| 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...
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)...
Computing 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--serendipitously a nice number: 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...
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)...
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,