Chapter 2: The elimination game

“Let's do a runoff,” says Ben. “First, count everyone's top choice. If one place gets more than half the votes, it wins.”

More than half of nine is five. Tacos has four, sushi has three and pizza has two. Nobody has five.

“Then whatever came last is out,” Ben says.

That's pizza, with two votes. But Hal and Ivy, the pizza fans, don't lose their say. Their ballots still have a second choice on them.

Both of them ranked sushi second. So their two votes move over to sushi.

Count again: sushi five, tacos four. Five is more than half.

Sushi wins!

That's instant runoff voting, or IRV. Knock out the option in last place, move its ballots to their next choice, and repeat until one option has more than half. Each round is like a new election, only instant, because everyone already wrote down their backup choices.

It's what most Americans mean by “ranked-choice voting,” or RCV. Some U.S. cities and states use it for elections, and it's how the Oscar for Best Picture is chosen.

Ben's a taco fan, but fair's fair. Gus, though, is frowning at the scoreboard.

“Wait. Pizza went out first. But pizza was everybody's first or second choice. Shouldn't that count for something?”

Gus spotted the catch. Instant runoff counts first choices, round by round. Pizza had only two fans, so it was knocked out before anyone's second choice was ever counted. An option that's everyone's solid second choice can get squeezed out early.

That doesn't make instant runoff wrong. In the last round, more friends preferred sushi to tacos, five to four. But is sushi the dinner the whole group is happiest with?

Fay thinks there's a better question to ask... Chapter 3: The tournament→