Achilles Heel of Steem
I don't see why 'flatter' is incompatible with the game theory; 'flat' would be. Would n^1.5 rather than n^2 be a disaster?
This is a complex question and I might mess up the analysis, because frankly I am not even confident I know what the current algorithm is. I've seen mentions of curation rewards being a function of both total author reward (which is afaik a function of the square of the total votes) and of that the earliness of your vote matters in some non-linear way (note for curation rewards and afaics not for author reward). That seems to indicate that a whale who votes for his own content will earn the author reward of at least the square of his/her vote power, regardless of how early or late the whale votes.
But the overriding factor seems to be that the debasement of STEEM POWER is apparently less than 4% yearly (and note I'll probably be making a blog post soon on the precise math), so there isn't much incentive for anyone to vote for themselves because offseting that debasement by voting your share to yourself for whales is not worth the cost of failure to the system it could cause. And for dolphins, the 4% is nominally so low that it is a pita to vote for anything other than your conscience.
So it seems even a linear weighting might be safe, except there is the consideration of the power of compounding in that whales who can automate to offset say 4% compounding advantage versus whales who vote their conscience, will over time become the controllers of the system (all other factors being equal, which might not be the case).
We also have to consider that upvoting drives other voting by raising ranking and thus viewership. Thus whales can influence which content gets the most rewards, thus upvoting their own content seems to make the most sense if that content is of otherwise equal potential to receive upvotes as any other content. Thus the game theory seems to be a power vacuum that will suck in the controller who can organize stake to vote for successful bloggers (to obfuscate this from other whales who might downvote the phenomenon) which pays back some % of the author rewards to the organized voting stake (power).
From one perspective the quadratic weighting seems to make this game theory more profitable because the one who captures even a slight advantage in this power vacuum can take exponentially more of the author rewards. However, the quadratic ranking also means that the dolphins can't benefit from organizing themselves to vote for their own posts collectively, because they would be at a quadratic disadvantage compared to the whale controller.
Thus I conclude that the quadratic weighting is necessary to squelch dolphins organizing to game the system, but it hands the control (and eventually the entire system) to the deviant whale who realizes this is a winner-take-all paradigm. We end up with a system of serious bloggers who work for the master whale and the rest are subservient minnows and dolphins who are beholden to the groupthink control over economics of the system.
That is why I have redesigned this concept so there can be linear weighting which the dolphins can't profit on by organizing themselves (as I add a cost to voting but not taken from the user's wallet, yeah that will really make you think!) and which whales can't game either because I squelch whale voting power (everyone becomes a dolphin in terms of voting power); and note this depends on very strong Sybil attack resistance on account identities and that whales won't trust other people to hold their money for them.
Additionally in my design for a Steem-like system, I have also added another reward vector which greatly reduces the incentive and ability to take control of the system by gaming the voting reward algorithm.
Edit: to clarify that with linear weighting, the dolphins would be incentivized to band together in order to upvote each others' posts in order to get amplification of rewards due to raising the attention their posts get. Of course if users band together then they lose the relative amplification effect, but that is the point that the game theory incentivizes them to band together until there are too many banded and then the site's voting is one (or several) groupthink(s).