One cannot understand influence without knowing how to quantify it.
What does it mean to have influence?
Dictionary.com provides the following definition:
“1. a person or thing that influences: 2. a person who has the power to influence many people, as through social media or traditional media”
This is not helpful. It does not provide an indication of what could be a quantifiable metric to measure “influence”.
BusinessDictionary.com provides a better clue:
“Individuals who have the power to affect purchase decisions of others because of their (real or perceived) authority, knowledge, position, or relationship.”
Per this definition, one could quantify the change in the overall purchases as a result of a given influencer’s actions.
The word “influencer” is usually used in relation to media figures with large social media following. Justin Bieber or Paris Hilton can serve as an example.
It is true that if one of them endorses a product, such as a new line of perfume or a movie, it is likely to impact the sales. These sales can be quantified and therefore one can confirm that these people are indeed influencers. This seems to validate an assumption that large social media following equals an influencer.
However, chairman of the Central Bank with 0 social media presence has the power to impact purchase decisions to a much larger degree; By changing interest rates.
Does this mean he/she is an influencer? Per this definition, yes.
It is not a given that somebody with a high follower count will be able to make an impact. A recent New York Times story revealed that a significant portion of the Twitter following is fake.
The number of followers is not a conclusive indication of whether somebody is or is not an influencer.
Furthermore, are we ready to accept that influence can only be measured by the ability to affect purchases? It would be too limiting and thus incorrect.
Cambridge Dictionary provides a more holistic definition:
“Someone who affects or changes the way that people behave.”
This seems to be a broad enough definition, but it once again leaves us with no quantifiable metric.
Let’s try to put this into perspective.
As proved before, Paris Hilton (17.8M followers ) is indeed an influencer. She has the power to affect people behavior that can be quantified in the value of purchases that result from that behavior change.
Vitalik Buterin (630k followers ) is also an influencer. Had he endorsed a line of perfume it would likely have little result in sales. However, his endorsement for a crypto-related startup would result in a massive investment round and talent flocking to the company.
This change of behavior can be quantified in monetary terms. None of them are purchases.
Paris Hilton has also dabbed in crypto. She endorsed Lydian Network that per her tweet was going to raise $100M in an ICO . The project raised ca. 1/10 of its goal .
The fact that the project underperformed is not a conclusive evidence that Hilton has no influence. However, it is reasonable to assume that she has little, if any, ability to help crypto startups raise money by endorsing them. One could argue that her endorsement can be counterproductive. It may decrease the legitimacy of the project in the eyes of industry insiders.
Why is that? There are probably more people who follow Hilton’s endorsements than crypto-insiders who will be put off by them. It should still be a net gain.
This perspective is missing an important caveat: an average insider will have much more resources at his/her disposal than Hilton’s average follower.
Among Butterin’s followers, there are multiple people who could single-handedly provide $100M funding.
Some of these people may even follow Hilton. It is likely to be for entertainment purposes rather than in order to gain investment advice. Despite getting their attention, she is not influencing them in this context. She still might be able to influence them in other contexts, e.g. choice of perfume.
Both of the above count for a change of behavior. However, there is a quantitative difference between influencing somebody for a $100M investment and for a $100 purchase of perfume.
Therefore, a true influence seems to be a result of combining the following:
How many people pay attention
How many of these people and to what degree are going to change their behavior
How many resources those people command on average
Definition and Metric
I suggest the following definition of “influence” that encompasses all three points:
“Ability to cause reallocation of capitals.”
This definition refers to various types of capitals that exist in our society. These are primarily: financial, human, social and political capitals. They are exchangeable. 
Reallocation may happen not only between the type of capital but also the object of allocation in one company or another, this or that product, left or right candidate.
This metric is quantifiable because the capitals can be exchanged for one another. Therefore, any sort of influence – be it in fashion, politics, business or pop-culture can, in theory, be boiled down to this metric.
Reallocation of capitals is quantifiable in theory. Tracking it, however, is extremely hard, if not impossible.
Furthermore, per this definition, one needs to track ability. Knowing how influential somebody has been in the past (value of capitals they caused reallocation of) is not directly translatable to the current ability.
