her honorably, his inability to act honorably drives him to kill Desdemona at the end of the play. (Ironically, Desdemona's father does not believe Othello.)
In Act One, scene three, Brabantio (Desdemona's father) accuses Othello of bewitching his daughter. Othello declares their mutual love was what allowed Othello to win his wife's heart.
How I did thrive in this fair lady's love
And she in mine. (137-139)
While they wait for Desdemona to corroborate his declaration, Othello speaks of his stories that fascinated her: she loved to hear his tales. Later he again explains that Desdemona's love of his stories, and her sorrow over what he had suffered during these times were what she wanted if any man would woo her. Othello says he did just that—told her more stories.
And [she] bade me, if I had a friend that loved her,
I should but teach him how to tell my story,
And that would woo her. Upon this hint I spake:
She loved me for the dangers I had pass'd,
And I loved her that she did pity them. (175-180)
Othello loves Desdemona because of her gentle heart. However, it is her kind feelings that cause trouble because she takes pity on Cassio when he loses his position for drinking and fighting. Desdemona agrees to meet with him to see how she might help. (Iago uses the time these two spent together to poison Othello's mind against his wife.
Othello forgets his wife's love, consumed by an unfounded jealousy. For the pity she feels for him and others, he believes that she has been unfaithful, and he kills her. Othello also believes Iago's stories over his wife's words when Iago tells Othello that Desdemona has been unfaithful. Though Desdemona denies it all and swears her abiding love for Othello, his doubt overrules his love, and he kills her.
Othello realizes his mistake too late. The tales he told, Desdemona accepted without question. Her protestations of love he disregarded. The things Iago told him he accepted without question—and he doubted his wife.
The term "poetic justice" dictates that...
...in literature, good should be rewarded and evil punished.
Many critics in the past saw that Shakespeare had not addressed "poetic justice" as he should have in the play. Based on this definition, we see that Desdemona is good, but is punished—as are Iago and Othello (who are both evil). There is no poetic justice in this sense.
However, please note that Percy Bysshe Shelley studied Othello and looked deeper to discover an accurate interpretation of the play. Shelley concluded...
...in Othello Shakespeare was portraying a man whose misfortunes were due to the intrigue of another, and were not intended by the dramatist to appear as retribution for any of his own misdeeds.
Shelley believes that Othello was not punished for being evil, but was victimized by evil Iago.
However, based on the earlier perceptions of Othello (and poetic justice), he was evil; "double poetic justice" is seen in his punishment because he believes the evil Iago, and disbelieves the innocent Desdemona. From an old-school perspective, Othello is punished in losing the woman he loves, and loses his life—because he is evil.