
Friendship Paradox - Xcelerate
http://en.wikipedia.org/wiki/Friendship_paradox
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murbard2
This is established by making a one-step random walk in the friendship graph.

Things get more interesting when you start taking longer walks. If you take a
long enough walk in a (strongly connected) graph, the probability of ending up
in a particular place becomes independent of your starting point.

In fact, social graphs are said to be "fast-mixing", which means that "long
enough" is typically only O(log n). In contrast, if you were walking in a two
dimensional lattice, "long enough" would be O(sqrt n). This is the idea behind
the "6 degrees of separation" factoid.

So what is the limiting probability distribution? That's actually the
pagerank.

Which means that if friends randomly pass on a token, it's likely to end up in
the hands of someone very influential with a lot of friends. It's been used
for vaccine delivery.

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jiggy2011
I wonder if this can be exploited for business networking purposes. Simply
choose a person in your "network" and ask them to introduce you to one other
person they know and repeat with the new person.

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jdmichal
I wonder whether people would tend to introduce you more influential friends,
over less influential friends, as a kind of status display. You could
potentially "climb" faster than a random walk would.

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lsc
All of the guided "ask X to introduce you to Y" systems that I have seen
are... poorly implemented. The thing is, asking for an intro is complex; it
depends on your relationship with the person doing the introduction, and with
their relationship with the end target, and with how beneficial the potential
relationship between the introduced parties is perceived to be.

You have a limited number of "waste your more important contact's time"
tokens. You get more when you successfully introduce someone who is useful to
your higher-status contact,

The odd thing is, even in an unsuccessful match, where you introduce two
people and they don't establish a relationship they both find pleasant, if you
connect a lower-status contact with the higher-status contact, even if the
match is unsuccessful, you are still seen to have done your lower-status
contact a favor, even though you have annoyed the higher status contact, so if
the lower-status contact is someone you want to curry favor with, it might
make sense to introduce them even if there is a lower probability of them
forming a mutually profitable relationship with the higher-status contact, but
normally it's a matter of "how interesting is the potential relationship
between the two people I am introducing," which takes some thought and often
times means not making the introduction.

The upshot here is that I'm not going to just right out introduce two of my
contacts. I mean, I will if I think they can have a beneficial relationship,
but I generally feel pretty weird when someone directly asks me for an intro
to another specific person, rather than 'Hey, do you know anyone who is good
with X" \- because with the latter, I can talk to each person individually,
and I can silently drop the whole thing without telling the other they were
rejected, whereas if X asks me to introduce them to Y, and either Y says they
are not interested or I think I would annoy Y, then I've gotta reject X, which
can be awkward.

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andrewstuart2
I may be oversimplifying, but thinking of it at this extreme helped me intuit
a bit better.

Imagine 1,000,001 people. One of them is friends with the rest, all of whom
only have this one friend. The average number of friends a person has is 2,
but the aggregate average for their friends is 1,000,000.

So most social graphs probably look like a spoke-hub where a minority of
people have a very large number of friends.

~~~
visakanv
An excellent way of thinking about it.

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jiggy2011
This might explain why introverts tend to think that everyone else is more
extrovert than them, there's probably a lot more introverts than we realise
but we're just less likely to meet them.

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jokoon
I'm not sure, but my intuition tells me there's half introverts, half
extraverts. (introversion/extraversion is a spectrum).

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dredwerker
Its not just your intuiton the bell curve tops outs squarely in the middle of
the two not with two nice peaks. I found this out looking in to Myers briggs(I
think its very qustionable). People can never work out whether I am introvert
or extrovert.

~~~
evincarofautumn
Yeah, Myers-Briggs seems only worthwhile if you’re an outlier on a particular
trait. It’s almost misleading to report which side of the mean you’re on if
you’re only a few percent to one side.

For example, I’m near the average on thinking vs. feeling and judging vs.
perceiving, so I don’t consider those traits terribly important or
informative. However, I am moderately more introverted than extraverted and
significantly more intuitive than sensory. Then again, I don’t need a
personality quiz to know that!

Any time you try to reduce people to a few traits—Myers-Briggs, the Enneagram,
whatever—you lose so much information that the exercise becomes nearly futile.

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philh
If someone asks, I say that I'm ITP. I deliberately forgot whether the last
test I took showed me as slightly S or slightly N, and introspection doesn't
reveal a preference between them.

