Which of the following terms could refer to a leader appealing to the irrational fears of the populace?

The term that best fits the description of a leader appealing to the irrational fears of the populace is "demagogue." A demagogue typically uses emotion-laden rhetoric and often incites fear, anger, or prejudice to manipulate public opinion and garner support. This type of leader capitalizes on the vulnerabilities of the populace, often distorting facts or exploiting social tensions to achieve their goals. This approach is characterized by populist sentiments, where the demagogue claims to represent the common people's interests but often does so through fear-mongering tactics.

In contrast, the other terms do not reflect this concept. "Droll" refers to something that is amusing or humorous, which does not align with the theme of fear. "Egregious" describes something remarkably bad or shocking, but it does not specifically relate to leadership or manipulation of fear. "Edify" means to instruct or improve someone morally or intellectually, which is quite the opposite of inciting fear or using negative emotions as a tool for leadership. Therefore, among the provided choices, the term "demagogue" correctly encapsulates the idea of a leader who manipulates the public by appealing to their irrational fears.