The evidence included in the second paragraph that is least relevant to the speaker’s argument is: "And finally, our neighboring town of Westmont also named its library by a vote."
While mentioning Westmont's process provides some context, it does not directly support the argument about the advantages of allowing residents to vote for the library's name compared to previous contest methods. The other points made (fairness of the process, higher approval rates, and efficiency) more directly bolster the speaker's case for a public vote.