The Universe of Disco

Smallest state capitals
I think it was James Kushner who first suggested that I consider the question of which U.S. state capital had the smallest population in relation to its state's largest city. For example, New York City is the largest city in the United States, but the state capital of New York State is Albany, with a population of about 850,000. The population of New York City exceeds that of Albany by a factor of around 20.

At the other end of the scale, of course, we have state capitals like Boston, Denver, Atlanta, and Honolulu that are their state's largest cities. For these states, the population quotient is 1, its theoretical minimum.

Well, James, it only took me thirty years, but here it is.

I tried to resolve the question manually a few weeks ago, by browsing Wikipedia for the populations of likely candidates. Today I took a more methodical approach, downloading the U.S. Census Bureau's July 2006 estimates for populations of metropolitan areas, and writing a couple of little programs to grovel the data.

I had to augment the Census Bureau's data with two items: Annapolis, MD, and Montpelier, VT are not large enough to be included in the metropolitan area data file. I used U.S. Census 2006 estimates for these cities as well.

I discarded one conurbation: the Census Bureau includes a "Metropolitan Division" in New Hampshire that consists of Rockingham and Strafford counties; this was the most populous identified area in New Hampshire. It didn't seem entirely germane to the question, so I took it out. On the other hand, including it doesn't change the results much: its population is 416,000, compared with Manchester-Nashua's 402,000.

The results follow.

State	Capital and its Population		Largest metropolitan area and its population		Quotient
MD	Annapolis	36,408	Baltimore-Towson	2,658,405	73	.02
IL	Springfield	206,112	Chicago-Naperville-Joliet	9,505,748	46	.12
NV	Carson City	55,289	Las Vegas-Paradise	1,777,539	32	.15
VT	Montpelier	7,954	Burlington-South Burlington	206,007	25	.90
NY	Albany	850,957	New York-Northern New Jersey-Long Island	18,818,536	22	.11
MO	Jefferson City	144,958	St. Louis	2,796,368	19	.29
KY	Frankfort	69,068	Louisville-Jefferson County	1,222,216	17	.70
FL	Tallahassee	336,502	Miami-Fort Lauderdale-Miami Beach	5,463,857	16	.24
WA	Olympia	234,670	Seattle-Tacoma-Bellevue	3,263,497	13	.91
AK	Juneau	30,737	Anchorage	359,180	11	.69
PA	Harrisburg	525,380	Philadelphia-Camden-Wilmington	5,826,742	11	.09
SD	Pierre	19,761	Sioux Falls	212,911	10	.77
MI	Lansing	454,044	Detroit-Warren-Livonia	4,468,966	9	.84
NJ	Trenton	367,605	Edison	2,308,777	6	.28
CA	Sacramento	2,067,117	Los Angeles-Long Beach-Santa Ana	12,950,129	6	.26
NM	Santa Fe	142,407	Albuquerque	816,811	5	.74
OR	Salem	384,600	Portland-Vancouver-Beaverton	2,137,565	5	.56
DE	Dover	147,601	Wilmington	691,688	4	.69
VA	Richmond	1,194,008	Washington-Arlington-Alexandria	5,290,400	4	.43
ME	Augusta	121,068	Portland-South Portland-Biddeford	513,667	4	.24
TX	Austin	1,513,565	Dallas-Fort Worth-Arlington	6,003,967	3	.97
AL	Montgomery	361,748	Birmingham-Hoover	1,100,019	3	.04
NE	Lincoln	283,970	Omaha-Council Bluffs	822,549	2	.90
WI	Madison	543,022	Milwaukee-Waukesha-West Allis	1,509,981	2	.78
NH	Concord	148,085	Manchester-Nashua	402,789	2	.72
KS	Topeka	228,894	Wichita	592,126	2	.59
MT	Helena	70,558	Billings	148,116	2	.10
ND	Bismarck	101,138	Fargo	187,001	1	.85
NC	Raleigh	994,551	Charlotte-Gastonia-Concord	1,583,016	1	.59
LA	Baton Rouge	766,514	New Orleans-Metairie-Kenner	1,024,678	1	.34
OH	Columbus	1,725,570	Cleveland-Elyria-Mentor	2,114,155	1	.23
AR	Little Rock	652,834	Little Rock-North Little Rock	652,834	1	.00
AZ	Phoenix	4,039,182	Phoenix-Mesa-Scottsdale	4,039,182	1	.00
CO	Denver	2,408,750	Denver-Aurora	2,408,750	1	.00
CT	Hartford	1,188,841	Hartford-West Hartford-East Hartford	1,188,841	1	.00
GA	Atlanta	5,138,223	Atlanta-Sandy Springs-Marietta	5,138,223	1	.00
HI	Honolulu	909,863	Honolulu	909,863	1	.00
IA	Des Moines	534,230	Des Moines-West Des Moines	534,230	1	.00
ID	Boise	567,640	Boise City-Nampa	567,640	1	.00
IN	Indianapolis	1,666,032	Indianapolis-Carmel	1,666,032	1	.00
MA	Boston	4,455,217	Boston-Cambridge-Quincy	4,455,217	1	.00
MN	St. Paul	3,175,041	Minneapolis-St. Paul-Bloomington	3,175,041	1	.00
MS	Jackson	529,456	Jackson	529,456	1	.00
OK	Oklahoma City	1,172,339	Oklahoma City	1,172,339	1	.00
RI	Providence	1,612,989	Providence-New Bedford-Fall River	1,612,989	1	.00
SC	Columbia	703,771	Columbia	703,771	1	.00
TN	Nashville	1,455,097	Nashville-Davidson--Murfreesboro	1,455,097	1	.00
UT	Salt Lake City	1,067,722	Salt Lake City	1,067,722	1	.00
WV	Charleston	305,526	Charleston	305,526	1	.00
WY	Cheyenne	85,384	Cheyenne	85,384	1	.00

Nineteen of fifty state capitals are their state's largest cities.

Vermont is an interesting outlier here. It makes fourth place not because it has a large city, but because its capital, Montpelier, is so very small. I tried doing some scatter plots, to see if anything else jumped out, but they weren't very illuminating. If anything, the data is suprisingly evenly distributed. Here's an example:

[ Addendum 20080129: Some remarks about the format of the Census Bureau's data file. ]

[ Addendum 20090217: A comparison of the relative sizes of each state's largest and second-largest cities. ]

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