Chapter 5: So who was right?

Let's add it all up. Same nine friends. Same nine ballots. Four ways of counting.

A show of hands picked tacos. The elimination game picked sushi. The tournament and the points both picked pizza.

Three different winners. Nobody changed their mind. Only the counting changed.

So which one is right?

You might hope that a clever enough mathematician could find the one perfect way to count. In 1951, an economist named Kenneth Arrow proved there isn't one. Once there are three or more options, no way of counting rankings can meet a short list of common-sense fairness rules all at once, every time.

Every method has some situation where it does something odd. The trick is knowing what each one is good at.

Show of hands (plurality, or FPTP)

Quick and simple, and fine with two options. With three or more, similar options split their fans, and a choice many people dislike can win.

Instant runoff (IRV)

The winner always has more than half the votes in the final round. But an option that's everyone's second choice can be knocked out early.

The tournament (Condorcet)

Finds the option that beats every other one head to head, when there is one. It needs a tiebreaker for loops, and it's slow to count by hand.

Keeping score (Borda)

Rewards the option that's high on the most lists, and puts every option in order. Piling on lots of nearly identical options can tip the points.

When a city elects a mayor, people argue about this seriously, and different places make different choices. For nine friends picking dinner, the goal is simpler: find the dinner the whole group will be happy with.

That's pizza. It's nobody's dream dinner, but it's nobody's nightmare either, and everyone's happy to eat it.

So they get pizza.

Whichever way you count, one idea beats them all: ask people to rank, instead of picking just one. A ranking tells the group what you love, what you'd be fine with and what you'd rather skip. A show of hands throws all of that away.

Next time your group can't decide, try ranking.

The end.

Told by the makers of Bestof, an app for ranked votes with friends and family.