Chapter 4: Keeping score
New here? Start with chapter 1
“Let's keep score,” says Dee. “Every place on your ballot is worth points. First place gets two, second gets one, and last gets zero. Then we add them all up.”
Every friend hands out three points in all. The only question is where they go.
Ana, Ben, Cal and Dee go first. Each gives two points to tacos and one to pizza. Sushi, last on their ballots, gets nothing.
Tacos: 8. Pizza: 4.
Then Eli, Fay and Gus. Each gives two points to sushi and one to pizza. Tacos, last on their ballots, gets nothing.
Tacos: 8. Pizza: 7. Sushi: 6.
Finally, Hal and Ivy each give two points to pizza and one to sushi.
Tacos: 8. Pizza: 11. Sushi: 8.
Pizza wins, with 11 points.
That's the Borda count, named for Jean-Charles de Borda, a French naval engineer who presented it to the French Academy of Sciences in 1784. It rewards an option for being high on lots of ballots. Pizza was only two friends' favorite, but it was second for the other seven, and those points add up.
With more options, the points go up. With five options, first place is worth four points, second is worth three, and so on down to zero for last.
You've probably seen points like these before. Baseball's MVP award and college football's Heisman Trophy are decided by voters who rank players and add up the points. So is the Eurovision Song Contest, where each country gives 12 points to its favorite song, 10 to the next, then 8 down to 1.
Points don't just pick a winner. They put every option in order, which makes them perfect for lists. A group's Top 10 movies works the same way: first place on a ballot is worth 10 points, second is worth 9, and so on down to 1 for tenth.
Points work from the bottom, too. The option with the fewest points is the one the group likes least.
Tacos and sushi are tied at 8, so the tie goes to whichever one more friends ranked dead last. That's tacos, last on five ballots. So the option with the most first-place votes is also the group's least favorite.
Dee laughs. She's a taco fan, and her own idea just named tacos the worst dinner of the night.
Four ways of counting. Three different winners. Somebody has to settle this Chapter 5: So who was right?