# Measuring Digital Influence

Michael Wu on TechCrunch touches upon what I have long thought is the fundamental problem with attempts to measure someone’s influence in social networks.

One of the reasons that brands don’t understand digital influence is
because they don’t seem to realize that no one actually has any
measured “data” on influence (i.e. explicit data that says precisely
who actually influenced who, when, where, how, etc.). All influence
scores are computed from users’ social activity data based on some
models and algorithms of how influence works. However, anyone can
create these models and algorithms. So who is right? How can we be
sure your influence score is correct?

Influence is not measured directly, it is measured through other variables (likes, retweets, etc.) that stand proxy for influence. So instead of this $influence \sim f(\dots)$ you have this $g(\dots) \sim f(\dots)$, which is not by itself a problem if you make sure that the variables in your influence model $f(\dots)$ are different from the variables in the model $g(\dots)$ standing proxy for influence.

But this is not easy to do when the thing that you are trying to measure and predict is something that people care about and can influence by altering their behavior.

As we learn from the behavior economics of humans, when we put a score
on something, we create an incentive for some people to get a better
score. This is human nature. Because people care about themselves,
they care about any comparisons that concern them, whether it is their
websites, cars, homes, their work, or just themselves. Some would go
so far as to cheat the algorithm just to get a better score. In fact,
Google’s PageRank algorithm has created an entire industry (i.e. SEO)
around gaming their score.

It’s not so hard to “cheat the algorithm”. Influence scores that include variables that you control directly (how many posts you make, for example) can be gamed by simply changing your own behavior. But even influence models that carefully avoid such variables by only including variables that represent what other people think of your behavior can be cheated.

Reciprocity is one way that this is done. Bob tweeted something you couldn’t care less about, but by retweeting Bob you’re helping to nudge up his influence score (on Klout, say), and you do that because Bob is the kind of guy who rewards retweets with retweets (or follows with follows, likes with likes, etc).

Suppose that an influence model $f(...)$ has as one of its variables how many tweets and retweets you make. The model is validated against $g(...)$, the proxy for influence, which has as one of its variables the number of times your tweets are retweeted by someone else. Now, a set of people who reciprocate retweets among themselves will have not only their $f(...)$‘s go up, but those scores will also correlate with $g(...)$, leaving the model’s designers/promoters with the impression that they are predicting influence. But all you have here is a bunch of people promoting one another’s influence scores.

One way that an influence modeler could hedge this reciprocity attack on his model would be to measure, for every retweet, the length of the shortest retweet cycle. If you retweet Bob and he retweets you, the cycle is length 1. If you retweet Bob, Bob retweets Alice, and Alice retweets you, the cycle is 2. The idea is that the longer a cycle is the more likely it is evidence of genuine influence; very short cycles smell like reciprocity.

The problem with this approach is that it makes the concept of influence look like an asymmetrical relationship: if you influence Bob, Bob cannot influence you, otherwise it’s classified as reciprocity. But a key stylized fact of social networks is that they are mostly made up of groups of people who identify with one another, and sometimes the group is self-contained.. there is no path to a node outside the group. Nobody would be happy with construing the concept of influence in such a way that it can’t apply locally, with people in the group influencing each other.

Did you retweet/like/comment Bob because he influenced you or did you do it in anticipation of his reciprocity? The intention seems inscrutable from data on social network graph alone.

Measuring influence is hard, and it is especially hard when people have an incentive to manipulate the measurement of it. Personally, I think this is just an instance of a larger problem all over the internet. It’s just so damn hard to find signal in data that is costless to generate. There is no cap on the number of tweets you can make, the number of likes you click, the number of posts you make, and so on. If there were some external friction placed on these activities so that people had to ration them, the tide of noise would recede and bring more signal into view.

So here’s an idea: make every tweet cost three minutes of CPU time, during which your machine runs some computations for a socially useful distributed computing project (climate prediction, genome sequencing, alien searching.. you choose). The friction caused by this would not only cause people to ration their social networking, greatly improving the signal-to-noise ratio, but the friction itself would benefit society. Who could complain (except the spoofers)?