City size distributions are driven by each generation's stay-vs-leave decision
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909188631822336 |
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| author | Spencer, Robin W. |
| author_facet | Spencer, Robin W. |
| contents | Throughout history most young adults have chosen to live where their parents did while a smaller number moved away. This is sufficient, by proof and simulation, to account for the well-known power law distributions of city sizes. The model needs only two parameters, $r$ = the probability that a child stays, and the maximum number of cities (which models the observed saturation at high city rank). The power law exponent follows directly as $α= 1 + 1/r$, with Zipf's Law simply the limiting case as $r \rightarrow 1$. Observed exponents $(α= 2.2 \pm 0.4, n = 158)$ are consistent with stay-or-leave data from large genealogic studies. This model is self-initializing and could have applied from the time of the earliest stable settlements. The driving narrative behind city-size distributions is fundamentally about family ties, familiarity, and risk-avoidance, rather than economic optimization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_02129 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | City size distributions are driven by each generation's stay-vs-leave decision Spencer, Robin W. Physics and Society Throughout history most young adults have chosen to live where their parents did while a smaller number moved away. This is sufficient, by proof and simulation, to account for the well-known power law distributions of city sizes. The model needs only two parameters, $r$ = the probability that a child stays, and the maximum number of cities (which models the observed saturation at high city rank). The power law exponent follows directly as $α= 1 + 1/r$, with Zipf's Law simply the limiting case as $r \rightarrow 1$. Observed exponents $(α= 2.2 \pm 0.4, n = 158)$ are consistent with stay-or-leave data from large genealogic studies. This model is self-initializing and could have applied from the time of the earliest stable settlements. The driving narrative behind city-size distributions is fundamentally about family ties, familiarity, and risk-avoidance, rather than economic optimization. |
| title | City size distributions are driven by each generation's stay-vs-leave decision |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2405.02129 |