When it's time for a new monarch, what is the most common way that the next
monarch is chosen?

An elective monarchy is a monarchy ruled by an elected monarch, in contrast to a hereditary monarchy in which the office is automatically passed down as a family inheritance. The manner of election, the nature of candidate qualifications, and the electors vary from case to case

Explanation:

An elective government is a government administered by a chosen ruler, rather than an innate government wherein the workplace is naturally passed down as a family legacy. The way of political race, the idea of applicant capabilities, and the balloters change from case to case

*automatically passed down as a family inheritance*