Carter loves philosophical discussions and theoretical debates; Dante becomes impatient with hypothetical speculations. Carter is most likely to be persuaded via processing, and Dante is most likely to be persuaded via .

Peripheral route; central route

Explanation:

In this scenario, it seems that Carter is most likely to be persuaded via Peripheral route processing, and Dante is most likely to be persuaded via central route processing. Peripheral route refers to when an individual evaluates a message or advertisement based on its surface-level characteristics such as its physical attractiveness. On the other hand, central route refers to evaluating with careful and thoughtful consideration of the message itself.

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