# The Medium Partnership — what makes it sustainable?

## A basic assessment based on a simple quantitative model

Being a full-time worker from Hong Kong who writes occasionally for self-entertainment, I am often curious of how Medium actually works in particularly after its Partnership Program introduced.

The ideology of providing sufficient incentive for writers to produce high-quality articles (which will eventually benefit the Medium community itself) is intuitive and understandable. The amount of money distributed to authors will be based on a clapping system plus a mysterious algorithm — in which Medium never reveals its magic recipe — that ultimately measure quality from various dimensions (reading time, number of shares, etc.).

Yes, quality should be the only thing that matters here. But an interesting feature of the Program is you DO NOT have to become a Medium member before locking your posts and earning money! Given that the pool of money to be distributed to authors should largely be from members’ subscription fees, will the Program be really sustainable in longer run?

### A basic model to illustrate the problem

To more closely look into the issue, I tried to establish a simple math model — trust me, it is really simple — which includes the following variables:

• Let user i be u_i .
• Let the member fee paid by user i be P_i
• Let the number of articles written by user i be a(u_i)
• There are n users in the community, i.e. u_1, u_2, …, u_n

The number of articles available for user j to clap will be ：

Now assume that all users pay as members and join the Partnership Program, and let the amount of money earned by an article be solely determined by number of claps. Suppose all members evenly distribute their claps to all articles, their member fees would be divided into smaller albeit equal portions.

For example, if the membership fee is set to be \$4 and there are four articles for me to clap, each article will receive \$1 from me when I treat them all equally. Let’s define w(u_j) as the amount of money received by user j,

Its respective proportion of money to the total sum of membership fees collected will be

Observation 1: write more, earn more.

#### A simple scenario to start with

Perhaps you will find the above formula rather difficult to comprehend. It is not. Consider a special case when everybody just publishes one article. Then,

The amount of payout and its portion in regard to the whole money pool：

Since all members are paying the same amount of fees：

Equations will eventually be reduced into the following form：

Observation 2：the subscription fee will be fully compensated by the Partnership Program earnings. Every member is rewarded equally

#### What if non-members also join the partnership

Suppose k out of n members do not pay but lock posts so as to earn money. (P_i=0) As a result, the number of members and the pool of money for distribution will be down to (n-k) and (n-k)P respectively.

Now if we further assume the locked articles by k non-members also receive claps from members, without any discrimination. The pay-outs become:

Observation 3：Members will not be able to cover their subscription fees anymore
Observation 4：Non-members, albeit paying zero, take a bigger share.

### Some points to make before moving further

A majority of Hong Kong people are reluctant to pay for read, especially for those published online.

From a purely economic point of view, a rational agent, should always write and lock their posts without joining the membership, as this will maximize their profit. Non-members will keep on increasing and diluting the share of profit. In worst case, the profit-seekers crowd out all members, eventually breaking down the partnership program.

Nevertheless, after further discussing the case with other bloggers / writers from Hong Kong, this may not be the only case due to:

1. Writing on Medium is time-consuming and consider the amount of money received is not really that much, it is not worth doing so.
2. Some people are willing to buy good services.
3. The model is too simple to explain the real-life situation.

The famous blogger “Relgitsjg (史兄)” also supplements with a crucial point,

Read-only members in the Medium Community besides authors should not be neglected. They paid the membership fees for an excellent reading experience, but do not write for the time being. Nor will they join the Partnership Program to earn extra money. If such population is sufficiently large enough relative to other groups in the community, this should mitigate the above problem.

#### We therefore introduce read-only members to the model…

• Number of users in the community remain to be n
• We set those read-only non-members as zero.
• Some h out of n are members, without writing anything (a=0)。They clap articles indifferently.
• The remaining n-h are authors (a=1). Some k pay zero fees.
• Number of members that write will be n-h-k.

The pay-out formula will be like:

Observation 4：Read-only members matter (a lot!)
Observation 5：No problem at all if member size is big enough

To obtain the break-even point (w=p) or (w>p)，the equation can be further rearranged into the following inequality.

Observation 6：To sustain the whole system, ”read-only members” should always be larger than “write-only non-members”

### Final Remarks

• To me, Partnership Program is a bold experiment by the Medium team. We can already see so many critical opinions from both sides who support or object the idea since its implementation.
• From the above, it is trivial to see that when more and more people are willing to pay for high-quality write-ups, the Program should continue to thrive even a relatively small group of people — writing without contributing monetarily to the community — exist.
• While the guidelines allow non-members to join the Partnership, I believe the Medium team remains optimistic about the ultimate change in reading/writing behavior (without seeking support from ads) and this is exactly what they are now making an effort to achieve (driving growth in members), so that they can expand and tap for a bigger market.
• Indeed, the quantitative model is a very crude one and some of the assumptions are plausibly strong that are not entirely reflecting the genuine situation. These are for illustrating my ideas logically but not for predicting / estimating anything precisely.
• Finally, I apologize for any miscalculations and typos made. All errors will be mine.

Originally published in Cantonese at Medium.com on August 12, 2018. This translation is for experimental purpose only.