The United States Senate
The process for selecting the Senate as originally detailed by the framers needs little improvement. States - not just the voters of the states - are entitled to equal representation in one branch of the Federal legislature. The 17th Amendment robbed the states of this, and this is one of the reasons for the catastrophic expansion of Federal power. One small improvement that could be offered would be to specify that bicameral legislatures meet in joint session to elect their US Senators (without this feature, many states required each legislative chamber to elect the same individual separately, which caused extended vacancies in this office).
The United States House of Representatives
Providing for direct elections to the US House of Representatives was the single greatest error the framers made (second only, perhaps, to their failure to address the issue of secessions). Direct elections make the US House an independent Federal body, exactly what a loose grouping of sovereign states should not have. However, the brief, 2-year term of the House, quite a desirable feature, would not be a good idea combined with election by state legislatures. With their Representatives on such a short leash, the states would be sending precise instructions on how to vote. This sort of intervention is far too direct. Furthermore, it would be in any state's interest to use a sort of winner-take-all system to prevent its members from canceling one another out, making it likely that all members of a delegation, no matter how big, would vote the same way. This would amplify and distort the results of legislative elections in large states.
A better alternative would be neither direct nor indirect election, but rather, randomly co-opting members of each state's lower legislative chamber to be US Representatives. Any system a state can devise is allowed, so long as it provides each lower-chamber member an equal chance of being selected. Thus it would behoove the states to make their lower-chamber size a multiple of their US House delegation, so a contiguous swath of lower-chamber districts could be knitted into a single selection pool for each US House seat. This would ensure that each large region (approximately 700,000 people) would get representation.
The currently used system of apportioning members to states on the basis of population is fine with me, as is the fairly generous Congressional paycheck.
Sessions of Congress
The Senate has the option to remain in session after the House goes out of session in June. The Senate creates an Executive Committee - one member from each state - to remain in the capital when it goes out of session.
The Executive Committee can call the Senate or the whole Congress into emergency session. The President can call an emergency session of Congress if national security demands. Finally, the House calls an emergency session of Congress when one fifth of its members transmit a demand for one to the Executive Committee.
State Legislatures: Upper Chambers
I support the continued power of states to choose how their governments are constituted, but I also have clear ideas on how their systems could be reformed. Each state's upper chamber should be elected statewide by list voting, using a simple system of partisan proportional representation. The body's membership should be quite limited in size, perhaps 25 to 30 members, for two reasons. First, because I envisage this as a professional, full-time body, so the per-member cost will be much higher for the upper than the lower chamber. Second, because limiting the size is an elegant way of creating an effective threshold of representation - a 25-member house naturally theoretically has an threshold of 4% of statewide votes to win a seat (though the largest-remainder system can reduce this in practice). More populous states can always move to a system of a few large constituencies of 15 to 20 members; this would retain the threshold while ensuring proper representation of large regions.
Though the election is partisan, parties need not be given a direct role in ballot access. Nonpartisan ballot access systems use both nominating petitions and deposits (though as far as I know the latter are not currently used in the United States). I advocate both a nominal petition requirement, say, the signatures of 25 or 50 people registered to vote in the state, plus a deposit, set to equal 1% of the annual salary of the highest-paid state official. This deposit would be used to create a free voters' pamphlet with information provided by the candidates. The deposit would be returned to each candidate on any list that won one or more seats.
State Legislatures: Lower Chambers
In marked contrast, I advocate state lower chambers be large, part-time bodies. To minimize costs, pay should be minimal, probably just enough to cover travel expenses. Members should number between 300 and 400, and be elected from small districts of between one and three members, depending on population. Ballots should be nonpartisan, and approval voting should be used (note that I don't agree with the Wikipedia article that approval voting is necessarily a single-winner system - it can easily be used in multimember constituencies, with the two or three most-approved candidates being elected).
