Yes, that's approximately how Steem used to work. That was changed a while ago so now payouts are proportional to the votes. No ^2 any more.
The ^2 was actually a cute idea, and I think it worked better than people thought it did. The purpose of ^2 was to make it so that people were incentivized not to waste their votes on low-value content, because their vote's strength would be maximized by voting on content that other people think is valuable also.
Everything in life is a tradeoff, and the downside to the n^2 algorithm was that small users never felt like their votes were ever worth anything.
Thank you for your explanation @biophil. I'm glad that formula changed, because that formula would make the reward pool abuse mathematically possible.
With the current system, all the bot promotions start with a loss. They can turn profit, only if other than the promoters vote the content.
In other words, if no one else than the promotion team upvotes a post, they are guaranteed to have a loss in Steem terms.
I will need to chew on this. Replying to your post...