The commonly used phrase "by popular election" can be substituted with various synonyms that denote the same meaning. One of the synonyms for this phrase is "via public voting," which refers to the process of voting by a general public for selecting representatives or leaders. Another synonym is "through democratic mandate," emphasizing the democratic process of elections that provides citizens with the opportunity to elect their representatives. Similarly, "by universal suffrage" can be used, indicating the right of all eligible citizens to participate and cast their vote. Additionally, "by ballot" or "by vote" are other synonyms used to denote the process of selection through voting.