Different uses for voting need different types of voting.
Against Budget Cards
Most reps hesitate to place cards against another's fiefdom.
Say for example, you chair the transportation committee so you watch that column closely. You notice when I place cards against the transportation budget and you're likely to take a dim view of the action -- which makes me reluctant to do it.
Also, if the reps tend to place more cards for departments than against them, advocates might gain more grants by subdividing a department.
Therefore the rules probably should require all reps to balance positive and negative cards.
A column for tax relief or increase still would allow a rep to influence the overall budget. And if she adds money to tax relief, she must balance that by taking away money from some other budget(s).
Secret ballots let a rep vote without coercion by colleagues or lobbyists, but a rep's constituents cannot evaluate her voting record when she runs for reelection.
Negative cards make the process terribly adversarial.
In the Hylland and Zeckhauser system of influence points, what motivates restraint in valuations is the rising marginal cost of influence, which results from a voter's "influence" over a parameter being defined as the square root of the number of points that the voter assigns to it. This scheme motivates voters to reveal the relative intensities of their concerns for different continuous parameters of public activity. It does not reveal the intensity of a voter's concern about public activities compared to money or private goods.. It does not show the strength of a voter's desire for a public good compared keeping that money for private goods.
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Median Voter Process
Table & Cards