For discussion, imagine this:
Every person has one vote. They may assign this vote to a representative, ANY representative. This would solve the situation of 50% +1 of the population electing someone that can claim to represent 100% of the population.
Representatives at the central government are NOT PAID. They may be paid by those whose proxies they hold, but they would recieve no money from the central cofers.
Any citizen may withdraw his/her proxy
at any time. All of the back room deals and vote tradeing would dissapear when those who engage in the practice try to sell their 10,000 proxies

end up with only their own vote to sell

.
Votes cannot be decided only by a simple majority. A 3/4 majority should be needed in order to preserve the federal governments energy and funds for those things that are most widely seen as needs.
Every program, law and department shall have a "sunset" provision. Unless a shorter time is specified, this will be set at 5 years. Everything that the government does will come up for review and reauthorisation. This will work in a similar manner to how the "assault weapon ban" died in America.
To see it in "action" look at the novel "The Probability Broach" by L. Neil Smith.