# New Region Planning in France? Better Order or More Disorder?

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## Abstract

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## 1. Introduction

**Table 1.**Number ${N}_{c}$ of municipalities and of departments (${N}_{d}$), in the (22 Mainland and Corse + 5 Départements d'Outre-Mer, or overseas departments—“Territoires d'Outre-Mer”, or overseas territories (DOM-TOM) France regions, on 1 January 2012 and 2014.

r | Region Name | ${N}_{c,r}$ | ${N}_{d,r}$ | ${N}_{c,r}$ |
---|---|---|---|---|

January 2012 | January 2014 | |||

1 | Midi-Pyrénées | 3,020 | 8 | 3,020 |

2 | Rhône-Alpes | 2,879 | 8 | 2,874 |

3 | Lorraine | 2,339 | 4 | 2,338 |

4 | Aquitaine | 2,296 | 5 | 2,296 |

5 | Picardie | 2,291 | 3 | 2,291 |

6 | Bourgogne | 2,046 | 4 | 2,046 |

7 | Champagne-Ardenne | 1,954 | 4 | 1,953 |

8 | Centre | 1,841 | 6 | 1,841 |

9 | Basse-Normandie | 1,812 | 3 | 1,812 |

10 | Franche-Comté | 1,785 | 4 | 1,785 |

11 | Nord-Pas-de-Calais | 1,545 | 2 | 1,545 |

12 | Languedoc-Roussillon | 1,545 | 5 | 1,545 |

13 | Pays de la Loire | 1,502 | 5 | 1,496 |

14 | Poitou-Charentes | 1,462 | 4 | 1,460 |

15 | Haute-Normandie | 1,419 | 2 | 1,420 |

16 | Auvergne | 1,310 | 4 | 1,310 |

17 | Île-de-France | 1,281 | 8 | 1,281 |

18 | Bretagne | 1,270 | 4 | 1,270 |

19 | Provence-Alpes-Côte d'Azur | 963 | 6 | 958 |

20 | Alsace | 904 | 2 | 904 |

21 | Limousin | 747 | 3 | 747 |

22 | Corse | 360 | 2 | 360 |

SUBTOTAL | 36,571 | 96 | 36,552 | |

23 | Martinique | 34 | 1 | 34 |

24 | Guadeloupe | 32 | 1 | 32 |

25 | La Réunion | 24 | 1 | 24 |

26 | Guyane | 22 | 1 | 22 |

27 | Mayotte | 17 | 1 | 17 |

TOTAL | 36,700 | 101 | 36,681 |

## 2. Brief Review of a Few Regrouping Plans in a Chronological Way

## 3. Data Analysis

**Figure 1.**Semi-log plot of the number, ${N}_{c,r}$, of municipalities in the 27 France (FR) regions ranked by decreasing order of “importance”: blue half filled squares are for the metropolitan area; red half filled squares for the Départements d'Outre-Mer, or overseas departments-“Territoires d'Outre-Mer”, or overseas territories (DOM-TOM). The best three-parameter function, Equation (1), fit is shown for the metropolitan area only (${R}^{2}$= 0.978), but including Corse; the DOM-TOM have to be considered as outliers.

**Table 2.**Summary of statistical characteristics for the number distribution of municipalities (${N}_{c}$) in the various regions (${N}_{c,r}$) or departments (${N}_{c,d}$) in FR on different years. (**) N.B. Paris forms a department with only one city, itself.

