By Warren D. Smith based on Michael J. Dubin: US Congressional Elections 1788-1997, McFarland & Co. 1998.
The current practice of a single election day was not the original practice in some states like VA which held elections over a 4-5 week period, different days in different counties. (1-day policy adopted 1837.) Also, many states had different days from each other.
The current practice of single-member districts was not eternal either. Up until 1970, every congress but the 30th, 44-47th, 51st, and 52nd contained at least one member elected "at large" (i.e. statewide not in districts). [The 52nd congress was during the years 1891-1893.] Multimember disticts were used in the 3-27th congresses, mainly in NY and PA. (Also in MD in one district and MA and NJ for 1 election.)
This suggests that "proportional representation" for congress seats is indeed constitutional (although presently illegal by acts of congress).
Note: WDS used to tell people PR's constitutionality was not a sure thing. However (Sept. 2007) WDS now changes his stance – in view of this information it must be constitutional.
Congress in its first law regulating elections made multimember districts illegal starting with the 28th congress (1842-3). They immediately vanished, but at-large members continued.
Jim Riley notes: The requirement for election by districts was first part of the 1842 Apportionment Act: "That in every case where a State is entitled to more than one Representative, the number to which each State shall be entitled under this apportionment shall be elected by districts composed of contiguous territory equal in number to the number of Representatives to which said State may be entitled, no one district electing more than one Representative." This appears to make both multimember districts and at-large congressmen illegal, but the fact is, the latter continued.
5 of the 6 New England states (all but CT) required election by a majority and if not achieved then additional elections called "trials" would be held until some candidate got a majority. These runoff systems were eventually dropped with the last being in RI in 1893. These were the only runoff elections ever held for congress seats. Even at its peak, less than 5% of congressmen won via runoff elections. In one case 13 trials were required, and in another a majority never arose so that the seat remained vacant.
Senators were not originally popularly elected. That was enacted as the 17th amendment in 1913. Oregon did it first in 1906, 12 other states followed (often enacted via citizen referendum), then finally the amendment was ratified.
Equi-populous congressional districts were uncommon until 1964 "Wesberry V Sanders" supreme court case mandated them. 2:1 population disparities were common. In 1942 IL-7 had population 914053 while IL-5 had only 112116; NY-12 had population 70307 versus NY-8 with 911210.
In 1960 FL created a district (immediately following the Census) FL-6 with population 660345 and another FL-9 with 237235.
After Wesberry, typically population disparities were below ±1000 people.
In Connecticut 1788-1818 they had a unique 2-phase process for electing congressmen. Phase 1 (April): voter's vote was to name N of the M candidates where 0<N<M and N was the number of CT congressmen. Kind of like multiwinner approval. Phase 2 (September): voters voted again (candidates being the winners of the preceding phase). All this was statewide; there were no districts. I'm not sure what voting system was used in phase 2, am guessing the same N-of-M system as in phase 1 (and I'm not completely sure I have that right either).
Example is the 12th congress 1811-1813. On 5 April, 18 candidates were chosen, in phase 1, from a field of at least 36. Then in phase 2, on 17 september, seven of these 18 were elected.
Congressmen running unopposed: Ranged from 2.3% to 20.9% of the seats in the 56-105th congresses (the 20.9% occured in both the 78th and 66th congresses) averaging about 10%. In the 4-22nd congresses it ranged from 9.4% to 33.2% averaging about 20%.
Incumbent re-election percentages: Starting in 81st congress always exceeded 90%. Before 57th, always was below 90% (typically about 70%).
Parties: there have been over 500 political parties (listed in the book!) with which congress-candidates have run. 95% of US citizens have never heard of 95% of these parties.
Bucklin & IRV: as far as I can tell, neither Bucklin nor IRV were ever used in any congress election ever.
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