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The 'Ross quota' is hyr nam'd for J F S Ross. In his 1955 bwk,
Elections and Electors, he identify'd a 'natural law' governing the
permisibl variations, in the number of konstituents per konstituensy in a
singl member system, with regard to lokal komunity boundarys.
The Ross quota jeneralises his rul for uon member systems to tw-member
systems, or thry-member systems, etc. In other words, the Ross quota aplys
to any uniform member system.
In a demokrasy, voters are supos'd to be equaly represented. Ych member of parliment ( MP ) represents an equal number of voters. A parliment of 600 MPs mIt represent 36 milion voters. So, ych MP shud be responsibl for 36 milion voters divided by 600. That is 60 thousand voters per MP.
This total voters, V, divided by total number of representativs, R ( or
the 'syts' they tak in parliment ) is kal'd the 'Hare quota'. That is V/R.
This quota is nam'd after Thomas Hare. In mid-nIntynth sentury Britain, he
propos'd proportional representation for jeneral elektions. His skym tryted
the kuntry as a singl konstituensy, in wich his quota of vots was enuf
to elekt a kandidat as an MP.
In the exampl, any kandidat, hw gather'd 60 thousand vots from anywer in
the kuntry, wud be elekted to parliment. Hare's system, wich
proportionaly kounts balot papers giving rank'd choises of kandidats,
virtualy maximises the voters' chois of representation.
At the other extrym to Hare's system, ther is the singl member system,
the most lokal system. This minimises chois, or the elektoral prinsipl, in
favor of the lokality prinsipl. But the Hare quota is stil nyded to giv
the requir'd number of konstituents per singl member konstituensy. That is 60
thousand, in the abov exampl.
In fakt, this requir'd averaj of voters per representativ is a starting
point for praktikly any system of representativ demokrasy. That inkluds
multi-member systems. A tw-member system wud requir the Hare quota to be
dubl'd, to estimat the requir'd number of konstituents per tw-member
konstituensy. That is 2 x 60 = 120,000. A thry-member system wud requir
konstituensys to be thry tIms the Hare quota or 180 thousand
konstituents.
Wen Hare introdus'd his system in 1857, the Hare quota was ment to be an
elektiv quota. But it sertainly dos not serv that purpos in a singl
member konstituensy. Uon kandidat must win haf the vots not to be defyted
by another. The Hare quota wud requir a kandidat to win al the vots, if
it wer us'd as the elektiv quota.
The proper elektiv quota is not the Hare quota of V/R but V/(R+1). This
later quota is nam'd the Droop quota, after H R Droop, hw explain'd it in
1869. Wen ther is uon representativ to be elekted ( R = 1 ) the Hare quota
wud giv total vots divided by uon ( V/1). But the Droop quota givs total
vots divided by uon, for the number of representativs, plus uon:
V/(1+1).
If both kandidats got haf the vots, a random chois wud hav to be mayd, to brek the tI.
In a tw-member konstituensy, the Droop quota, or elektiv minimum vots a
kandidat nyds to be elekted, is uon-third of the vots. Thus, tw elekted
kandidats garanty a minimum proportional representation of tw-thirds the
voters in that tw-member konstituensy.
In a thry-member konstituensy, the Droop quota is uon-quarter the vots,
giving a 'PR' of thry-quarters the vots. And so on.
Thus, for a 600-member konstituensy of the houl nation, lIk that propos'd by
Hare, the striktly korekt elektiv quota wud not be V/R = 36m./600 =
60,000.
Insted, the Droop quota givs V/(R+1) = 36m./(600+1) = 59,901 ( rounded-up to
the nyrest houl number to ensur no kandidat is rongly elekted on les
than the minimum ).
The Hare quota desIds how many voters ych representativ wil serv. But the Droop quota is nyded to desId betwyn voters hw the reps wil be. Ther is another quota that folows direktly on from thys tw. I'v kal'd it the Ross quota bekaus it is implisit in his explanation of the limit to alow'd variations in the number of konstituents, with regard to natural boundarys, in a singl member system.
Supos the abov exampl that requirs ych singl member konstituensy be of 60,000 konstituents. Thys ar to giv lokal representation. That argius ther boundarys must be tru to the lokalitys. The question is how much biger or smaler than 60 thousand shud be alow'd, with respekt to natural variations in the population sizes of lokal komunitys?
J F S Ross anser'd this. A konstituensy shud not be biger than 80 thousand nor smaler than 40 thousand. WI? Bekaus, a konstituensy of 80,001 is 20,001 biger than the equal konstituensys' bench-mark of 60,000. If yu divid the over-sIz konstituensy into tw singl member konstituensys of 40,000 and 40,001, they ar both kloser to the requir'd 60,000.
Ther was no praktikal ryson for Ross to go on to ask wat ar the permisibl variations for a tw-member system, wich was the English jeneral elektion system, that had byn gradualy abolish'd over the nIntynth sentury and erlier part of the twentieth sentury.
