You’re completely right that the amount of information contained in a vote is far too small, especially when it’s effectively a vote between two alternatives. A similar problem applies to shopping: you might choose not to shop with X, but often that just means you need to shop with Y or Z instead. Even if the binary choice of who to shop with is expanded to a scalar choice of how much you want to spend on what, you’re not automatically getting a meaningful choice on how your money’s being spent — only how much goes on what.
But yes, your pragmatarian approach has distinct advantages over existing systems of democracy, addressing problems I am also keen to address (don’t know if you read the piece I linked to — which I wrote — from the words ‘democracy is hard’; if so then you know this already). I think we are both concerned that more meaningful information is conveyed about how things are run, so that people’s values and priorities are better represented in government.
However, I have concerns. In particular, about the fact that you apparently want people to decide only how their tax dollars are spent. Poorer parts of the population pay far less tax than the rich; presumably they therefore have proportionally less say? For example, in the UK the richest 1% of the population pay 26.9% of all income tax; that’s a slightly larger share than the entire poorest 75% (who pay 25.1% of all income tax between them). So if I’m reading your proposal correctly, you’d be vastly increasing the power of the wealthy relative to the rest of us. This in the context of an economic system which already gives them far, far more power than anyone else. Perhaps that’s not what you intended?
An alternative approach which avoids this criticism, while retaining what strike me as the main advantages of your proposal (but losing the intuitive appeal of people controlling ‘their own’ tax contributions) would be to allocate everyone, say, 100 points to distribute as they see fit between the different forms of government expenditure, and use that to allocate a fraction of government spending equal to the average tax contribution.
I don’t know if you’ve also considered in any depth how to deal with the different levels, or scales of decision-making? Various cities have experimented with participatory budgeting, for example, to help allocate local spending. The whole problem of how to distribute power across different scales is an interesting and difficult one.