I had similar idea long time ago. I though about 'Honest Ratings' for ICOs. The same algorithm that works on this site could be used to rate ICOs in a more unbiased, democratic way. The fact that a vote cost a real money makes the results extremely valuable. Imagine a website where you can rate an ICO (paying 0.002 BCH) choosing from 0-5 stars (bendersnatch:), and you get full results of these ratings only if you rated 50 projects or if you paid for full access. I know there exists sites like icorating.com or icobench.com that do it for free but you need to keep in mind that they are biased. An ICO could grant them a portion of tokens for a better review, and a site is incentivised to overrate the project because they own the tokens. It's called a positive feedback loop, but it has nothing in common with positiveness here.
Best bitcoincracy would be for elections (voting on a political party) where the weight of vote is based on wealth (bitcoin holdings). For the other purposes people would have to get reward, otherwise they would be to lazy to vote.
There are sites where lists are compiled but they are done for free by the users. I think this would be a novel way to compile lists of all kinds. Where you have to pay to impact a list and only do so because you think you'll get a return on that payment. You put things you think really are the best and have value.
I really like the idea of stake backed rankings/lists. Instead of doing any sort of single increment voting with the 'Yours' like pyramid distribution you describe, however, what I see being neat would be to instead just let anyone choose their price for each entry, and for entries to be ranked in order of most to least stake. For example, someone could create a new list, pay as little or much as they like to create an entry or multiple entries on it. From there, anyone can "outbid" entries, or add stake to entries to fortify them or raise or maintain their position on the list. Now this could be done similar to Bitcoinocracy where you could just sign addresses you control, rather than actually having to make any transactions, but that does defeat the goal of increasing usage, so let's assume instead that users actually have to make a transaction to an address that is associated with each item on the list.
Now for the interesting part, what to do with the coins spent to the voting addresses. You could just burn them, which is an OK idea if you solely want to see how much conviction people will put behind these rankings, however without some sort of reward system, I wouldn't expect much usage (although a burn-only option would still be cool). To provide incentive, what could be done is that upon creating the first entry in a list, a smart contract sets an expiry on the list X blocks from present. When the list expires, the user who has the largest stake in the list can claim the entirety of all coins sent to entries on the list. The catch is, the expiry time is extended, by say, 50 blocks for every 1% increase in funds. Eventually the expiry will be hit as increasing the total funds in a list by 1% becomes increasingly more expensive, then a winner claims all funds in this "list wallet". From here the list doesn't actually disappear, just new addresses are generated and the game restarts, starting initially with the same rankings as the list left off on before expiry.
Now, I don't know the limitations of BCH smart contracts, so maybe this is a bit too complicated and would be a better suited idea on a more robust smart contract platform, but I imagine it could be done. Preferably everything would be transparent on chain. Each list could simply be an HD wallet, with the smart contract's only job to set and extend expiry time, and trustlessly award winnings.
This "Winner takes all" is just one sort of game mode possible, if things get heated on a list it will turn into a whale war, but hey, that's still a pretty cool thought eh? If someone wants to throw down a boat load thinking no one will dare to throw down more, well things could get interesting if their challenge is met… Other more complicated game modes could include users losing their funds for having them in the lowest rated entries on expiry (throwing those funds into a split pot), users with stake in upper-middle rated entries getting their stake back, and users with stake in top rated entries getting their stake back plus making profit.