Learning through the Grapevine: The Impact of Noise and the Breadth and Depth of Social Networks

TL;DR

This paper investigates how social network structure and noise affect information learning, highlighting thresholds for effective communication and strategies to optimize learning despite message mutations and failures.

Contribution

It introduces a model analyzing how depth and breadth of social networks influence learning under noisy conditions, providing thresholds and strategies for optimizing information transmission.

Findings

Learning diminishes with increased depth due to noise buildup.

Limiting breadth can improve the signal-to-noise ratio in message transmission.

Optimal learning strategies involve capping either depth or breadth based on mutation rates.

Abstract

We examine how well people learn when information is noisily relayed from person to person; and we study how communication platforms can improve learning without censoring or fact-checking messages. We analyze learning as a function of social network depth (how many times information is relayed) and breadth (the number of relay chains accessed). Noise builds up as depth increases, so learning requires greater breadth. In the presence of mutations (deliberate or random) and transmission failures of messages, we characterize sharp thresholds for breadths above which receivers learn fully and below which they learn nothing. When there is uncertainty about mutation rates, optimizing learning requires either capping depth, or if that is not possible, limiting breadth by capping the number of people to whom someone can forward a message. Limiting breadth cuts the number of messages received but also decreases the fraction originating further from the receiver, and so can increase the signal to noise ratio. Finally, we extend our model to study learning from message survival: e.g., people are more likely to pass messages with one conclusion than another. We find that as depth grows, all learning comes from either the total number of messages received or from the content of received messages, but the learner does not need to pay attention to both.