---
title: "Conditional Importance Networks: A Graphical Language for Representing Ordinal, Monotonic Preferences over Sets of Goods"
authors:
  - "Sylvain Bouveret"
  - "Ulrich Endriss"
  - "Jérôme Lang"
doi: ""
url: "https://ijcai.org/proceedings/2009/22"
pdf: "https://ijcai.org/proceedings/2009/0022.pdf"
venue: "Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence"
year: 2009
pages: "67-71"
track: ""
keywords:
---

# Conditional Importance Networks: A Graphical Language for Representing Ordinal, Monotonic Preferences over Sets of Goods

Sylvain Bouveret, Ulrich Endriss, Jérôme Lang

*Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence*, pages 67-71.

## Abstract

While there are several languages for representing combinatorial preferences over sets of alternatives, none of these are well-suited to the representation of ordinal preferences over sets of goods (which are typically required to be monotonic). We propose such a language, taking inspiration from previous work on graphical languages for preference representation, specifically CP-nets, and introduce conditional importance networks (CI-nets). A CI-net includes statements of the form if I have a set A of goods, and I do not have any of the goods from some other set B, then I prefer the set of goods C over the set of goods D. We investigate expressivity and complexity issues for CI-nets. Then we show that CI-nets are well-suited to the description of fair division problems.Sylvain Bouveret, Ulle Endriss, Jérôme Lang