Replacing representative bodies at all levels of government with what I propose here will 1) guarantee that every taxpayer is equally represented, 2) greatly lessen the power of special interests, and 3) provide a mechanism that incentivizes right-sizing government based on the real needs and desires of the citizens.
I believe it is safe to assume that representative democracy has proven to be the best form of government, as it has been used successfully around the world (in “democratic” countries) and at all levels of government (national, state, county, and municipal).
Unfortunately, we have also come to depend on the mechanism of elections to determine who an individual taxpayer’s representative will be. I say “unfortunately”, because, where the value systems of the electing group are very diverse (e.g., in a congressional district), the person elected as representative will certainly only represent the values of some minority of the group. This problem is made worse by expensive elections, which require large sums of money to fund campaigns, providing the opportunity for special interests to have a disproportionate influence on both the election and on the person subsequently elected.  Both of these problems are bad for the general population of citizens, who are left feeling, quite accurately, that their elected representatives do not represent them very well at all.
A second problem is the way revenues are distributed, in a winner-take-all system. In most cases it takes a simple majority to determine how the revenues of all taxpayers are spent, even though some large number of those taxpayers may take great exception, for reasons both fiscal and moral.
In short: representative democracy is a useful form of government, but choosing representatives by elections and distributing resources by majority rule both have serious problems.
What I am proposing is a solution to these problems: better representation WITHOUT elections. This new system of representative democracy is based on “selected” rather than “elected” representatives. Let me explain.
First, I need to introduce a new set of terms, and then explain how such a representative body would function, and why it would be better. Here are the new terms: Canton, Champion, and Canton Forum.
A Canton is similar to, but not the same as, a political party. It is similar in that a canton is a membership organization, where the members share a set of values. It is not the same as a political party in that its purpose has nothing to do with elections. Taxpayers choose the canton that most closely aligns with their principles and values once a year (e.g., by August 1).
One member of the canton is the Champion, the member who represents all the members of his canton in the Canton Forum. A Canton Forum is the collection of the Champions of all the Cantons in a particular territory. The Canton Forum is a viable replacement for any form of representative body at any level of government: national (the House of Representatives), state (state assemblies), county (county boards), and municipalities (town and city councils; school boards).
Think of it this way. The champion of a canton is like the head of a political party. But instead of the party putting up candidates for election to a position in a representative body, the champions themselves are the representatives.
The canton forum functions as the representative body, with the champions of all the cantons as representatives of the citizens. When votes come up in the forum, it is not one vote per canton, but one vote for every member of the canton. Passage of a bill is successful when the aggregate number of members of the cantons approving passage constitutes a majority.
Once a bill is passed, only the cantons that approved it must finance it. To do this, each champion is allocated funds from the total available revenues for the year, using this formula: the average revenues per taxpayer (humans only), times the number of members of the canton.
At the end of a year, any funds not spent by a canton are returned to its members proportionately. This is a huge incentive for champions to spend only on what their members truly support. I call this right-sizing government. What will probably happen over time is that fewer things get handled at the national level, getting pushed down to the states, counties, and municipalities (perhaps even to non-governmental associations), where control of resources and prevention of corruption are better handled.
Replacing representative bodies at all levels of government with canton forums will 1) guarantee that every taxpayer is equally represented, 2) greatly lessen the power of special interests, and 3) provide a mechanism that incentivizes right-sizing government based on the real needs and desires of the citizens.
 An excellent description of the role of special interests in elections can be found in this TED talk by Lawrence Lessig (though I disagree with his solutions). https://www.youtube.com/watch?v=PJy8vTu66tE