There is a high correlation. In most cases, this would be a metric providing accurate results. However, one can identify scenarios in which it would be vastly inaccurate. An example of such a scenario is an investment that an influencer has caused a lot of capital to get allocated to. This turned out to be a terrible decision and now people who listened to him or her are disappointed. They will not listen again.
Another way to think of this is this: somebody who spent $1M is not necessarily a millionaire. They did have a $1M in the past, but it’s not a conclusive evidence of whether they have one now.
This metric accurately tracks past influence, but not present. The right metric would provide insights into the state of affairs in the current moment.
This leaves us with one candidate — attention.
Attention is the common denominator in all interactions that result in a reallocation of capitals.  Therefore by tracking who pays attention to whom one can predict the ability for causing said reallocation.
If A and B pay attention to C, then C is an influencer. How influential is C depends on the level of influence A and B have themselves.
Often attention flows bi-directionally. C can both influence B and be influenced. Nevertheless, in most cases, some imbalance will remain, where one person is more influential than the other.
To put this in perspective, think of a group of friends where some people in the group are into fitness. C has been working out for many years and is in a great shape. She has knowledge of nutrition and has done many sports. Both A and B listen when she gives them advice.
B started getting seriously into this topic a couple of months ago. He is keen to learn and does a lot of his own research. Sometimes he brings up information C had not been aware of, so she pays attention to what he has to say.
A is a couch potato. He went to the gym for the first time recently and he is in a bad shape. His friends might respect his expertise in other fields — but when it comes to fitness, they will disregard his opinions.
It is likely there is somebody else that C pays a lot of attention to. Perhaps a personal trainer or internet fitness guru. By influencing C, D is indirectly influencing A and B. Even if they are not aware of it.
These dynamics exist both in small and large groups.
Attention and Money
The graph could as well illustrate flows between Bitcoin wallets. This is no coincidence.
Attention is an equivalent of money.
One can cause reallocation of capitals indirectly by impacting others. One can also cause reallocation of capitals with the capital in their control.
Maciej Ołpiński introduced a useful framework to think about this. In Userfeed’s whitepaper, he talks about “horizontal relevance”, which is context independent. This is money and assets, which are universally acceptable. “Vertical relevance” is context-dependent, this could be social standing, reputation – or rankings and feeds. 
I’d like to suggest another framework — thinking about this in the context of entities and identities.
Entities’ influence is measured in money.
Identities’ influence is measured in attention.
This is helpful in understanding influence beyond the context of people. And it is important to do so.
Each Bitcoin wallet is its own entity. Its influence depends on how much money it stores. A person can create a thousand wallets and thus control a thousand entities. A single wallet can be controlled by multiple people.
The same dynamic applies to identities.
We can have multiple identities. Anonymous Twitter accounts often gain a significant level of influence in the crypto community. This influence is detached from the ‘real’ identity of the person(s) controlling an account. In fact, multiple people can control this online identity.
Anonymous identities can become more influential than the ‘real’ ones. In fact, “Satoshi Nakamoto” identity is almost certainly more influential than the real identity of the person or people behind it.
But these are outliers in a peculiar community. As a society, we are distrustful of anonymity and we discount anonymous contributions.
We have developed methods for evaluating the credibility of real name identities. We use job, academic and other titles. We associate people with institutions they represent or accolades they received. Reputation transfers rely on 3rd parties as much as money transfers.
Replacing financial 3rd parties is not enough to build a decentralized society. We also need a way to replace reputation 3rd parties.
Key to doing that is measuring reputation for individual identities. And we can’t measure what we can’t quantify.
Thanks to Maciej Ołpiński and Tomasz Kolinko for reading the draft of this post.
 Money can buy work and expertise, reputation or political support. Human capital – one’s skills, abilities, knowledge and time can be exchanged for money, reputation or political support. Reputation and connections may allow one to raise or make money, gain political capital or convince people to lend their skills and time to their cause. Finally political capital may lead to winning elections, which grants one direct access to resources (money, human capital) and can affect his/her reputation in the communities he or she chooses to support.
 Examples may include: convincing somebody to buy something, to invest in a business, to apply or accept a job, to move from one place to another, to donate money to a political campaign etc.