${N}_{c,r}$ | ${N}_{c,r}$ | ${N}_{c,d}$ | ||||
---|---|---|---|---|---|---|

1 January 2012 | 1 January 2014 | 1 January 2014 | ||||

min | 17 | 360 | 17 | 360 | 1 (**) | 1 (**) |

Max | 3,020 | 3,020 | 3,020 | 3,020 | 895 | 895 |

${N}_{c}$ | 36,700 | 36,571 | 36,681 | 36,552 | 36,681 | 3,652 |

${N}_{r}$ or ${N}_{d}$ | 27 | 22 | 27 | 22 | 101 | 96 |

Mean (μ) | 1,359.3 | 1,662.3 | 1,358.6 | 1,661.5 | 363.18 | 380.75 |

Median (m) | 1,462 | 1,545 | 1,460 | 1,545 | 332 | 339.50 |

RMS | 1,608.4 | 1,781.8 | 1,607.6 | 1,780.9 | 413.32 | 423.91 |

Std Dev (σ) | 876.30 | 656.61 | 875.94 | 656.44 | 198.31 | 187.33 |

Std Err | 168.64 | 139.99 | 168.57 | 139.95 | 19.732 | 19.119 |

Skewness | –0.1017 | 0.2179 | –0.1018 | 0.2167 | 0.3331 | 0.4416 |

Kurtosis | –0.7728 | –0.2192 | –0.7745 | –0.2232 | –0.2857 | –0.1904 |

$\mu /\sigma $ | 1.5512 | 2.5316 | 1.5510 | 2.5311 | 1.8314 | 2.0325 |

$3(\mu -m)/\sigma $ | –0.3516 | 0.5359 | –0.3473 | 0.5324 | 0.4717 | 0.6606 |

## 4. Result Discussion

**Figure 2.**Semi-log plot of the number, ${N}_{c,r}$, of municipalities (blue diamonds) and ${N}_{i,r}$, of inhabitants (red triangles), in the 22 FR mainland regions ranked by decreasing order of importance for the R22 plan. The best three-parameter function, Equation (1), fit is shown for values and regression coefficient found in Table 3.

**Figure 3.**Semi-log plot of the number, ${N}_{c,r}$, of municipalities (blue diamonds) and ${N}_{i,r}$, of inhabitants (red triangles), in the 22 FR mainland regions ranked by decreasing order of importance for the B15 plan. The best three-parameter function, Equation (1), fit is shown for values and regression coefficient found in Table 3.

**Figure 4.**Semi-log plot of the number, ${N}_{c,r}$, of municipalities (blue diamonds) and ${N}_{i,r}$, of inhabitants (red triangles), in the 22 FR mainland regions ranked by decreasing order of importance for the M11 plan. The best three-parameter function, Equation (1), fit is shown for values and regression coefficient found in Table 3.

**Figure 5.**Semi-log plot of the number, ${N}_{c,r}$, of municipalities (blue diamonds) and ${N}_{i,r}$, of inhabitants (red triangles), in the 22 FR mainland regions ranked by decreasing order of importance for the H14 plan. The best three-parameter function, Equation (1), fit is shown for values and regression coefficient found in Table 3.

**Figure 6.**Semi-log plot of the number, ${N}_{c,r}$, of municipalities (blue diamonds) and ${N}_{i,r}$, of inhabitants (red triangles), in the 22 FR mainland regions ranked by decreasing order of importance for the V12 plan. The best three-parameter function, Equation (1), fit is shown for values and regression coefficient found in Table 3.

**Figure 7.**Semi-log plot of the number, ${N}_{c,r}$, of municipalities (blue diamonds) and ${N}_{i,r}$, of inhabitants (red triangles), in the 22 FR mainland regions ranked by decreasing order of importance for the P13 plan. The best three-parameter function, Equation (1), fit is shown for values and regression coefficient found in Table 3.

**Table 3.**Parameter values allowing with Equation (1) nice fits, as indicated by the regression coefficient R${}^{2}$ values.

${N}_{c,r}$ | R22 | B15 | H14 | P13 | V12 | M11 |
---|---|---|---|---|---|---|

$A{m}_{1}$ | 915 ± 120 | 638± 148 | 211 ± 91 | 216 ± 114 | 601 ± 241 | 1774 ± 270 |

${m}_{2}$ | 0.155 ± 0.081 | 0.012 ± 0.042 | –0.101 ± 0.068 | –0.099 ± 0.085 | –0.015 ± 0.077 | 0.108 ± 0.036 |

${m}_{3}$ | 0.390 ± 0.038 | 0.674 ± 0.078 | 1.162 ± 0.153 | 1.227 ± 0.195 | 0.864 ± 0.151 | 0.458 ± 0.058 |

