Are you familiar with the logic behind Google’s PageRank algorithm? I was thinking about it the other day, and it occurred to me that its operation is rather reminiscent of the income flows in a free market. I expand on this notion below.
PageRank
You can read a pretty detailed description of PageRank (PR) on WikiPedia (with copious references to even more detailed descriptions), but I think that the following is a pretty fair summary of the thing:
- The web is made of pages.
- Each page is assigned a rank.
- Pages are joined by links.
- Each link has an origin and a destination.
- Each link is assigned a score.
- A link’s score is equal to the rank of its origin, divided by the number of links sharing that origin.
- A page’s rank is equal to the sum of the scores of the links having that page as a destination.
Shortcomings
It could be argued that a simplistic link score computation is a shortcoming of the PR algorithm. PR simply divides an origin page’s rank between all its outgoing links when assigning scores to those links; in effect, it assumes that all outgoing links are equally important to the origin page.
Wouldn’t it be nice if the origin page could explicitly allocate its PR between its outgoing links? This would let website authors clearly say, for example, “this link to fish.com is really important, while this other link to wordpress.com is just boilerplate”. If the page author knew his page’s rank, he could even parcel it out point by point: “0.2 to this link, 0.5 to this other, …” and so on.
Okay, no, it wouldn’t be nice: It would be an enormous hassle, and prone to gaming, and generally awful. But it’s an interesting thought experiment …
Income
The thing is, money works exactly like this. (Okay, more precisely: income works a lot like this. Happy?)
If we swap some words in the earlier (simplified) PR description:
- The economy is made of people.
- Each person is assigned an income.
- People are joined by transactions.
- Each transaction has a buyer and a seller.
- Each transaction is assigned a value.
- A transactions’s value is equal to the income of its buyer, divided by the number of transactions sharing that buyer.
- A person’s income is equal to the sum of the values of the transactions having that person as a seller.
And, if we drop the silly assumption that an origin page’s PR is divided equally between its links, and replace it with the reality that people explicitly divide their incomes between their purchases, well, hey, we’ve just described a simple economy.
Interpretations
What can one take away from this little thought experiment? Well, I’d suggest it implies that income disparities are likely at least as reflective of some underlying reality as Google’s PR rankings. Not that either can’t be gamed, and not that either are in any way reflective of the intrinsic worth of the rankees, but neither are they random or meaningless, and fretting about “inequalities” in either PR results or income is sort of missing the point.
