The "artificial currency" would ensure votes accurately reflect the importance an individual attaches to an issue
relative to other votes, but in practice this gives significantly more "voting power" to groups which seldom participate in votes, even where it is difficult to believe the intensity of their preferences are stronger. Given a fixed budget to be used over a number of votes, an essentially apolitical person told by their community leader to use all their votes in opposing a particular issue they know little about will have more influence on the outcome than a highly-informed, politically-motivated and civic minded regular referendum participant, yet it's difficult to argue the absolute intensity of the preference of the regular voter is lower (this is of course related to the standard welfare economics criticism of cardinal utilities).
This isn't a problem if the individuals apportioning their vote budget are similarly-highly-motivated legislators prioritising from a known raft of policies whilst being well informed about which initiatives are most likely to meet with strong opposition (though it significantly advantages parties able to coordinate the efficient distribution of their votes). Probably they can handle the complexities of a voting budget that compensates the losers too.
But for a broader electorate that doesn't excel in performing stochastic optimisation problems, doesn't have good intelligence to help them vote tactically, doesn't know what future votes might be, the quadratic nature of the voting system doesn't deal with the problem of budgeted and secret voting being a game of iterated prisoners' dilemma; it might even intensify the problems.
It's not too difficult to devise a scenario in which it actually makes the "tyranny of the majority" problem worse: a minority of bigots wish very strongly to enact a law against a minority of regular targets. The disinterested majority wishes to avoid diluting their future voting power by participating, whilst the victimised minority wishes to hold back some of their voting power to avoid being disenfranchised when faced with conceivable future bullying initiatives[1]. In a secret ballot, the bigots can conceivably win if the groups are a similar size (even if they can subsequently reverse the decision)
[1]This is mitigated if the losers get their own votes back as compensation, but actually worsened if they get higher compensation, in which case optimum strategy in a iterated electoral battle is to win by the narrowest possible margin, whilst voting for something incredibly unpopular is a practical way to increase your future influence.
This isn't a problem if the individuals apportioning their vote budget are similarly-highly-motivated legislators prioritising from a known raft of policies whilst being well informed about which initiatives are most likely to meet with strong opposition (though it significantly advantages parties able to coordinate the efficient distribution of their votes). Probably they can handle the complexities of a voting budget that compensates the losers too.
But for a broader electorate that doesn't excel in performing stochastic optimisation problems, doesn't have good intelligence to help them vote tactically, doesn't know what future votes might be, the quadratic nature of the voting system doesn't deal with the problem of budgeted and secret voting being a game of iterated prisoners' dilemma; it might even intensify the problems.
It's not too difficult to devise a scenario in which it actually makes the "tyranny of the majority" problem worse: a minority of bigots wish very strongly to enact a law against a minority of regular targets. The disinterested majority wishes to avoid diluting their future voting power by participating, whilst the victimised minority wishes to hold back some of their voting power to avoid being disenfranchised when faced with conceivable future bullying initiatives[1]. In a secret ballot, the bigots can conceivably win if the groups are a similar size (even if they can subsequently reverse the decision)
[1]This is mitigated if the losers get their own votes back as compensation, but actually worsened if they get higher compensation, in which case optimum strategy in a iterated electoral battle is to win by the narrowest possible margin, whilst voting for something incredibly unpopular is a practical way to increase your future influence.