The Universe of Discourse

Second-largest cities
A while back I was in the local coffee shop and mentioned that my wife had been born in Rochester, New York. "Ah," said the server. "The third-largest city in New York." Really? I would not have guessed that. (She was right, by the way.) As a native of the first-largest city in New York, the one they named the state after, I have spent very little time thinking about the lesser cities of New York. I have, of course, heard that there are some. But I have hardly any idea what they are called, or where they are.

It appears that the second-largest city in New York state is some place called (get this) "Buffalo". Okay, whatever. But that got me wondering if New York was the state with the greatest disparity between its largest and second-largest city. Since I had the census data lying around from a related project (and a good thing too, since the Census Bureau website moved the file) I decided to find out.

The answer is no. New York state has only one major city, since its next-largest settlement is Buffalo, with 1.1 million people. (Estimated, as of 2006.) But the second-largest city in Illinois is Peoria, which is actually the punchline of jokes. (Not merely because of its small size; compare Dubuque, Iowa, a joke, with Davenport, Iowa, not a joke.) The population of Peoria is around 370,000, less than one twenty-fifth that of Chicago.

But if you want to count weird exceptions, Rhode Island has everyone else beat. You cannot compare the sizes of the largest and second-largest cities in Rhode Island at all. Rhode Island is so small that it has only one city, Seriously. No, stop laughing! Rhode Island is no laughing matter.

The Articles of Confederation required unanimous consent to amend, and Rhode Island kept screwing everyone else up, by withholding consent, so the rest of the states had to junk the Articles in favor of the current United States Constitution. Rhode Island refused to ratify the new Constitution, insisting to the very end that the other states had no right to secede from the Confederation, until well after all of the other twelve had done it, and they finally realized that the future of their teeny one-state Confederation as an enclave of the United States of America was rather iffy. Even then, their vote to join the United States went 34–32.

But I digress.

Actually, for many years I have said that you can impress a Rhode Islander by asking where they live, and then—regardless of what they say—remarking "Oh, that's near Providence, isn't it?" They are always pleased. "Yes, that's right!" The census data proves that this is guaranteed to work. (Unless they live in Providence, of course.)

Here's a joke for mathematicians. Q: What is Rhode Island? A: The topological closure of Providence.

Okay, I am finally done ragging on Rhode Island.

Here is the complete data, ordered by size disparity. I wasn't sure whether to put Rhode Island at the top or the bottom, so I listed it twice, just like in the Senate.

