The princess- "not as if the decision of the question depended upon yourself, but upon that hot-blooded, semi-barbaric princess, her soul at a white heat beneath the combined fires of despair and jealousy. She had lost him, but who should have him?"

This proves that the princess is deeply jealous and conflicted. She is desperate because she might rather have her lover die than marry another woman.

The tiger came out of the door because it said " Would it not be better for him to die at once, and go to wait for her in the blessed regions of semi-barbaric futurity?" This hints to us that she felt it was better he die than be with somebody else.

 she loved him with an ardor that had enough of barbarism in it to make it exceedingly warm and strong.- This shows the princess' attitude toward the young man which is that she liked him a lot and so would not choose for him to die

Her right arm lay on the cushioned parapet before her. She raised her hand, and made a slight, quick movement toward the right.

This shows that the princess is hinting to the man to choose the wrong door, because she feels that it is better that he die than be with someone else

with all the intensity of the savage blood transmitted to her through long lines of wholly barbaric ancestors, she hated the woman who blushed and trembled behind that silent door.

This shows that the princess hates the maiden because she didn't want her to marry her lover. Since she is barbaric, like her ancestors, she might make a cruel decision and have her lover die.

"Think of it, fair reader, not as if the decision of the question depended upon yourself, but upon that hot-blooded, semi-barbaric princess, her soul at a white heat beneath the combined fires of despair and jealousy. She had lost him, but who should have him?"

This quotes shows that the princess is jealous, because she doesn't want her lover to die but she also doesn't want him to fall in love with another person.

It was one of the fairest and loveliest of the damsels of the court who had been selected as the reward of the accused youth, should he be proved innocent of the crime of aspiring to one so far above him; and the princess hated her. Often had she seen, or imagined that she had seen, this fair creature throwing glances of admiration upon the person of her lover

This shows that the princess may hint to the wrong door to make sure that the woman behind the doors doesntget her lover

and she loved him with an ardor that had enough of barbarism in it to make it exceedingly warm and strong.

This is showing how she liked him a lot

  " And not only did she know in which room stood the lady ready to emerge, all blushing and radiant, should her door be opened, but she knew who the lady was. It was one of the fairest and loveliest of the damsels of the court who had been selected as the reward of the accused youth, should he be proved innocent of the crime of aspiring to one so far above him; and the princess hated her."

this shows the princesss is jealous and hates her.

"Wouldn't it be better for him to die right away and wait for her in the happy place of the future?"

This quote is a good example of characterization impacts the outcome because this quote clearly tells us that the princess is going to show for her lover to open the door on the right that was the tiger behind it.

"Her right arm lay on the cushioned parapet before her. She raised her hand, and made a slight, quick movement toward the right."

She was showing him to the wrong door because she would not let him get married to another person but make him die and take revenge