# Mutual Assent or Unilateral Nomination? A Performance Comparison of Intersection and Union Rules for Integrating Self-reports of Social Relationships

## TL;DR

This study compares intersection and union rules for combining self-reports of social relationships, finding mutual assent (intersection) generally yields more accurate network inferences across various data sets.

## Contribution

It provides empirical evidence and theoretical analysis showing mutual assent outperforms union in social network data integration, considering error rates and network sparsity.

## Key findings

- Mutual assent performs better across all examined data sets.
- Theoretical analysis links rule performance to error rates and network sparsity.
- Sparsity favors mutual assent in typical social network scenarios.

## Abstract

Data collection designs for social network studies frequently involve asking both parties to a potential relationship to report on the presence of absence of that relationship, resulting in two measurements per potential tie. When inferring the underlying network, is it better to estimate the tie as present only when both parties report it as present or do so when either reports it? Employing several data sets in which network structure can be well-determined from large numbers of informant reports, we examine the performance of these two simple rules. Our analysis shows better results for mutual assent across all data sets examined. A theoretical analysis of estimator performance shows that the best rule depends on both underlying error rates and the sparsity of the underlying network, with sparsity driving the superiority of mutual assent in typical social network settings.