TY - JOUR
T1 - Congressional symmetry
T2 - years remaining mirror years served in the U.S. House and Senate
AU - Carey, James R.
AU - Eriksen, Brinsley
AU - Rao, Arni S.R.Srinivasa
N1 - Funding Information:
We thank UC Davis undergraduate interns Angela Liu, Yuwei Jiang, Monte Patrick de Castongrene, Aditi Hosangadi and Hunter Jade Hammons for their assistance in data gathering. Appreciation is extended to emeritus Professor Walter Stone for his comments on earlier versions of the manuscript as well as to Lanny Winberry, Christopher Gibson, members of the Lindgren Research Enterprise and to an anonymous reviewer for their input. We are particularly grateful to Genus Editors Daniele Vignoli, Alessandra Derose, Elisabetta Barbi and Graziella Caselli for inviting us to write this paper.
Funding Information:
Open access funding provided by Università degli Studi di Roma La Sapienza within the CRUI-CARE Agreement. Research funded in part by a grant from the Center for the Economics and Demography of Aging, UC Berkeley (NIH 2P30AG012839).
Publisher Copyright:
© 2023, The Author(s).
PY - 2023/12
Y1 - 2023/12
N2 - Our overarching goal in this paper was to both test and identify applications for a fundamental theorem of replacement-level populations known as the Stationary Population Identity (SPI), a mathematical model that equates the fraction of a population age x and the fraction with x years to live. Since true stationarity is virtually non-existent in human populations as well as in populations of non-human species, we used historical data on the memberships in both chambers of the U.S. Congress as populations. We conceived their fixed numbers (e.g., 100 Senators; 435 Representatives) as stationary populations, and their years served and years remaining as the equivalent of life lived and life remaining. Our main result was the affirmation of the mathematical prediction—i.e., the robust symmetry of years served and years remaining in Congress over the approximately 230 years of its existence (1789–2022). A number of applications emerged from this regularity and the distributional patterns therein including (1) new metrics such as Congressional half-life and other quantiles (e.g., 95% turnover); (2) predictability of the distribution of member’s years remaining; (3) the extraordinary information content of a single number—the mean number of years served [i.e., derive birth (b) and death (d) rates; use of d as exponential rate parameter for model life tables]; (4) the concept of and metrics associated with period-specific populations (Congress); (5) Congressional life cycle concept with Formation, Growth, Senescence and Extinction Phases; and (6) longitudinal party transition rates for 100% Life Cycle turnover (Democrat/Republican), i.e., each seat from predecessor party-to-incumbent party and from incumbent party-to-successor party. Although our focus is on the use of historical data for Congressional members, we believe that most of the results are general and thus both relevant and applicable to all types of stationary or quasi-stationary populations including to the future world of zero population growth (ZPG).
AB - Our overarching goal in this paper was to both test and identify applications for a fundamental theorem of replacement-level populations known as the Stationary Population Identity (SPI), a mathematical model that equates the fraction of a population age x and the fraction with x years to live. Since true stationarity is virtually non-existent in human populations as well as in populations of non-human species, we used historical data on the memberships in both chambers of the U.S. Congress as populations. We conceived their fixed numbers (e.g., 100 Senators; 435 Representatives) as stationary populations, and their years served and years remaining as the equivalent of life lived and life remaining. Our main result was the affirmation of the mathematical prediction—i.e., the robust symmetry of years served and years remaining in Congress over the approximately 230 years of its existence (1789–2022). A number of applications emerged from this regularity and the distributional patterns therein including (1) new metrics such as Congressional half-life and other quantiles (e.g., 95% turnover); (2) predictability of the distribution of member’s years remaining; (3) the extraordinary information content of a single number—the mean number of years served [i.e., derive birth (b) and death (d) rates; use of d as exponential rate parameter for model life tables]; (4) the concept of and metrics associated with period-specific populations (Congress); (5) Congressional life cycle concept with Formation, Growth, Senescence and Extinction Phases; and (6) longitudinal party transition rates for 100% Life Cycle turnover (Democrat/Republican), i.e., each seat from predecessor party-to-incumbent party and from incumbent party-to-successor party. Although our focus is on the use of historical data for Congressional members, we believe that most of the results are general and thus both relevant and applicable to all types of stationary or quasi-stationary populations including to the future world of zero population growth (ZPG).
KW - Brouard’s theorem
KW - Carey’s equality
KW - Congressional half-life
KW - Congressional life cycles
KW - Congressional turnover
KW - Period-specific populations
KW - Population stationarity
KW - Stationary population identity
UR - http://www.scopus.com/inward/record.url?scp=85148450541&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85148450541&partnerID=8YFLogxK
U2 - 10.1186/s41118-023-00183-z
DO - 10.1186/s41118-023-00183-z
M3 - Article
AN - SCOPUS:85148450541
SN - 0016-6987
VL - 79
JO - Genus
JF - Genus
IS - 1
M1 - 5
ER -