"I think that part of the problem is that there's inflation in upvotes because people have an unlimited supply."
It's not obvious to me that this is true. Here is a counterexample:
In the extreme case, if the user base consisted of a set of 'wise old users' who only up voted the 'good' content and a set of 'mindless new users' who literally up voted every post, then the votes from the latter group just add to the baseline vote count without having any power at changing the orderings of submissions. In this situation the submission ranking is determined solely by the 'wise old users' even if they are greatly outnumbered.
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The problem you describe is that the new people are interested in different things to the old and can use their number advantage to push things in that direction.
It seems to me that there are a few possible solutions.
1. a) Restrict the topics of discussion on the website by restricting the people who can add to the conversation. Eg, disallowing new accounts to be created or starting a new website and only selectively inviting people.
1. b) Restricting the topics of discussion on the website by empowering a certain subgroup of people who share a particular interest. This could be done by moderators deleting submissions or via your suggestion of having 'super votes'.
2. a) Allow free submission of topics but provide manual mechanisms for organising the information better so people can choose the subset that they are interested in. Eg, the subreddit approach or having comments marked as insightful/funny/etc.
2. b) Allow free submission of topics but provide personalised rankings tailored to each user. Eg, user rlpb tends to like posts which RiderOfGiraffes likes and also posts which include the word "thinking" so give those a bonus in the rlpb ranking.
In my opinion the ideal solution is 2.b. I dislike the 'elitist' philosophy of 1.a and b, they seem unworkable as long term solutions and pragmatically if I can find the information useful to me on pages 1 and 2 I don't care if pages 3-100 are junk.
Option 2.a seems to work ok on Reddit. However, it does rely on people playing by the rules and probably also a willingness to subdivide subdivisions quite liberally.
I'm sure there are problems with 2.b as well: people need to be actively providing information about their interests to get the classification benefit, and the computational load is likely higher.
tldr: The premise of any vote based ranking site is that there is one set of universally accepted 'good content.' The success of this mechanism depends crucially on the homogeneity of the population it is applied to. If this assumption is broken it can be re-established by exiling part of the population or segregating the population into more homogeneous subgroups (explicitly or invisibly.)