TE ATATU, New Zealand — New Zealand is as beautiful as it is isolated. We live a long way from anyone and anything, and we like it that way. We have almost four and a half million people and more than five million dairy cows. We have snow-capped mountains and deep dark woods where hobbits roam, as directed by Peter Jackson in his interminable “Lord of the Rings” movies. We sing (Lorde) and act (Russell Crowe) and throw stuff (rugby balls).

The rest of the world rarely notices our country, but this month everyone — well, some people — seems to be taking note. Our green and pleasant archipelago is heading to the polls for a national referendum on whether or not to do away with our current flag and replace it with something that kind of looks like a beach towel.

The redesigned flag — a white fern leaf laid over a black-and-blue background — looks happy and foolish, not unlike our prime minister, John Key. The head of New Zealand’s government likewise has a floppy, casual charm. This is the guy whose biggest scandal came after a waitress told the world about his strange, compulsive habit of pulling her by the ponytail every time he visited her cafe.

Unlike the flag, the prime minister resonates with voters: He’s won the last three elections. Mr. Key has driven the flag-change proposal. It’s his passion, his grand project. But many people here loathe the prospect — he’s been in office almost eight years, and all we got was this lousy flag? — and wish the whole thing would just go away. It will soon. The referendum, which began March 3, ends March 24.