Last week we left off with this simple(?) graph and its related matrix
Probability changes everything
We discussed a matrix with probabilities. Above, all the non-zero probabilities are 1, meaning a 100% chance that you will go in the direction indicated. On the right below each of those 1’s are probabilities less than .5. They are all different probabilities.
Allowing probabilities to be between one and zero opens up a huge array of possibilities, but also introduces MASSIVE complexity. Below is the not-so-simple graph associated with the last matrix above (on the right). Note that each of the six nodes is allowed to go to any of the other five nodes or circle back to itself. What we care about is the relative conditional probabilities of a significant number of people ending up on A4 or A6 given that they began at A1.
OK, so you need one Russian
Over 100 years ago Andrey Markov came up with a theory of probability now known as a Markov Process. This permits calculating the probability of an event which is dependent upon nothing other than the current state of affairs.
Recall you wanted to go from A1 to A6 and I wanted you to go to A4. Markov permits us to calculate the probability that you will end up on A4. Computers can do this very fast. For instance, My computer can simulate 1,000 Markov paths using our matrix of non-zero numbers in less than two seconds. Try it to see how long it takes you.
I will wait here.
Given the matrix I started with, the average probability 1,000 people will end up where I want them is .3 so if I want to increase my catch from 300 to 400, I just tweak the clickbait to hook a more gullible crowd. P. T. Barnum supposedly said “There is a sucker born every minute”. He did not know about the internet, where one flits by every nano-second with a mouse in his hand. Staying with the .3 average, that is nearly a third. Elections are decided by much narrower margins, so how hard can it be to tip those scales?
Well, let’s just see. Here is a link to a picture of the trailer where Elvis is living right now.
[next week: Choices, choices, choices]