However, the question of permisibl variations in any uniform member system is of mor than theoretikal interest. Yusing the previus exampl, a tw member system wud myn konstituensys had tw syts representing 60,000 konstituents ych. The total konstituents per tw-member konstituensy is 120,000.
We kan trI a formula that fits the kais of singl member systems, and sy
if it works for tw member systems. The vots per konstituensy divided by the
number of syts plus tw, or V/(R+2), givs 60,000/(1+2) = 20,000. This givs
the permited variation of konstituents in the singl member system.
This formula also lwks promising as the Ross quota, bekaus it folows
direktly on from the Hare quota, V/R, and the Droop quota, V/(R+1).
Now to aply V/(R+2) to a tw member system: 120,000/(2+2) = 30,000.
Uon konsiders that the variations in a singl member system wer determin'd in terms of variations in the permited number of konstituents per representativ. We hold to this, rather than konstituents per konstituensy: it wud be rong to think that the permited variation in tw member konstituensys was 120,000 plus or minus 30,000 konstituents.
Wat is rong with the 150,000 to 90,000 variation? The smalest permisibl konstituensy is alow'd to go down to tw syts representing 45,000 ych. But the larjest permisibl konstituensy wud only be alow'd to run down to tw syts representing 50,000 ych, after a third portion of 50,001 was transfer'd towards making-up another tw-member konstituensy.
Only the lower limit is korekt: 90,000. This myns that the tw syts in
the dubl member konstituensy must not be mor than 15,000 ych below the
requir'd 60,000 konstituents per representativ.
The uper limit on tw-member konstituensys is not 150,000 but 135,000.
Konsider that a komunity numbers 135,001. It wud then be mor equitabl, in
terms of the 120,000 'bench-mark' of equal konstituensys, to mak this tw
member konstituensy into thry syts, helping to mak up other tw-member
konstituensys, say, a minimal konstituensy of 90,000 plus a syt of
45,001.
Kompar going over a 150,000 limit. Such a tw-member konstituensy wud be chanj'd into thry syts to be fit konveniently into the tw-member system. The konstituensy lower limit wud be 100,000, lyving, say, 50,001 for a syt in an other konstituensy. This myns a 50,000 variation betwyn maximum and minimum permited variation. Wer-as the 135,000 to 90,000 limits show only a 45,000 variation.
Uon mIt argiu, a 135 thousand konstituensy implys tw syts ych
representing sixty-seven and a haf thousand. They ar both only seven and a
haf thousand from the requir'd averaj voters per syt. This sujests making
a koresponding lower limit of tw syts representing fifty-tw and a haf
thousand, for a konstituensy of 105,000. But then the uper limit wud hav
to be thry tIms 52 1/2 or uon hundred and fifty seven and a haf thousand.
In other words, tu big a variation ( 52 1/2 thou. ) is being mayd again.
Beyond the singl member system, the equal variation about a konstituensy averaj dos not work. For instans, the 45,000 variation betwyn 90,000 and 135,000 kud be ajusted to an equal twenty-tw and a haf thousand variation about 120,000. That is nInty seven and a haf thousand to uon hundred and forty tw and a haf thousand. But this wud be inequitabl, bekaus it wud imply a lower limit of tw tIms forty eit and thry-quarter thousand kompar'd to an uper limit of thry tIms forty seven and a haf thousand, befor a transfer of uon of thos thry portions.
Uon mIt also ask wI not hav a smaler variation than 45,000? It kan not be smaler than 40,000, bekaus that wud put the limits of variation betwyn tw and thry tIms 40,000, or 80,000 and 120,000. That wud mak the requir'd averaj as also the uper limit of variation. That fails the kondition of alowing a variation about the averaj for natural variations in lokal komunitys.
Wer-as, it is not til 45,000 variation is rych'd that we ariv at a formula konsistent with the kais for the singl member system. Naimly, V/(R+2) = 60,000/(1+2) = 20,000. This formula hapens to giv the variation for the uper limit, as wel as the lower limit. But the formula we kan jeneraly yus for the uper limit in multi-member systems also works for singl member systems.
Thus, for a tw member system, the uper variation may be given by the
formula: V/(R+2)R = 120,000/(2+2)2 = 15,000. Aded to 120,000 this givs the
maximum konstituensy of 135,000.
The formula also works for singl member systems: 60,000/(1+2)1 = 20,000 for
the uper variation, as wel as the lower. But this is just an aksident of tw
formulas for uper and lower variations giving the saim result for singl
member systems.
