You mediate this.

"Let's try and be rational here for a minute," you say, "Alicia, have you ever borrowed Ashley's Books without asking?"
"...once or twice."
"When she asked you about it, were you 100% honest?"
"...no, not really."
"So when she found out the truth, it probably hurt her, right?"
"I...I could see that," Alicia says, looking a little sad.

Alright- one down, one to go.

"Okay, so that is progress. Now Ashley, have you ever thought you bought something for Class when you didn't?"
"...yes."
"It's alright- it happens. So when people asked you about it, did you admit your simple mistake?"
"...no, I didn't. I was too embarrassed."

Okay, now for the final touch.

"Alright, so taking all of that into account, it is possible that Alicia borrowed the book. Did you? Be honest with us AND yourself."
"...no, I didn't. I swear."
"Ashley, are you 100% certain without the shadow of a doubt that you bought the Book?"
"Well...no, I guess not."

Now take it home.

"Okay, so if Alicia here didn't take it and it is possible that Ashley here made a simple mistake, why not deal with it later? Don't you want to enjoy the Party?"
"Yes," the pair say in unison.
"I'm sorry," Alicia says.
"Me too," Ashley says.

The pair softly hug in the middle of the room and have a quick cry. Everyone around them sighs- apparently hoping for a blow-up- and disperses.

"So...speaking of enjoying the Party," Ashley says, "How about us three enjoy it together...upstairs?"
"I'm game," Alicia says, "Are you Andrew?"