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City"}],"butte":[{"name":"Chico","pop":102911,"pop2020":103289,"changePct":-0.4},{"name":"Oroville","pop":19712,"pop2020":20039,"changePct":-1.6},{"name":"Paradise","pop":9114,"pop2020":5089,"changePct":79.1},{"name":"Gridley","pop":7355,"pop2020":7410,"changePct":-0.7},{"name":"Biggs","pop":1941,"pop2020":1953,"changePct":-0.6}]},"sources":[{"name":"U.S. Census Bureau, Population Estimates Program — Vintage 2024 city and town totals, California","url":"https://www2.census.gov/programs-surveys/popest/datasets/2020-2024/cities/totals/sub-est2024_6.csv","note":"POPESTIMATE2024 for every incorporated place (SUMLEV 162, active governments)"},{"name":"Gabaix, X. (1999) \"Zipf's law for cities: an explanation\", Quarterly Journal of Economics 114(3):739","url":"https://doi.org/10.1162/003355399556133"}],"method":"Every incorporated city and town in California ranked by the Census Bureau's 2024 estimate, with a straight line fitted to log population against log rank: the rank-size rule, whose slope ζ is 1 when the second city is half the size of the first, the third a third, and so on — Zipf's law. Gabaix showed that exponent follows from cities growing at the same average rate whatever their size, and it comes out near 1 for most countries; above 1 the biggest cities are larger than the rule allows, below 1 smaller. The line is fitted twice, over all 482 places (ζ = 1.27, r² = 0.73) and over the hundred largest (ζ = 0.70, r² = 0.98), where the rule holds best; the population predicted at Chico's rank is read off the top-100 line.","fetched_at":"2026-11-02T00:21:51.124Z"}