How are the scores calculated in a ranked choice poll?

How are the scores calculated in a ranked choice poll?

Ranked choice voting takes into account members' first, second, and third choices (and beyond), not just their top pick. Each book's score is a weighted average of how members ranked it: the higher the score, the better ranked the book, and the book with the highest score wins.

The formula

• In a poll with N books, a 1st-choice rank is worth N points, a 2nd-choice rank is worth N-1, and so on down to 1 point for last place.
• If a member doesn't rank every book, the ones they leave off don't score 0. Instead, those unranked books split the remaining points evenly among themselves, so a member's vote carries the same total weight whether they rank one book or all of them. This keeps a partial ballot from outweighing a complete one.
• A book's score is the sum of the points it earned from every member who voted, divided by the number of members who voted in the poll.
• If two or more books tie for the highest score, no single winner is declared.

Example

In a 5-book poll, 6 people vote.

• Four of them rank all 5 books, placing a given book 1st, 4th, 2nd, and 3rd, worth 5, 2, 4, and 3 points.
• A fifth person ranks only their top 2 favorites and leaves this book off their ballot. Since 3 books were left unranked, those 3 books split the remaining points (3, 2, and 1) evenly, so this book gets 2.
• A sixth person doesn't vote at all, so they aren't counted.

This book's score is (5 + 2 + 4 + 3 + 2) / 5 = 3.2.