Why No App Can Ever Split Things Perfectly Fairly

Two researchers, Tomer Ezra and Tamar Garbuz, just published a mathematical proof about splitting up things that can't be divided. Think of a house, a car, a prized painting, or the worst chores in a shared apartment. There's a fairness standard called the "maximin share" — basically, the best share you could guarantee yourself if you cut everything into equal piles and let everyone else pick first. Their result: in some situations, no method on Earth can get everyone close to that share.

What's new is how bad it can get. A 2021 paper showed that in the worst case someone could end up short by about 1 in n⁴ (with n being the number of people) — tiny for big groups. The new proof shows the shortfall is far larger, shrinking only very slowly as groups grow. Translated: fairness guarantees fall apart much faster than we thought as more people are added to the pile.

Why does abstract math matter? Because these bounds are the ceiling for every real system that divides things. Split-the-bill apps, inheritance settlements, cloud computing resources handed out to apps, ad slots sold to advertisers — all of them run on allocation algorithms. Knowing the true limit tells engineers when to stop chasing perfect fairness and aim for the best achievable compromise instead.

The paper also sharpens the small cases. With just four people and eleven items, fairness can't beat about 20/21 for desirable goods (up from 39/40), and about 31/30 for chores — meaning one person can be forced to take roughly 5% less than fair, or do 3% more work, even in a tiny group.

The catch: these are carefully constructed worst-case scenarios, not everyday life. Real splits are usually far fairer. So don't panic — just know that perfect fairness has a price no algorithm can pay.