In a weighted voting system it might be possible for some members to have many more voting weights than others. The dominance of these members can be dampened by scaling weight allocations down using the square root function, directly inspired by Quadratic Voting.
Quadratic Scaling allows a voting system to retain a preference for those who contribute more since the square root function increases monotonically, but doesn't allow those who contribute more to dominate many small voices since the the square root function's rate of growth decreases monotonically.
Quadratic Scaling, at least in the context of Quadratic Voting, has been mathematically proven to perfectly navigate between tyranny of the majority vs normal tyranny of the minority.
However, Quadratic Scaling has some possible problems:
- Quadratic Scaling complicated and "mathy", and so to many people will feel arbitrary, confusing, and lack legitimacy.
- Quadratic Scaling is particularly vulnerable to collusion and sock puppets.
Quadratic Scaling is likely appropriate in settings where member contributions are highly variable, therefore making some form of participation-based weighting necessary, where members are tolerant of the method's exoticism, and where it's difficult to fraudulently create accounts.
Quadratic Scaling or something like it is probably essential in settings where members are possibly in literal market competition with each other, such as would be the case if a cooperative online marketplace were created. Being able to exert greater influence on a cooperative platform in a way that would enable a member to gain greater sales could directly create a runaway reinforcing feedback loop, and such feedback loops must be carefully prevented.