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frandroid
\- The notation for that is IxTP. \- Introversion doesn't reveal the
preference between the two values of the second letter because it measures the
first letter. :)

~~~
philh
\- Thanks, that makes sense.

\- Introspection, not introversion.

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andrey-p
That's actually quite depressing. "You are always surrounded by people who are
more popular than you."

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kstenerud
Actually, I prefer it that way. Let other people deal with the hassle of
dealing with people. My greatest fear is discovering too late that something
I'm doing will make me famous.

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tzs
> My greatest fear is discovering too late that something I'm doing will make
> me famous

Careful. That quip is almost good enough to become famous for.

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sjwright
An even simpler explanation:

Start with the baseline assumption that people are broadly similar to the
people they're friends with -- i.e. socialites are friends with socialites,
loners are friends with loners.

Overlay that with the observation that you're more likely to be friends with
someone who has lots of friends, and less likely to be friends with someone
who has few friends.

Consider the extremes: You're certain to be friends with someone who is
friends with everyone, and certain to not be friends with someone who has no
friends.

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cJ0th
I don't think it is a paradox when you look at it from a "better" perspective.
Just plot a graph displaying the frequency people have x friends. Chances are,
there are some outliers with enormous amounts of friends who thus push the
average.

I think it is not as much a paradox but rather a good demonstration of how the
average can be an inappropriate measure to describe some samples.

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sjwright
Another simple explanation:

Imagine that there was one single person who was friends with all 7 billion
people on Earth. Assuming nobody else had more than about 250,000 friends,
this would cause every other person on the planet to have fewer friends than
their friends have, on average. That one person skews the mean.

What happens in reality is of course much, much more subtle.

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mariusz79
Oh, so now I know why I have no friends.. Someone must be at the very bottom
of this pyramid. :)

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exo762
I can be your friend.

The popular one.

xD

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pizza
Good article by Strogatz, with clear explanation:
[http://opinionator.blogs.nytimes.com/2012/09/17/friends-
you-...](http://opinionator.blogs.nytimes.com/2012/09/17/friends-you-can-
count-on/)

~~~
clairity
yay for strogatz! he was one of my favorite math profs in school because he
really knew how to explain counter-intuitive phenomena like this.

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goblin89
This is a fun property of scale-free networks in general
([https://en.wikipedia.org/wiki/Scale-
free_network](https://en.wikipedia.org/wiki/Scale-free_network)).

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gitonup
Head Squeeze did a bit on this a while ago, as applied to Twitter:
[https://www.youtube.com/watch?v=Z_15zbgNpHk](https://www.youtube.com/watch?v=Z_15zbgNpHk)

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Paul_S
Can you really have more than 1 or 2 friends? You only have two kidneys and a
friend is someone you'd be willing to give a kidney to (compatibility aside).

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mehrdada
Yes. You can oversubscribe your friends to your kidneys. You just have to be
willing to give them, but that does not need to actually happen. You'll be
fine as long as you pick your friends wisely.

~~~
Turibur
Think of it as a farm of virtual machines.

Lets say the total amount of RAM in your cluster is X. Depending on the
average usage in your farm, you might still be able to assign 2X to your
virtual machines because the average usage for a machine is 50% or lower.

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taliesinb
When I was working on [http://blog.stephenwolfram.com/2013/04/data-science-of-
the-f...](http://blog.stephenwolfram.com/2013/04/data-science-of-the-facebook-
world/), a lot of bizarre results (such as a huge gender difference in number-
of-friends for people older than 40) went away after I took into account the
friendship paradox. It would be really interesting to revisit that anomaly and
try to explain why.

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_RPM
I don't have any friends, am I excluded?

~~~
sjwright
No, you're just a divide-by-zero error.

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dangayle
I've never heard this before. It kinda hurts my brain a little to think about.

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vacri
If you think about it like a computer network, most nodes have fewer
neighbours than their neighbour nodes. Most nodes are endpoints with only a
few neighbours, but some nodes are networking midpoints with a lot of
neighbours, and every endpoint knows at least one midpoint.

On a network segment with one gateway and ten endpoints, all nodes can see ten
other nodes... except the gateway, which can see more nodes outside the
segment. The average is therefore higher than ten, so most nodes see less than
the average.

Hrm, I'm not sure if that clears it up at all. Maybe :)

~~~
dangayle
That makes good sense. Yeah, thanks for clearing that up