R${}^{2}$ | 0.980 | 0.973 | 0.968 | 0.962 | 0.965 | 0.984 |

${N}_{i,r}$ | R22 | B15 | H14 | P13 | V12 | M11 |

$A{m}_{1}/{10}^{6}$ | 7.36 ± 1.97 | 5.66 ± 2.81 | 7.4 ± 2.0 | 4.2 ± 1.8 | 43 ± 1.9 | 13.96 ± 2.2 |

${m}_{2}$ | 0.678 ± 0.034 | 0.521 ± 0.083 | 0.510 ± 0.070 | 0.382 ± 0.080 | 0.334 ± 0.092 | 0.554 ± 0.042 |

${m}_{3}$ | 0.141 ± 0.084 | 0.269 ± 0.175 | 0.168 ± 0.131 | 0.385 ± 0.157 | 0.379 ± 0.169 | –0.053 ± 0.063 |

R${}^{2}$ | 0.983 | 0.936 | 0.948 | 0.947 | 0.931 | 0.981 |

## 5. Entropy Connexion

${N}_{c,r}$ | R22 | B15 | H14 | P13 | V12 | M11 |
---|---|---|---|---|---|---|

$ln\left({N}_{r}\right)$ | 3.0910 | 2.7081 | 2.6391 | 2.5649 | 2.4849 | 2.3979 |

$-\sum p\phantom{\rule{0.277778em}{0ex}}ln\left(p\right)$ | 3.0126 | 2.6056 | 2.4809 | 2.3871 | 2.3260 | 2.3334 |

${d}_{c,r}$ | 0.0254 | 0.0378 | 0.0599 | 0.0693 | 0.0639 | 0.0269 |

${N}_{i,r}$ | R22 | B15 | H14 | P13 | V12 | M11 |

$ln\left({N}_{r}\right)$ | 3.0910 | 2.7081 | 2.6391 | 2.5649 | 2.4849 | 2.3979 |

$-\sum p\phantom{\rule{0.277778em}{0ex}}ln\left(p\right)$ | 2.8284 | 2.5128 | 2.4837 | 2.4038 | 2.3419 | 2.3178 |

${d}_{i,r}$ | 0.0850 | 0.0721 | 0.0589 | 0.0628 | 0.0575 | 0.0334 |

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix: Department Analysis

**Table 5.**Best fit parameter values (top) in Equation (1) for the ${N}_{c,d}$ data, distinguishing 101 or 96 departments; see Figure 8; some ${N}_{c,r}$ data fit values are repeated for ease.

${N}_{c,d}$ | ${N}_{c,r}$ | ${N}_{c,d}$ | ${N}_{c,r}$ | |

Whole FR | FR _{metrop} | |||

$A{m}_{1}$ | 446.4 | 111.0 | 848.0 | 916.1 |

${m}_{2}$ | 0.131 | 0.048 | 0.148 | 0.155 |

${m}_{3}$ | 0.654 | 0.991 | 0.525 | 0.389 |

${R}^{2}$ | 0.989 | 0.955 | 0.990 | 0.978 |

**Figure 8.**Semi-log plot of the relationship between the number, ${N}_{c,d}$, of municipalities in the 101 FR departments (red diamonds) ranked by decreasing order of “importance” and in the 96 metropolitan departments (blue triangles); the best three-parameter function fits values, Equation (1), are shown. N.B. Paris changes rank, from 101 to 96; best three-parameter fit values are found in Table 5.

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Ausloos, M.
New Region Planning in France? Better Order or More Disorder? *Entropy* **2015**, *17*, 5695-5710.
https://doi.org/10.3390/e17085695

**AMA Style**

Ausloos M.
New Region Planning in France? Better Order or More Disorder? *Entropy*. 2015; 17(8):5695-5710.
https://doi.org/10.3390/e17085695

**Chicago/Turabian Style**

Ausloos, Marcel.
2015. "New Region Planning in France? Better Order or More Disorder?" *Entropy* 17, no. 8: 5695-5710.
https://doi.org/10.3390/e17085695