Because the derivative of a quadratic is linear, meaning meaning you spend votes proportionally to the strength of your preference (indifference at the margin).

Sadly there is a showstopper.

Quadratic voting can be bypassed if whales can make a large amount of identities. The lack of strong identity and Sybil attacks is the biggest unsolved problem in distributed systems of the free-to-join class.

Q̶u̶a̶d̶r̶a̶t̶i̶c̶ voting can be bypassed if whales can make a large amount of identities. This has nothing to do with quadratic or not. As long as the voting system satisfies the non dictatorship property of Arrows theorem they are vulnerable to Sybil.

I think what OP meant is that if you have an organisation with 100 votes or 100 organisations with 1 vote there's no difference in linear, but there's a huge difference in quadratic.

Yes but that's the point of the system, more individuals voting for something means more. Like any voting system, it doesn't work if one person can impersonate other people.

In my experience with writing quadratic voting contracts in Solidity, the exponent of 2 is mandatory because there's no way to calculate an nth root in Solidity.

Writing that out though, I realize that the root could be calculated by the client and simply verified on chain.

One token, one vote is an exponent of 1, it should be up to the voters to decide the exponent used based on the issue in order to choose the degree money influences decision making.

False. You can very much implement the n-th root. Details depend on the number format chosen (fixed vs floating point emulation). The most obvious method is binary search. You calculate the n-th power for some number and see if it is larger or smaller then then the number you want the root from and narrow it down.

Equivalents of the doom trick using integer division and instead of >>1 (which is ÷2) of the exponents + a few newton iterations would also do the trick in floating point format

Apparently it is possible. [1] I guess I missed that when I was trying before.

[1] https://ethereum.stackexchange.com/questions/38468/calculate...

qv measures degree of preferences, instead of direction of preferences.

qv is robust under various non-ideal behavior (in large groups)

qv does not suffer from cyclic collective preferences (voting paradox)

qv does not suffer from discursive dilemma and doctrinal paradox.

qv counteracts majority rule problem. A small minority can get their voice heard if the intensity of their desire is strong.