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What is Influence
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 indicate 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 due to a given influencer’s actions.
The word “influencer” is usually used in relation to media figures with large social media following. Justin Bieber and 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 sales. These sales can be quantified; 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, the chairman of the Central Bank, with 0 social media presence, has the power to impact purchase decisions 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 can 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 leaves us with no quantifiable metric.
Let’s try to put this into perspective.
As proved before, Paris Hilton (17.8M followers ) is an influencer. She has the power to affect people's behavior which 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 had 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, which per her tweet, she would raise $100M in an ICO . The project raised ca. 1/10 of its goal .
The fact that the project underperformed is inconclusive evidence that Hilton has no influence. However, it is reasonable to assume that she has little ability to help crypto startups raise money by endorsing them. One could argue that her endorsement can be counterproductive. It may decrease the project's legitimacy 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, multiple people could single-handedly provide $100M in funding.
Some of these people may even follow Hilton. It is likely to be for entertainment purposes rather than 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 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 do 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 capital that exist in our society. These are primarily: financial, human, social, and political capitals. They are exchangeable. 
Reallocation may happen between the type of capital and the object of allocation in one company or another, this or that product, left or the 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.
The reallocation of capital is quantifiable in theory. Tracking it, however, is extremely hard, if not impossible.
Furthermore, per this definition, one needs to trackability. 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 was a terrible decision, and now people who listened to him or she is 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 conclusive evidence of whether they have one now.
This metric accurately tracks past influence but is not present. The right metric would provide insights into the state of affairs at the current moment.
This leaves us with one candidate — attention.
Attention is the common denominator in all interactions that result in a reallocation of capital.  Therefore, by tracking who pays attention to whom, one can predict the ability to cause said reallocation.
If A and B pay attention to C, C is an influencer. How influential C is depends on the level of influence A and B have.
Often attention flows bi-directionally. C can both influence B and be influenced. Nevertheless, some imbalance will remain in most cases, where one person is more influential than the other.
To put this in perspective, think of a group of friends where some people are into fitness. C has been working out for many years and is in great shape. She knows 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 research. Sometimes he brings up information C was unaware of, so she pays attention to what he says.
A is a couch potato. He went to the gym for the first time recently, and he is in bad shape. His friends might respect his expertise in other fields, but they will disregard his opinions when it comes to fitness.
There is likely somebody else that C pays a lot of attention to. Perhaps a personal trainer or internet fitness guru. By influencing C, D indirectly influences A and B, even if they are unaware 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 the equivalent of money.
One can cause the reallocation of capital indirectly by impacting others. One can also cause the reallocation of capital 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, such as 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 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 significant influence in the crypto community. This influence is detached from the ‘real’ identity of the person(s) controlling an account. Multiple people can control this online identity.
Anonymous identities can become more influential than the ‘real’ ones. The “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 the reputation 3rd parties.
The key to doing that is measuring the reputation of 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.
 Source: http://www.dictionary.com/browse/influencer, accessed on Feb 11, 2018
 Source: http://www.businessdictionary.com/definition/influencers.html, accessed on Feb 11, 2018
 Source: The Follower Factory, https://www.nytimes.com/interactive/2018/01/27/technology/social-media-bots.html, accessed on Feb 20, 2018
 Source: https://dictionary.cambridge.org/dictionary/english/influencer, accessed on Feb 11, 2018
 Source: https://twitter.com/parishilton, accessed on Feb 11, 2018
 Source: https://twitter.com/VitalikButerin, accessed on Feb 11, 2018
 Source: Paris Hilton is supporting an ICO backed by a man who was convicted of domestic violence, http://www.businessinsider.sg/paris-hilton-backs-ico-lydian-celebrities-endorsing-cryptocurrencies-2017-9/?r=UK&IR=T, accessed on Feb 11, 2018
, accessed on Feb 11, 2018
 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, invest in a business, apply for or accept a job, move from one place to another, donate money to a political campaign, etc.
 Source: Userfeeds – an open protocol for establishing information relevance in crypto-economic networks, https://userfeeds.io/Userfeeds_Protocol_Whitepaper_[Draft].pdf, accessed on 22 Feb 2018