Spliddit's goods calculator fairly divides jewelry, artworks, electronics, toys, furniture, financial assets, or even an entire estate between two or more people. You begin by providing a list of items that you wish to divide and a list of recipients. We then send the recipients links where they specify how much they believe each item is worth. Our algorithm uses these evaluations to propose a fair division of the items among the recipients.

# Fairness Properties

## Envy-freeness

A division of goods is envy free if each participant believes that her bundle of goods is at least as valuable as every other participant's bundle, i.e., no participant envies any other participant. While our algorithm may often find an envy-free division, no algorithm can guarantee one.

Our algorithm guarantees a division that is envy free up to one good: A participant would never envy another participant if we removed a single good from the other participant's bundle. In fact, if the contested good is divisible, in the sense that it can be broken down into smaller pieces (e.g., cash, stocks), then we could eliminate envy by removing a hundredth (1%) of it.

## Efficiency

Our algorithm divides the goods in such a way that it would be impossible to find another division that benefits a participant without making another participant worse off.

# Algorithm Overview

We assume that the value a participant derives from a bundle of goods is the sum of points the participant assigns to individual goods in the bundle. Our algorithm then finds the division of goods into bundles that maximizes the product of values derived by participants. The optimization problem is formulated as a mixed integer linear program. This division is guaranteed to be envy free up to one good and efficient, and provably satisfies other approximate fairness guarantees.

**Reference:** "The Unreasonable Fairness of Maximum Nash Welfare", by Ioannis Caragiannis, David Kurokawa, HervĂ© Moulin, Ariel D. Procaccia, Nisarg Shah, and Junxing Wang.