Ballot access should be by petition only, using the same small number of signatures as for upper-chamber races. Parties could of course still endorse candidates, though party label wouldn't appear on the ballot (and in my opinion it would not really be feasible for party bosses to keep track of so many candidates).
The first thing you'll note about the above proposals is the dramatic differences between the ways each body is composed. This is intentional. One of the advantages of bicameralism is the ability to cancel out the disadvantages of the various systems.
Specifically, at both levels of government the upper house is composed of full-time legislators who will accept being in the capital most of the time, and who rely for their office both on popularity among voters and the support of other politicians. The lower houses, in contrast, are composed of part-time legislators, with state legislators not generally receiving a significant salary (but US Representatives would continue receive compensation equal to that of US Senators). The former provide experience and political skill; the latter provide the voice of ordinary working people, and a close local connection.
There are two reasons for making the smaller house professional and the larger house part-time: first, because beyond legislation (which can and should be done during a limited season, rather than year-round, see below), it is the traditional job of the upper houses to approve or reject executive appointments (which can happen at any time of year), and second, because in any joint session, the citizen legislators will outweigh the professional legislators by sheer weight or numbers.
Timing of Legislative Sessions
Given that both Congress and the state legislatures used to meet for only a small part of the year, it should be quite feasible to time their sessions for minimal overlap. States could replace any lower-chamber member who became a US Representative, but with the sessions properly timed, they wouldn't have to. Regular sessions of the US Congress should be limited to January through June; regular state legislative sessions should run July through December. In addition, the US Senate and state upper chambers would be called into brief sessions for confirming executive appointments, or they could simply have extended regular session of their own. The latter alternative would allow the upper-house committees spare time to study various technical issues. Finally, provisions for emergency sessions of each legislature would be advisable.
Political parties are a fairly natural phenomenon. They have their pros and cons, but I think it is best if their energies are channelled instead of suppressed. A zero-party system may be best of all, but a multi-system is better than a two-party system (which, it must be admitted, is better than a one-party system). Partisan influence is minimized by a multitude of small-scale legislative races, in which candidates can physically meet a large percentage of their voters (New Hampshire legislators each represent an average of 3000 people, not all of whom are voters). Using list voting, with any party list topping 5% guaranteed a seat in state upper chamber, should effectively abolish the duopoly.
Since only a small fraction of each state legislature would go on to the US Congress, local issues would dominate election campaigns. The public would have no choice but to focus on their own state governments. The character of US House would almost exactly match that of the states, yet no deal-making would influence their selection.
There are several arguments against proportional representation, and none of them is applicable here. First, a common American perception of PR is that it necessarily represents every group, not merely ideological groups, in proportion to its numbers. This is false. The racial PR system advocated by the likes of Jesse Jackson is a complete novelty, it is not in use anywhere that I am aware of. Actual PR attempts to represent parties fairly, not genders, races, sexual orientations, or religions.
Second, PR is said to produce an unlimited number of parties. This is false, since constituency magnitude, or formal thresholds, can limit the number of parties to any number desired.
Third, when combined with a cabinet that serves at the pleasure of the legislature, PR is said to create unstable coalitions. It is indeed the option of a state to create this sort of cabinet government (i.e. the "parliamentary system"), but in the unlikely event that one of them did, it would probably make the cabinet dependent on support in the lower chamber, which under this proposal would be nonpartisan.
Constituency Size and the Legislator-Citizen Connection
Looking at the upper chamber, it's easy to criticize a constituency the size of a small state (or, say, one-third the size of a large state) for being too large to allow much connection between elected officials and their electors. I counter that the system I advocate, when applied to most states, would provide closer legislator-citizen connections (in the lower chamber) while not significantly increasing the salary cost of the legislature (because the bulk of the members would be almost unpaid).
Constituency size, at the Congressional level, is a mostly intractable problem. With each Congressional district having twice the population of Iceland, we shouldn't kid ourselves that national legislators are going to have much personal connection to their constituents. After these reforms, the public will be talking to the Federal government through their state governments, which is exactly as it should be.