Representation, Apportionment, Voting

A selection-win by votation must meet the needs of the voters: and that need can be described mathematically-- to the extent that voting is a system or science (denoted Political Science, a specific system application of statistics)

[under reconstruction - from my 1995-(election) web-published article]

Insight lead the country's Founders (USA in this example) to Constitute government with written laws that need never change,- save by emendation. But these sufficient laws do need rightful interpretation. The Representation in Congress received by voters was first estimated as one per thirty-thousand free Persons (a number deemed by the Founders, both too large and too small). But even-so if that rule were applied directly today, the House (of Representatives) would number eight thousand members;-- the main meeting-building proportions alone would equal a small stadium (unless by Internet: as would be virtual).

Could the original intent be interpreted? Yes, mathematical systematics attempts it;- but which historically has produced some weird conclusions that don't meet the voters needs as well as say, a -better- reduction.

REPRESENTATION:

Taking pertinent facts from 1787 (USA) as reproducible references, we can systematically accommodate the present, 1993, to the Constitutional designation of numericities ... our mathematics may include simple notions of entropy-energy, and evaluation techniques as powerful as the Gaussian Normal distribution.

Contemporarily, by Census 2000, we find some 281.4 million Persons (USA) Represented for their concept of nation in 50 States (excluding the Capitol, a District); in 1787, extrapolating back-beyond the 1790 Census, some 3.55 million Persons in 13 States (the number of Persons was a best-estimate: not a regular tally). Assigning to each equal-but independent energy-of-diversity to apply collectively to the whole, the average potential-of-diversity is proportional to the square-root of this total:-- cf energy:potential::square:root.

But, Congressional Houses within themselves operate by thorough discussion and agreement among their equal members: -potentially additive (before the vote), and- energetically by the square.-- An ideal Representation may thus equal (or above) the square-root of the population, or a portion above square-root (much-less than linear)....

We try in thousands for scale, plus an extra half for each State (United States) to allow for rounding-up, as suits the Constitutional notion of minimum Representation:-- √ (3550000/1000) + (13/2) = 59.6+6.5 = 66.1 Representatives ... a nice number, serendipitously: they actually took 65.

But thereafter, Congress itself several times reestimated how-many Representatives the apportionment should elect:-- it was done by artistic feel still based on the simple direct rule: which means they had no rule for following the rule ... and today, stuck since ca 1910, the number is 435;- while the entropic -better reduction- would elect √ (281400000/1000) + (50/2) = 530 + 25 = 555, minimum (more-linear would go more).

APPORTIONMENT:

Representatives are popularly elected (on merit and ability) to serve the collective Persons in their respective districts. Workloads deemed proportional to their Numbers, apportionment of Representatives among the States should minimize the maximum workload-per-Representative; and while small States are favored, they would never be excessively burdened: the most-worked Representatives ought have lots of close company: A matched system. Idealized minimax adjusts the total House to redistribute the largest States within the top tier. Of five renown schemes, minimax or idealized minimax, caps the workload, and distributes it optimally. (The actual total Number might also adjust to the sum of States.)

VOTATION:

Ideally Congress has a constant output capacity for legislation reviewed and voted; but a size-proportional input from independent legislators, addingenergetically, means a square-root-of-size-proportional potential diversity legislated, and similarly the (diverse) ways in which such legislation may (fail) Constitutionality before the Supreme Court, which itself has but a constant throughput capacity for challenges (ways) reviewed and judged. We cannot ask a larger Congress to produce less (diverse) legislation: we must ask (it) for surer legislation, to keep challenges constant. Presuming the dominant causal, (failure) mode of passed legislation is (was) random voting centered about equivocation (yes:no::50:50), (we) must raise the pass-threshold to suppress that entropic zone to below passing: the random (tail) still passing shall be as frequent as half the reciprocal of the square-root-of-size of the House: Approximating with the Normal QZ: ZQ(1/2√N)×(√N/2)+(N/2)+0.5, gives us 24 over 268 [535/2], and 9 over 50 [100/2], "ayes", in the two Houses.

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ELECTION:

A secondary note in relation to the subject of "term limits"-- Two consecutive plus one non-consecutive third term, provides for election, reelection, and retro-election ... any additional terms are reduplications (save the partial term, typically limited to a half term, that comes in the case of a vice president ascending in the absence of the president).

A premise discovery under the title,

Grand-Admiral Petry
'Majestic Service in a Solar System'
Nuclear Emergency Management

© [1995] 2004 GrandAdmiralPetry@Lanthus.net