Final answer:
The rhetorical appeal used in the excerpt from Plato's The Republic is ethos, highlighting the importance of a judge's virtuous character and the respectability of their role for making just decisions.
Step-by-step explanation:
Plato's excerpt from The Republic discusses the characteristics that judges should possess. In this excerpt, the speaker uses ethos as the rhetorical appeal by relying on the authority of virtuous character and the respectability of a judge's role. Ethos is emphasized through the argument that judges should not be exposed to evil or crime in their formative years to maintain a virtuous and honorable mindset, which enables them to make healthy judgments unaffected by personal experience of evil habits. This selection argues that a lack of exposure to evil gives good men a naivety in youth, allowing them to be deceived by the dishonest, showcasing the importance of character-built judgments in positions of authority.