Same votes, different winners

Nine friends are choosing dinner: 🍕 pizza, 🍜 Thai or 🍣 sushi. Change how each one feels, and see who wins under each way of voting. The counting is the same code that counts every TallyLab poll.

Try an example:

The dinner example Everyone's second choice Pizza fans feel strongly A three-way loop

Pizza beats Thai, Thai beats sushi, and sushi beats pizza, each 6 to 3. No option is the group's favorite, so every method has to break a tie: ranked choice for last place, the others for first. The Marquis de Condorcet noticed this in 1785; it's the puzzle behind Arrow's theorem, which shows that no ranked voting method can be fair in every way at once.

Who wins

Plurality Pizza after a tie Approval Pizza after a tie Ranked choice Thai after a tie Quadratic Pizza after a tie STAR Pizza after a tie

The same votes give two different winners. Pick a method to see how it counts.

How ranked choice counts

Each friend ranks the options. Count first choices; if nothing has a majority (5 of 9), the last-place option is out and its votes move to each friend's next choice.

Round 1

Pizza 3 Thai 3 Sushi 3

Pizza, Thai and Sushi tied for last; a fixed random draw put Pizza out.
Round 2

Thai 6 Sushi 3

Thai has a majority and wins.

Head to head

For each pair, how many friends rank one above the other.

Pizza beats Thai, 6 to 3
Sushi beats Pizza, 6 to 3
Thai beats Sushi, 6 to 3

No option beats both others one on one: they go round in a loop.

The nine friends

Each friend's ranking, from favorite to least favorite.

Friend	Ranking	Happy with	Feels strongly
1
2
3
4
5
6
7
8
9

Happy with is how far down their ranking a friend would still be glad to go; it's what they tick in an approval poll, and the options they give 3 stars in STAR. Feels strongly only changes quadratic voting, where friends can show how much they care.

Try it with your own group

Make an approval or ranked choice poll in a minute and share the link. Free, no sign-up.

Create a poll How the methods work