Why Can’t Anyone Agree on the Best Pizza Topping? The Math Behind It

A Hawaiian and a pepperoni, side by side. One of these is an argument. Photo: Avelludo, CC BY-SA 4.0, via Wikimedia Commons.

Run a pizza topping poll three different ways and you will get three different winners. Nobody is lying and nobody is bad at counting. The method decides the answer before anybody votes.

Here is what each method actually measures.

Method one: rate everything out of five

Ask a hundred people to score thirty toppings from 1 to 5 and almost everything lands between 3.1 and 3.9. Pepperoni gets 4.2, mushrooms get 3.8, and the gap that decides the winner is smaller than the difference between a person who rounds up and a person who rounds down.

Ratings also punish anything divisive. Pineapple collects a pile of 5s and a pile of 1s, which average out to something forgettable in the middle. The scale cannot tell the difference between “everyone is lukewarm about this” and “half the country loves it and half is offended by it.”

Method two: pick your one favourite

This looks cleaner and has a worse problem: similar options eat each other.

Pepperoni, sausage, bacon and ham are four versions of the same answer. Somebody who wants meat has to spend their single vote on one of them, so the meat vote arrives split four ways. Mushrooms face no such competition and can win a poll in which most voters wanted meat.

Political scientists call this vote splitting. It explains how a topping nobody calls their favourite can still finish first.

Method three: two at a time

Show two toppings, take a winner, show two more. Repeat a few thousand times across a few thousand people.

Each question is small enough to answer instantly and specific enough to mean something. Pepperoni against mushrooms is a real question. Pepperoni against bacon is a real question. Neither is affected by what else is on the list, which is the whole point — adding a thirty-first topping cannot change how the first thirty did against each other.

This is the same idea behind chess ratings. Arpad Elo built his system on the results of individual games rather than on anyone’s opinion of a player’s overall strength, and it has outlived every alternative because head-to-head results are hard to argue with.

So which topping actually wins

That depends on which question you asked.

If you want to settle it for yourself, the thirty-two topping version on YouPickBest runs on the third method. Pepperoni, mozzarella, mushrooms, olives, bacon, sausage, ham, pineapple, anchovies, artichokes and twenty-two more, compared in pairs until an order falls out.

The chain question gets the same treatment. Domino’s, Pizza Hut, Papa John’s, Little Caesars and twelve other chains go head to head in pairs, which is a harder test than it sounds: most people have only ever ordered from whichever one delivers to their street.

Anchovies are on the topping list, by the way. Somebody has to defend them.

 

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