# Aggregating Relational Structures

## TL;DR

This paper extends Arrow's impossibility theorem to higher-arity relations, exploring properties of k-ary relations and establishing an analogue of a graph aggregation result.

## Contribution

It generalizes a fundamental social choice theorem to k-ary relations and introduces new properties and aggregation results for these higher-arity structures.

## Key findings

- Generalization of Arrow's theorem to k-ary relations
- Introduction of natural properties for k-ary relations
- Proof of an analogue of graph aggregation results for k-ary relations

## Abstract

We generalize the Arrow's impossibility theorem--a key result in social choice theory--to the setting where the arity $k$ of the relation under consideration is greater than $2$. Some special but natural properties of $k$-ary relations are considered, as well as an analogue for such $k$-ary relations of Endriss and Grandi's result on graph aggregation is proved.