In Defence of Liberty

Driven by data; ridden with liberty.

The Majority Illusion

friendship-paradox-majority-illusion-yaph

Ideas in social media may be less popular than they appear. (Edited: yaph)

After the House of Commons voted to extend its airstrikes against ISIS into Syria, a friend wondered on social media:

I realise the algorithms of social media show you what it thinks you want to see and will agree with. And I realise voting on military intervention had eloquent arguments on both sides it wasn’t just “aghhh go bomb the terrorists” (though that’s pretty much all I heard). But literally 99% of what I have seen and heard since 10:30 last night is outrage at the outcome of the vote so how the fuck is this a democracy?

 

friendship-paradox-majority-illusion-sw-syria

This is ultimately a question about differences between the local perception in a social network, and the national reality among all users. This goes beyond simply having disparities from the country to the friendship circle.

When the polling company YouGov [1] asked respondents if they would “approve or disapprove of the RAF taking part in air strike operations against Islamic State/ISIS in Syria”, a plurality consistently answered that they approved of such military action.

friendship-paradox-majority-illusion-yougov-syria

Labour and Liberal Democrat voters were more apprehensive about launching air-strikes against ISIS in Syria. (Source: YouGov)

The Friendship Paradox

In network analysis, there is the friendship paradox: most people have fewer friends than their friends have, on average.
This is not a true paradox, but a difference between our human intuition and the mathematical truth.

friendship-paradox-majority-illusion-maths-1

friendship-paradox-majority-illusion-maths-2.JPG

A social network may be thought of as an undirected graph, where each person is a node or vertex, and the edges are the requited friendships.

This may be better illustrated through an example. In this graph featured in The Economist [2], four people called Alice, Bob, Chloe and Dave form a network.

friendship-paradox-majority-illusion-economist

Alice has only one friend: Bob. Bob is friends with the other three. Chloe and Dave are also friends. The average number of friends is two: eight friends divided by two people.

Now, we should consider how many friends each person’s friends have. The same person may be counted multipled times.

Alice’s one friend Bob has three friends. Chloe has two friends, Bob and Dave, who have five friends in total. This is the similar for Dave.
Bob’s friends are Alice, Chloe and Dave, who in turn have five friends (counting Bob three times). Hence, there are eighteen friends of friends.

The average number of friends of friends is 2.25 each, greater than the average number of friends, which is two. Some people are more popular than others, and increase the average for the network as a whole.

Active and Inactive

A similar principle arises through analysing a social network, considering binary attributes, such as having red hair and not having red hair. Kristina Lerman, Xiaoran Yan and Xin-Zeng Wu, of the USC Information Sciences Institute [3], separated nodes into ‘active’ and ‘unactive’.

friendship-paradox-majority-illusion-paper

Even though the connections are the same, the perceptions are completely different. (Source: arXiv.)

Under certain conditions, a majority of nodes are joined to ‘active’ nodes, even though a minority of nodes are actually ‘active’.

The local perception greatly differs from the global reality.

The authors called this phenomenon the “majority illusion” [4]. When the attribute is an opinion, there will be circumstances under which a minority viewpoint appears extremely popular for certain users.

When the authors studied actual networks, they found this effect was largest in the disassortative political blogs network, where “as many as 60%-70% of nodes will have a majority active neighbors, even when only 20% of the nodes are active”.

All you saw

This has numerous consequences for social network analysis, epidemics, and marketing strategies.

It is why self-selecting polls on Twitter can be highly misleading [5].
It is why people may overestimate the drug use and alcohol consumption of their peers.
It is why, even though outright opposition to air-strikes against ISIS was unpopular, it may have been all you saw on Facebook.

References

[1] Dahlgreen, W., 2015. Syria air strike approval drops below 50% as Labour support falls. YouGov. Available from: https://yougov.co.uk/news/2015/12/01/support-air-strikes-dips-below-majority/ [Accessed: 29th December 2015]

[2] The Economist, 2013. Why are your friends more popular than you? Available from: http://www.economist.com/blogs/economist-explains/2013/04/economist-explains-why-friends-more-popular-paradox [Accessed: 29th December 2015]

[3] Lerman, K., Wu, X., and Yan, X., 2015. The Majority Illusion in Social Networks. arXiv. Available from: http://arxiv.org/pdf/1506.03022v1.pdf [Accessed: 29th December 2015]

[4] MIT Technology Review, 2015. The Social-Network Illusion That Tricks Your Mind. Available from: http://www.technologyreview.com/view/538866/the-social-network-illusion-that-tricks-your-mind/# [Accessed: 29th December 2015]

[5] Masters, A., 2015. Statistics and Lampposts XXII: Self-Selection. In Defence of Liberty. Available from: https://anthonymasters.wordpress.com/2015/11/30/statistics-and-lampposts-xxii-self-selection/ [Accessed: 29th December 2015]

Advertisements

Information

This entry was posted on December 29, 2015 by in National Politics and tagged , , , .
%d bloggers like this: