The plan begins with the General Lottery. In a two-hour, televised event, there will be a giant, interactive, touchscreen map of the United States, subdivided by Congressional Districts. The Lottery will proceed by rounds. In the first round, all of the states that are themselves a district, Alaska, Delaware, Montana, North Dakota, South Dakota, Vermont, and Wyoming, will have a ball placed into the hopper. From these seven, one will be selected, and in the subsequent House of Representatives Lottery, the Congressman for this seat will be chosen by lots.
In round two, Hawaii, Idaho, Maine, New Hampshire, and Rhode Island will each have two balls placed in the hopper, one representing each of their Congressional Districts. From these eight choices, two balls will be selected. Nebraska, Nevada, New Mexico, Utah, and West Virginia each have three Congressional Districts, for a total of fifteen, from which three balls will be drawn.
At this point, each of the remaining states has at least four House Representatives. Arkansas, Kansas, Mississippi, Connecticut, Iowa, Oklahoma, Oregon, Kentucky, S. Carolina, Alabama, Colorado, and Louisiana will each have their turn, and the rounds will proceed state by state, selecting one Congressional District for each. Arizona, Maryland, Minnesota, Wisconsin, Indiana, Missouri, Tennessee, Washington, Massachusetts, Virginia, Georgia, New Jersey, and North Carolina will have two Districts selected. Michigan will have three; Ohio, Illinois, and Pennsylvania will have four; Florida will have five; New York and Texas will have six; and California will have ten.
By the end of this process, 86 of the 435 House seats will have been selected by the General Lottery; this represents only 19.7% of the total number of Representatives. In the second phase of the General Lottery, all hundred Senate seats will be placed in the hopper, and ten will be drawn. On Election night, there will be a second House/Senate Lottery conducted by the states, and the new Congresspeople will be selected. #DidYouSeeJoeWinTheLottery!
By adding a Lottery to the system you succeed in meeting several goals all at once. First, this places de facto if not de jure term limits on all Congressmen. Second, these term limits make "investing in a politician," I much riskier gamble since a corporation will never know when their (wo)man's time is up. Third, there is nothing more democratic than lots, so there can be no argument that this system infringes on American standards of justice. Fourth, this system could break the duopoly of American politics by allowing people of various political persuasions to enter Congress. This influx of new blood may also be a catalyst for greater discussion and dialogue which could lead to increased cooperation and compromise. Fifth, all of these goals could be met with one change to the election laws.
An important addendum: I also propose a 20% Democracy Tax to be levied on every contribution to every Congressional campaign. These moneys would be put in a fund that winners of the Lottery, ostensibly every-day Americans with no war chest, could access to run for re-election if they so desired. Not only would this Democracy Tax allow citizens to hold onto their seats if they did a good job, but it would also place a check on SuperPACs and angel-investors from buying elections.