What convinces Sir Andrew that Olivia prefers him to Cesario?

Sir Andrew is convinced that Olivia prefers him to Cesario for several reasons:

1. Olivia's flirtatious behavior towards Sir Andrew: Throughout the play, Olivia flirts with Sir Andrew and shows him attention, which makes him believe that she is more interested in him than Cesario. For example, she dances with him at the party and praises his looks.

2. Olivia's rejection of Cesario: When Olivia declares her love for Cesario, he rejects her advances and makes it clear that he cannot reciprocate her feelings. Sir Andrew takes this as a sign that she will eventually turn her attention to him instead.

3. Olivia's declaration of love: When Olivia mistakenly believes that Cesario has taken offense and left, she confesses her love for him publicly. However, Sir Andrew interprets this as confirmation of his own desirability, assuming that Olivia's declaration is meant for him instead.

4. Sir Toby's encouragement: Sir Toby, Sir Andrew's friend and enabler, continually assures him that Olivia is more interested in him than Cesario. Sir Toby's manipulation and flattery further convince Sir Andrew that Olivia prefers him.

Ultimately, Sir Andrew's naïveté and desire to believe in his own attractiveness contribute to his conviction that Olivia prefers him over Cesario.

To determine what convinces Sir Andrew that Olivia prefers him to Cesario, we can look into the play "Twelfth Night" by William Shakespeare.

In Act 2, Scene 3 of the play, Sir Toby Belch and Sir Andrew Aguecheek plot to convince Sir Andrew that Olivia favorably responds to his affections over Cesario (who is actually Viola disguised as a man). They come up with a plan to write a challenge letter to Cesario, supposedly on behalf of Sir Andrew. The purpose of this challenge is to test Cesario's bravery and provoke jealousy in Olivia.

However, the actual turning point for Sir Andrew occurs in Act 3, Scene 2, during an encounter with Cesario. Prior to this scene, Olivia has just professed her love for Cesario and sent Malvolio to deliver a ring to him. When Sir Andrew shows up, he believes that the ring was meant for him and concludes that Olivia prefers him over Cesario.

The key factor that convinces Sir Andrew of this preference is the miscommunication and misunderstanding regarding the ring. Sir Andrew assumes that the ring was intended for him and interprets it as a sign of Olivia's affection. This misinterpretation, fueled by Sir Toby's manipulations and his own desire to believe that Olivia loves him, serves as the primary catalyst in Sir Andrew’s conviction that Olivia prefers him to Cesario.

Overall, it is a series of mistaken impressions and manipulations orchestrated by Sir Toby and Sir Andrew's own wishful thinking that leads him to believe that Olivia prefers him over Cesario.