ysights.algorithms.paradox

Visibility Paradox Analysis

This module provides functions for analyzing the visibility paradox in social networks. The visibility paradox describes situations where content created by agents receives asymmetric visibility compared to content they see from their neighbors.

The module includes: - Visibility paradox detection and statistical significance testing - Comparison of user visibility vs. neighbor visibility - Population-size effects on the paradox - Null model generation for hypothesis testing

Key Concepts:

The visibility paradox occurs when there’s an imbalance between: 1. How much of your neighbors’ content you see (inbound recommendations) 2. How much your neighbors see your content (outbound visibility)

This can lead to situations where most users feel their content is under-represented in their neighbors’ feeds, even though the aggregate statistics might suggest balance.

Example

Detecting the visibility paradox:

from ysights import YDataHandler
from ysights.algorithms.paradox import visibility_paradox, user_visibility_vs_neighbors

# Initialize data handler and extract network
ydh = YDataHandler('path/to/database.db')
network = ydh.social_network()

# Calculate visibility paradox with statistical testing
paradox_results = visibility_paradox(ydh, network, N=100)

print(f"Paradox score: {paradox_results['paradox_score']:.4f}")
print(f"Z-score: {paradox_results['z_score']:.4f}")
print(f"P-value: {paradox_results['p_value']:.4f}")

if paradox_results['p_value'] < 0.05:
    print("Visibility paradox detected (statistically significant)")

# Compare user visibility with neighbor averages
user_vis, neighbor_vis = user_visibility_vs_neighbors(ydh, network)

import numpy as np
print(f"Average user visibility: {np.mean(user_vis):.2f}")
print(f"Average neighbor visibility: {np.mean(neighbor_vis):.2f}")

References

The visibility paradox is related to concepts from: - Friendship paradox (Feld, 1991) - Attention inequality in social networks - Filter bubble and echo chamber effects

See also

visibility_paradox(): Main function for paradox detection user_visibility_vs_neighbors(): Compare visibility metrics visibility_paradox_population_size_null(): Analyze population size effects

Functions

user_visibility_vs_neighbors(YDH, g)

Calculate the visibility for each user in the graph and the average of its neighbors' visibilities.

visibility_paradox(YDH, g[, N])

Calculate the visibility paradox metric for a given YDataHandler and graph.

visibility_paradox_population_size_null(YDH, g)

Calculate the visibility paradox metric for a given YDataHandler and graph, considering the population size.
ysights.algorithms.paradox.user_visibility_vs_neighbors(YDH, g)[source]

Calculate the visibility for each user in the graph and the average of its neighbors’ visibilities.

Parameters:
Returns:

ysights.algorithms.paradox.visibility_paradox(YDH, g, N=100)[source]

Calculate the visibility paradox metric for a given YDataHandler and graph.

Parameters:

  • YDH (YDataHandler) – YDataHandler, the data handler containing the YSocial simulation data

  • g – networkx.Graph, the social network graph

  • N – int, number of null models to generate for statistical testing

Returns:

ysights.algorithms.paradox.visibility_paradox_population_size_null(YDH, g, N=10, subject_to_rec=[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])[source]

Calculate the visibility paradox metric for a given YDataHandler and graph, considering the population size.

Parameters:

  • YDH (YDataHandler) – YDataHandler, the data handler containing the YSocial simulation data

  • g – networkx.Graph, the social network graph

  • N – int, number of null models to generate for statistical testing

  • x – float, fraction of users to randomize (between 0 and 1)

Returns: