Representation, Apportionment, Votation, Election

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

[reconstructed and updated from my Election 1996 web-published articles]

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 for implementation; The Representation in Congress received by voters was first estimated as one-per-thirty-thousand free Persons, a number deemed by the Founders, as both too large and too small... But even-so if that rule were applied directly today the House of Representatives would number ten thousand members--their main meeting-building proportions alone would equal a small stadium (unless by Internet as would be virtual and could be remote)--exceeding by fourfold even the old USSR itself copycatting the USA and ballooning to two thousand-some peoples deputies, but which we'll show next was overly much...

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 to the Constitutional designation of numericities... our mathematics may include simple notions of entropy-energy ("square law"), and evaluation techniques as powerful as the Gaussian Normal distribution...

Contemporarily by Census 2010 [USA] we find some 309.2 million Persons Represented for their concept of nation in 50 States (excluding the Capitol District of Columbia); And in the earliest past, 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, co-operate by thorough discussion and agreement among their co-equal members: potentially additive, before the vote, and, energetically by the square; An ideal Representation may thus equal the square-root of the population, (or, some portion above but much-less than linear)...

We compute in thousands for scale (the base for large numbers, American millions, billions, trillions, etc.), plus an extra half for each State to allow for rounding-up, as suits the Constitutional notion of minimum Representation: √ (3.55e6/1000) + (13/2) = 59.6+6.5 = 66.1 Representatives--a nice number serendipitously: they actually took 65, (again, by their best-estimation), And thereafter Congress, by its Constitutional provision, several times reestimated how-many Representatives the apportionment should elect--again, it was done by artistic feel still based on the simple direct rule--which means they had no rule for following, the rule--'til since ca 1910, they abruptly capped, their numbers at 435, where today it remains, stuck, 'capped'... whereas the entropic -better reduction- would elect √ (309.2e6/1000) + (50/2) = 556 + 25 = 581, minimum (before District considerations)...

N.B. More-linear would apportion more if diversity were more-linear, for example consider the earliest notion of family, as a unit-vote husband-or-wife...

SIDEBAR: THE LAWFUL DUTY: [2016] Congress is, Constitutionally, responsible, for setting its Numbers... Not, a prior Congress, Not, 'communist overlords' specifying their quotations for self-governance, as Congress has worn-ragged its 435-cap a century... And-yet, How shall today's student-of-thinking-law explain the necessity of duty and fulfillment when they're taught by that old-ivy-school-hack of 'how-to-let-deterioration-make-money-on-representational-government'... Something more is needed in the higher education, and it's not-unlike what science-students need do to explain-why a certain proof or demonstration approach is better than another when multiple approaches may all be understood in examples, But, human-law-studies require that perception sooner, as essential-to law... (*)

* (Explaining-the-why, goes beyond merely recognizing the better-equivalence of two-or-more example constructions or equations, to perceiving why, one is, better, and, the path-to-it, how-to-get-there-from-the-others... but which was new in the elementary students school-training, to say how or why, it was better, and seems to be 'experience' to-come in college... but... comparatively, Congress, by-definition, has-had-plenty of that, experience, or so-it-is-written in numbers as age-minima...)

SIDEBAR: OTHER PERSONS, VOTING: [2016] Although not stated as such, the original notion of free Persons, and Indians-not-taxed, and other persons 3/5ths of a Vote, persists in the Constitutional text, if-not in discussion: So we may estimate whether the 1910 cap-automaticity constituted a preplanned popular defection by reduction of voting power, (There was also the notion of Biblical-Revelation prophecy that only 102-million-or-plus persons should be saved), using this formulation herein: OP+FP=1, OP(3/5) + FP = (435-25/556) before State-roundups, = 0.74 ⇒ OP ≈ 65% or 203-million of the United States constituted of other persons...

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 some small States may be thus 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 total Number would also adjust by the sum-of-per-State-roundings-up.)

A NEW MINIMUM: [2016] Because, Representation in the House is actually per-State/by-State, (and no cities-on-the-borders crossovers), it should have the same minimum-two-(2)-per-State as has the Senate, (meaningful to the extent they'd collaborate more-within-each-State than between States, on their voting)... This'd be at the top of rounding-up for the small States, and of less-consequence for larger States, towards little-to-no-significance for the very-large-to-largest... (the meaning of two-each we'll not discuss but note that it does allow for one to be away on occasion, and provides for internal conversation, per State)...

VOTATION:

Ideally Congress has a constant output capacity for legislation reviewed and voted; but a size-proportional input from independent legislators, adding-energetically, 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, or less-diverse, legislation: we must ask (it) for surer, legislation, to keep Supreme-challenges constant... Presuming, the dominant causal (failure) mode of passed legislation is (was) random-voting centered about equivocation (yes:no::50:50), we (or simply the President) by-choice 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 P(Z≥): ZP(1/2√N)(√N/2)+(N/2)+0.5, gives us 24.6 over 291.0 [of 581 as above] = 316, and 9 over 50 [100/2] = 59, "ayes", in the two Houses, (significantly below the two-thirds-majority, 388 and 67, for overriding a Presidential Veto).

ELECTION:

A note on the subject of "term limits"--Two consecutive, plus, one non-consecutive, third, term, provides for election, reelection, and retro-election, (for a maximum total of three-and-a-half terms in the rare case of a partial term, term-limited to a half-term, that comes in the case of a vice president ascending in the absence of the president)... any more terms would be time-like reduplications unnecessary to get-the-'promised'-job-done, among a large population of qualified candidates... (And, all, elected, Offices, should probably be accountable to these same '2+1+½' term limits, except maybe in the smallest-'local'est populations)...

And a final comment on the inter-timings of Elections among Presidents, Representatives, and Senators [USA]: It would seem, the explanation, for alternately-overlapping-alternate-Senators with the Presidential Election, is missing in elementary and high schools--It would seem wiser to completely separate, all, Senatorial Races, from the Presidential Race, and therefor set Senate terms to 8-years-each in two, parts, (we currently have 6-years-each in three, parts, one fallow, and alternately coinciding with the President), and, have each elected by their whole, State, rather than two 'half-State'-senators, (and resignations restricted to running for higher, offices, President or, Governor of their own State)... the national transition to sorted-out should be brief...

A premise discovery under the title,

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

[1995] 2004, 2016 GrandAdmiralPetry@Lanthus.net