Politicians often seek to tap voters younger than themselves. Not Kansas gubernatorial candidate Jack Bergeson.

He is only looking for older voters, because come Election Day in November 2018, he’ll still be too young to cast a ballot himself.

Thanks to his state’s vague election rules on candidate ages, Mr. Bergeson, a 16-year-old high-school student from Wichita, has thrown his hat in the ring to run for his state’s highest office. Last year, he signed papers that allow him to start raising money for his campaign—the same step taken by all the major candidates.

His running mate is 17-year-old Alexander Cline, who is vying to become Kansas’ next lieutenant governor. The friends, who are seeking the Democratic Party nomination, have known each other since seventh grade.

“As long as I’m giving people the option of my candidacy, it doesn’t really matter too much that I won’t be able to vote for myself,” said Mr. Bergeson, who works summer shifts busing tables and washing dishes at his family’s burger and beer joint, called Fizz.