A Markov Chain is simply a set of states and a set of probabilities describing where an entity in one state is likely to go the next step. It may help to think of the entity as you and the states as places you like to go, but this can also be applied on a macro-level to economics (supply chain, sharing economy, etc.)
There’s some interesting results that, when read as real-life analogies, are quite intriguing.
- We call the initial state is recurrent if the entity is bound to return to its initial state with probability 1 in a finite number of steps.
- If we split all the states up into ‘districts‘, where the entity can go between any two states within the district with probability > 0, then either every state in the district is recurrent or every state isn’t.
- If any state in the district is recurrent, the district is closed – the entity is forever trapped like in Hunger Games (somewhat).
- If there’s only a finite number of states total, there’s at least one recurrent state (or at least one closed district).
- If the entity can go from any state to another with > 0 probability (a case of 2.), every state is recurrent.
So, suppose in our distant dystopian future we have a sharing economy where we rotate living arrangements from house-to-house, what the above results mean are:
- We say citizen has a return guarantee if he/she is bound to return to the first house he/she ever lived.
- If the city is seen as a collection of districts, then either all folks initially in the district get to return to their first home (with guarantee) or none of them.
- But if even one folk is guaranteed a return to their first home, that means the district is closed and everyone is trapped.
- Unless we invent teleportation and the living arrangements in our universe is infinite, we can assume there’s finite houses in this city. Then, there’s at least one folk who is guaranteed to return a return to their first home.
- If every person in any house has a chance of being assigned to any other state, everyone has a guarantee to return to their initial houses.
Suppose in the distant future the world does become one large AirBnb or Uber. The concept of the sharing economy is becoming pervasive, and is in full force in some Southeastern Asian countries.
If we want to design a system with Markov Chains, perhaps we can set this up in a way where return guarantees are issued to certain people (veterans, people with disabilities, etc.), and discriminate (in a good or bad way) against demographics by allocating them to different probabilities. In some sense, this is already ongoing in places like Chicago; the mass incarceration system is essentially placing African Americans in “closed districts” so they never escape the negative feedback loop of bad credit scores and criminal records. The algorithms are designed by private companies as trade secrets and not accessible to the public. If you’re interested in this, I recommend you check out Weapons of Math Destruction.
Hope this was easy to read.