Changing population patterns created a particularly rotten political situation in the United Kingdom over a period of several hundred years, remaining uncorrected until the middle of the Nineteenth Century. The House of Commons, the lower house, has its roots all the way back to the Thirteenth Century in England. Each borough — roughly analogous to a town — could send two representatives or burgesses to Parliament, by Royal charter. Some boroughs gained this privilege as early as the 1295 Parliament of England assembled by King Edward I. That’s an intentionally simplified version of history so feel free to review a more detailed source if you want a better explanation. The basic point to keep in mind is that boroughs were allowed to participate in a manner in the larger political process.
A normal ebb and flow of events transpired over the centuries. Towns expanded, contracted or moved. New towns flourished or faltered, sometimes replacing or enveloping older towns, sometimes not. Populations grew and shifted considerably over a five hundred year period. However, the original borough boundaries remained largely unchanged. The result: some localities were horribly underrepresented in the House of Commons and some were grossly overrepresented.
The imbalance sometimes happened on an epic, mind-boggling scale.
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Some boroughs dwindled to just a few residents, yet retained their two burgesses for centuries. They became known as rotten boroughs because of the rot in their population and importance over time and the the rot they brought to an ostensibly representative institution.
It became quite fashionable for politically-connected individuals to control their home boroughs if the population was small enough. They likely already served in the House of Lords and were then able to orchestrate the election of allies or family members to borough seats they controlled in the House of Commons. Elections were public affairs with open balloting during this period so the Lords knew exactly how their minions voted, and could reward or punish accordingly. They could exert a similar influence on the two burgesses now in their pocket and serving in the House of Commons. For that reason these areas were sometimes called Pocket Boroughs, too.
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The worst, or at least the most notorious, was Old Sarum. It started as an important Cathedral town but its influence waned to near nothingness after being supplanted by nearby Salisbury. The bishop moved but the spot retained its two burgess slots long after it became an empty hillside. The voting population dwindled to a mere seven voters, while other boroughs might contain tens of thousands. Reputedly Old Sarum once sold for £60,000 when its land and manorial rights were worth perhaps £700 a year, such was the value of the attached seats in the House of Commons that came with it.
The situation got so bad that, "by the time of the 1831 general election, out of 406 elected members, 152 were chosen by fewer than 100 voters, and 88 by fewer than 50 voters each.". A measure of reform came in 1832 with the disestablishment of 57 rotten boroughs, and again in 1872 with the introduction of the secret ballot.
Do rotten boroughs exist today in the United States? There’s nothing nearly as extreme as the situation that sparked reform in the United Kingdom in the Nineteenth Century, but imbalances certainly exist.
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For example, Wyoming, with a population of 563,626 has two U.S. Senators representing their interests, the same as California with 37,593,222 people. It’s probably unfair to single-out Wyoming as several other states also have fewer than a million residents: Alaska; Delaware; Montana; North Dakota, South Dakota; and Vermont. Also I don’t think the situation meets the standard of "rotten." It’s much more difficult to corner a half-million votes than to corral a few dozen. Disproportionate? Absolutely. Rotten? I think not.