Every spring the smell of delicious, spicy chili fills the air, and you get to taste all the entries at Tusculum University.
In previous years, voting was done by filling out a piece of paper, and counting the entries by hand. This was a tedious and labor intensive process. So last year, I helped to create a simple, mobile friendly, web app. Votes were automatically tabulated, and overall, it was a huge hit, having the most number of votes cast in years.
However, if you’ve ever been to an event like this, you know when it comes time to vote, you have a tough choice. You like more than one chili, and so do your friends. How do you decide which one should win? So I went to some math professors to try to find a better option.
Anyone who knows me has heard me say, a math degree doesn’t prepare you to solve bigger multiplication problems. Math majors work to help solve problems using logic and finding patterns. One way is in how we can vote. In fact, they helped me learn more about a voting system called ranked-choice.
This means instead of picking your favorite, you get to pick multiple choices to hopefully pick a winner that more people agree upon. While there are various ranked-choice systems, we’re using a point based system.
So why do mathematicians love ranked-choice voting? Let’s break it down in a way that makes sense—even if you’re not a math whiz!
What is Ranked-Choice Voting?
Ranked-choice voting (RCV) is a system where voters rank their favorites instead of choosing just one. It’s used in real-world elections and competitions to make voting more fair.
There are different ways to count votes in RCV. As I mentioned, the method used in the Tusculum Chili Cookoff is called a points-based system. Here’s how it works:
- Your 1st place choice gets 5 points.
- Your 2nd place choice gets 3 points.
- Your 3rd place choice gets 1 point.
- Chilis you don’t vote for get 0 points.
At the end of voting, all the points are added up. The chili with the most points overall wins. This system makes sure every vote counts, even if your top choice doesn’t win.
How the Math Works Behind the Scenes
Let’s look at an example with four chili competitors: Spicy Surprise, Smoky Heat, Veggie Delight, and Classic Comfort.
Step 1: Voters Rank Their Choices
Imagine five people vote, ranking their top three choices. Their ballots might look like this: (FYI – these examples were created before the system cook-off as an example. We won’t know what the scores will look like until Wednesday.
| Voter | 1st Choice | 2nd Choice | 3rd Choice |
|---|---|---|---|
| A | The Penny Pinching Peppers (5) | Chilin with the Spirit (3) | TRiO Triple Threats (1) |
| B | Chilin with the Spirit (5) | TRiO Triple Threats (3) | Ghost Hunters (1) |
| C | TRiO Triple Threats (5) | The Penny Pinching Peppers (3) | Chilin with the Spirit (1) |
| D | Ghost Hunters (5) | TRiO Triple Threats (3) | The Penny Pinching Peppers (1) |
| E | The Penny Pinching Peppers (5) | Chilin with the Spirit (3) | TRiO Triple Threats (1) |
etc…etc…
Step 2: Assign Points and Add Them Up
Now we calculate the total points for each chili:
| Chili | Points from 1st Place | Points from 2nd Place | Points from 3rd Place | Total Points |
| The Penny Pinching Peppers | 15 (3×5) | 6 (2×3) | 1 (1×1) | 22 |
| Chilin with the Spirit | 15 (3×5) | 6 (2×3) | 2 (2×1) | 23 |
| TRiO Triple Threats | 5 (1×5) | 18 (6×3) | 5 (5×1) | 28 |
| Ghost Hunters | 10 (2×5) | 3 (1×3) | 1 (1×1) | 14 |
Step 3: Declare a Winner
The two chilis with the most first place points are The Penny Pinching Peppers and Chilin with the Spirit. However, it seems that more people really like the TRiO Triple Threats, as they had more second place voters. That means that they were liked overall more, and their score represents that. If people had only been able to vote once, then it would have been a tie between The Penny Pinching Peppers and Chilin with the Spirit.
There still could be a tie, in which case a tiebreaker might be used (such as looking at which chili got the most first-place votes). Otherwise, they could be declared co-winners!
This system ensures that even if someone’s favorite chili doesn’t win, their second and third choices still help decide the best overall chili, and thus people are more willing to accept the results. This is also true for when people vote for politicians.
Why Ranked-Choice Voting is a Smart Solution
Ranked-choice voting is used in competitions and elections because it solves common problems in voting, such as:
1. Preventing “Vote Splitting”
If two similar chilis (let’s say two extra-spicy ones) are in the competition, they might split the votes of people who love spicy food. With simple majority voting, neither might win. Ranked-choice voting ensures that a strong runner-up still has a chance.
2. Rewarding Broad Appeal
A chili that’s most people’s second choice might be better than one that only a few people love. This system finds a chili that’s liked by the most people overall, not just a small, passionate group.
3. More Accurate Representation of Preferences
Instead of just picking one option, voters get to express their full opinion by ranking their favorites. This makes the final results feel fairer and more satisfying for everyone.
There’s More Than One Way to Do Ranked-Choice Voting
As I mentioned previously, the points-based system used at the Chili Cookoff is just one way to do ranked-choice voting. Other methods include:
- Instant Runoff Voting (IRV): Instead of using points, votes are counted in rounds. The lowest-scoring option is eliminated, and those votes transfer to the voter’s next choice. This continues until one option has more than 50% of the votes.
- Borda Count: Similar to the points system, but with different values assigned to rankings.
- Condorcet Method: Looks at head-to-head match-ups between choices.
Different methods work better in different situations, but they all use math to create a fairer and more logical way to pick winners.
The Bigger Picture: Math Solving Real Problems
You might not think about math when you’re voting for your favorite chili, but systems like ranked-choice voting are examples of math solving real-world problems.
- Similar ranking systems are used in sports playoffs, college admissions, and even how search engines rank websites.
- Voting math helps in political elections, making sure results reflect what most voters actually want.
- Math is used everywhere to help make fair decisions when there are multiple choices.
So next time you rank your favorite songs, video games, or even pizzas, remember—you’re using the same logic that mathematicians use to solve big problems! And mathematicians can solve even more types of problems. This is why computer science students are often required to take multiple high level math classes.
So Try It Out at the Chili Cookoff!
At the Tusculum University 2025 Chili Cookoff, so if you’re in the area, come on by, and you’ll get to experience ranked-choice voting in action. After tasting the delicious chilis, you’ll rank your top three favorites, and the results will be fair, balanced, and math-powered!
So, get ready to vote, enjoy some great chili, and see how math makes competitions better for everyone. May the best chili win!
How Ranked-Choice Voting Uses Math to Solve Real-World Problems was originally found on Access 2 Learn
