In this paragraph you clearly identify that there is a n-person Prisoner's Dilemma (let's start calling it nPD, for short?)

Is there anything we can do to make the system fairer?

The only real way to stop the so call "circle-jerk" is to get everyone to vote, there are plenty of big whales that do not vote on any witness and this is actually prejudicial to the system. If big whales do not vote, then they contribute to making the "circle-jerk" stronger as witnesses just vote for each other and decide who gets to be on the top 19.

In bold I have highlighted the factor that precisely maps to this:

• each player has two options: cooperate or defect
• defecting is the dominant strategy for each player (i.e. each player is better off choosing to defect than to cooperate no matter how many other players choose to cooperate)
• the dominant strategies (to defect) intersect at a deficient equilibrium point (if all players choose to defect, the outcome is worse than if each player had chosen non-dominant strategies (to cooperate))

It is also known in another form as "The Tragedy of the Commons", as the issue is the same. If only we could make people conserve a resource that does not cost them anything to exploit. Except the other way around, how to get them to exploit the resource that costs them nothing to conserve. A perfect mirror, with the same dynamic, regardless.

I think this is why the witness account should simply not be able to vote at all. Neither should it be able to power down until it is inactive for long enough for a power down payment. This enables others to shuffle up until the witness has powered down enough to fund a project.

In the Prisoner's Dilemma, in general, defecting means ratting out the others. In the Witness prisoner's dilemma, it is participating in a voting pattern that is about buying the votes of others, like you say. Thus, if witnesses votes on witnesses, were not counted, while the witness is active, then they have no dilemma to deal with.

This is a starting point for how I would address the problem. There is too many people saying 'it's my stake blah blah' This does not extend to abusing privilege as a witness. Either you can decide with your stake who is a witness, or you can be a witness.

The only real influence a witness has, compared to, say, someone like me, who is not a witness (and note, this also effectively includes the backup witnesses, because their veto does not count in a hardfork quorum) is that they can block a hardfork. Anyone can propose a hardfork change, and anyone can wage a campaign of persuasion upon the general population of users to get a shrieking cry for something to rise up and bite Steemit and make them do it.

Of course, the most potent enablers of this, are large stakeholders (rightly) who can raise the profile of those who are supporting what they want to see happen. But there is nothing that also stops a small user starting a campaign, and recruiting whales to support it either.

In the top comment, also @aggroed has pointed out that there should be a witness downvote. I can wholeheartedly agree with that. I might also add, that a slider would be a good thing, but still limit it to 30 votes, for the sake of bandwidth conservation and computation conservation.