State	Largest city and its Population		Second-largest city and its population		Quotient
Rhode Island	Providence-New Bedford-Fall River	1,612,989	—
Illinois	Chicago-Naperville-Joliet	9,505,748	Peoria	370,194	25	.68
New York	New York-Northern New Jersey-Long Island	18,818,536	Buffalo-Niagara Falls	1,137,520	16	.54
Minnesota	Minneapolis-St. Paul-Bloomington	3,175,041	Duluth	274,244	11	.58
Maryland	Baltimore-Towson	2,658,405	Hagerstown-Martinsburg	257,619	10	.32
Georgia	Atlanta-Sandy Springs-Marietta	5,138,223	Augusta-Richmond County	523,249	9	.82
Washington	Seattle-Tacoma-Bellevue	3,263,497	Spokane	446,706	7	.31
Michigan	Detroit-Warren-Livonia	4,468,966	Grand Rapids-Wyoming	774,084	5	.77
Massachusetts	Boston-Cambridge-Quincy	4,455,217	Worcester	784,992	5	.68
Oregon	Portland-Vancouver-Beaverton	2,137,565	Salem	384,600	5	.56
Hawaii	Honolulu	909,863	Hilo	171,191	5	.31
Nevada	Las Vegas-Paradise	1,777,539	Reno-Sparks	400,560	4	.44
Idaho	Boise City-Nampa	567,640	Coeur d'Alene	131,507	4	.32
Arizona	Phoenix-Mesa-Scottsdale	4,039,182	Tucson	946,362	4	.27
New Mexico	Albuquerque	816,811	Las Cruces	193,888	4	.21
Alaska	Anchorage	359,180	Fairbanks	86,754	4	.14
Indiana	Indianapolis-Carmel	1,666,032	Fort Wayne	408,071	4	.08
Colorado	Denver-Aurora	2,408,750	Colorado Springs	599,127	4	.02
Maine	Portland-South Portland-Biddeford	513,667	Bangor	147,180	3	.49
Vermont	Burlington-South Burlington	206,007	Rutland	63,641	3	.24
California	Los Angeles-Long Beach-Santa Ana	12,950,129	San Francisco-Oakland-Fremont	4,180,027	3	.10
Nebraska	Omaha-Council Bluffs	822,549	Lincoln	283,970	2	.90
Kentucky	Louisville-Jefferson County	1,222,216	Lexington-Fayette	436,684	2	.80
Wisconsin	Milwaukee-Waukesha-West Allis	1,509,981	Madison	543,022	2	.78
Alabama	Birmingham-Hoover	1,100,019	Mobile	404,157	2	.72
Kansas	Wichita	592,126	Topeka	228,894	2	.59
Pennsylvania	Philadelphia-Camden-Wilmington	5,826,742	Pittsburgh	2,370,776	2	.46
New Hampshire	Manchester-Nashua	402,789	Lebanon	172,429	2	.34
Mississippi	Jackson	529,456	Gulfport-Biloxi	227,904	2	.32
Utah	Salt Lake City	1,067,722	Ogden-Clearfield	497,640	2	.15
Florida	Miami-Fort Lauderdale-Miami Beach	5,463,857	Tampa-St. Petersburg-Clearwater	2,697,731	2	.03
North Dakota	Fargo	187,001	Bismarck	101,138	1	.85
South Dakota	Sioux Falls	212,911	Rapid City	118,763	1	.79
North Carolina	Charlotte-Gastonia-Concord	1,583,016	Raleigh-Cary	994,551	1	.59
Arkansas	Little Rock-North Little Rock	652,834	Fayetteville-Springdale-Rogers	420,876	1	.55
Montana	Billings	148,116	Missoula	101,417	1	.46
Missouri	St. Louis	2,796,368	Kansas City	1,967,405	1	.42
Iowa	Des Moines-West Des Moines	534,230	Davenport-Moline-Rock Island	377,291	1	.42
Virginia	Virginia Beach-Norfolk-Newport News	1,649,457	Richmond	1,194,008	1	.38
New Jersey	Trenton-Ewing	367,605	Atlantic City	271,620	1	.35
Louisiana	New Orleans-Metairie-Kenner	1,024,678	Baton Rouge	766,514	1	.34
Connecticut	Hartford-West Hartford-East Hartford	1,188,841	Bridgeport-Stamford-Norwalk	900,440	1	.32
Oklahoma	Oklahoma City	1,172,339	Tulsa	897,752	1	.31
Delaware	Seaford	180,288	Dover	147,601	1	.22
Wyoming	Cheyenne	85,384	Casper	70,401	1	.21
South Carolina	Columbia	703,771	Charleston-North Charleston	603,178	1	.17
Tennessee	Nashville-Davidson--Murfreesboro	1,455,097	Memphis	1,274,704	1	.14
Texas	Dallas-Fort Worth-Arlington	6,003,967	Houston-Sugar Land-Baytown	5,539,949	1	.08
West Virginia	Charleston	305,526	Huntington-Ashland	285,475	1	.07
Ohio	Cleveland-Elyria-Mentor	2,114,155	Cincinnati-Middletown	2,104,218	1	.00
Rhode Island	Providence-New Bedford-Fall River	1,612,989	—

Some of this data is rather odd because of the way the census bureau aggregates cities. For example, the largest city in New Jersey is Newark. But Newark is counted as part of the New York City metropolitan area, so doesn't count separately. If it did, New Jersey's quotient would be 5.86 instead of 1.35. I should probably rerun the data without the aggregation. But you get oddities that way also.

I also made a scatter plot. The x-axis is the population of the largest city, and the y-axis is the population of the second-largest city. Both axes are log-scale:

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