A Graphical Illustration of Representation

How accurate will representation be with sortition? To illustrate this I wrote a short program to mimic choosing assemblies at random, and to show how members of a particular group or class are represented. In this example each assembly has 500 members, and the group forms 50% of the population. Typical output looks like this (I have left out twelve pretty boring lines):

Total number of assemblies drawn 400
Population 10 000 000
Assembly size 500
Proportion of class in population 0.500
Expected no of class members in assembly 250.0

251 242 244 251 263 237 257 241 239 232 256 235 244 253 229 241 257 256 250 268
276 241 222 267 270 256 247 …
… 238 244 243 259 263 245 216 260 235 250 240 241 245
227 271 249 263 224 237 251 238 249 263 260 238 247 255 239 243 255 254 237 249
242 246
265 232 252 249 241 259 239 268 252 247 242 227 246 240 237 245 240 241
263 250 241 247 257 278 248 257 257 244 236 256 233 257 243 260 263 250 238 235
251 246 260 267 257 250 258 254 247 242 250 255 250 235 273 255 247 252 260 240
261 235 250 248 247 252 233 266 252 252 257 261 253 258 272 252 249 234 261 235
270 249 251 244 247 256 253 248 239 258 256 250 245 273 253 246 253 247 259 234

Greatest deviation from the expected number of class members = 34.0 or 6.8% of assembly.
Standard Deviation (sigma) = 10.7.
Mean no of class members for all assemblies = 249.60.
2 × sigma = 21.4 or 4.3% of assembly. 95.5% of deviations will be less than this.
3 × sigma = 32.1 or 6.4% of assembly. 99.7% of deviations will be less than this.
Number of over-representations = 182.
Number of under-representations = 198.
Greatest number of consecutive over- or under-representations = 9 (in 400 assemblies).

Some explanations are necessary here. For simplicity, the results in the table above are presented as if all members were drawn at the same time, but there is no such assumption in the program code, and we might regard the results above as a series of snapshots of the assembly composition taken every time its membership is completely renewed. In this case I have taken the proportion of the class in the total population as 0.5.
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Against elections, the video

A surprisingly militant video from David Van Reybrouck.