Is the unequal variation from 90,000 to 135,000 about 120,000 inequitabl? It may be asum'd that under-representation in the konstituensy system wil be match'd by a koresponding over-representation in an other part of the system. This is the inequitabl konsequens of having to alow for natural variations in the sIz of lokal komunitys. I belyv its implikation for the lop-sided variation of nInty to uon hundred and thirty fIv thousand is as folows:
The over-sIz konstituensys ar not alow'd to be as over-sIz as the under-sIz konstituensys ar alow'd to be under-sIz. Therfor, voters, in over-sIz konstituensys, kan not be as under-represented, voter for voter, as ther kounter-parts kan be over-represented in under-sIz konstituensys. This myns that the system balans of under-representation to over-representation must be met by ther being mor voters with ther leser degry of under-representation than voters, in under-sIz konstituensys, alow'd a greiter degry of over-representation.
In other words, in the lop-sided 90 to 135 thousand system, under-representation shud be sher'd mor betwyn voters in over-sIz konstituensys. Inkrysing the over-sIz limit to 150 thousand wud only myn an equaly greit spred of the voters' under-representation, to ther over-representation. But it wudnt, I ges, chanj the over-al amount of under-representation.
However, this isnt the saim as sying working models inkluding the Ross quota. Sy the sektion, after next.
Bryfly, the abov exampl kan be shown for a thry-member system. The
requir'd averaj thry member konstituensy bekom thry tIms 60,000 equals
180,000. The Ross quota givs the variation to the lyst sIz konstituensy, as
V/(R+2) = 180,000/(3+2) = 36,000.
So, the lyst sIz konstituensy is 180,000 - 36,000 = 144,000.
To get the uper variation, jeneraly divid the variation again by the
number of syts per konstituensy. Or, V/(R+2)R = 180,000/(3+2)3 = 12,000.
So, the maximum konstituensy is 192,000.
The Ross quota, V/(R+2) dosnt just giv the lower limit of variation. In terms of the requir'd averaj vot, it also givs the elektiv quota in the smalest permited konstituensy. It derivs the saim valu as the Droop quota in terms of the minimum permited voters per konstituensy. ( Kal the smalest vot: V,n wer n stands for minimum. ) That is to say: V/(R+2) = V,n/(R+1).
Yusing the exampl, this is: 180,000/(3+2) = 144,000/(3+1) = 36,000.
In this respekt, the relation betwyn the Ross quota and the Droop quota is, in turn, similar to the relation betwyn the Droop quota and the Hare quota, konsider'd both in terms of quotas or portions of representation and variations in representation. This may be shown as folows:
The Hare quota, V/R givs the requir'd averaj of voters per konstituensy. The Droop quota, V/(R+1) givs the elektiv quota for representativs in such a konstituensy. The proportion of representation in that konstituensy is: VR/(R+1). Thus, in a thry member konstituensy the proportional representation ( 'PR' ) is R/(R+1) = 3/(3+1) or thry-quarters of the vots.
Asuming al the konstituents vot ( wich of kors they normaly dont ) the permited variation in number of vots from number of elektiv vots is: V - VR/(R+1) = V/(R+1). That is, the Droop quota is both the elektiv quota and the variation in vots from elektiv vots. This kompars to the Ross quota as the elektiv quota in a minimal konstituensy and the variation from the averaj konstituensy to that minimal konstituensy.
For further symetry, kompar the Droop quota's proportional representation within konstituensys to the Ross quota's proportional representation akros konstituensys. The Droop quota's PR is the number of syts tIms the quota: RV/(R+1). The Ross quota PR is the ratio of the minimal konstituensy to the maximal konstituensy, say, V,n/V,x.
From abov, V/(R+2) = V,n/(R+1). So, V,n = (R+1)V/(R+2).
Also from abov, V,x = V + V/(R+2)R = V( (R+2)R + 1)/(R+2)R ) =
V(R+1)²/(R+2)R.
After kanseling, V,n/V,x = R/(R+1). This is the saim ratio of
representation akros konstituensys with the Ross quota, as the Droop quota
givs within a konstituensy.
In any konstituensy, the elektiv vot is the PR of the total vot. Akros
konstituensys, the minimal konstituensy is analjus to the elektiv vot and
the maximal konstituensy analjus to the total vot of any given konstituensy,
in an akros-konstituensy proportional representation, wer-by V,n =
V,x.R/(R+1).
The theoretikal distribution of natural konstituensys, bas'd on lokal komunitys with varying elektorats, in a uniform-member system, has to be within limits impos'd by the nyd for equal representation.
From the previus sektion, the minimum permited konstituensy has a greiter variation from the requir'd averaj konstituensy than the maximum permited konstituensy: the diferens is in the ratio of R to uon, respektivly.
Ther-for ther ar R tIms as many voters over-represented in the minimum permited konstituensy as ther ar voters under-represented in the maximum konstituensy. To kompensat for this imbalans, the distribution of konstituensys mIt be weited, with R tIms as many maximum-sIz konstituensys as minimum konstituensys.
With regard to the houl ranj of konstituensys betwyn thos tw uper and lower limits, the binomial distribution models for the aproximat number of over-sIz to under-sIz konstituensys about a requir'd averaj. Sy tabl uon, wer weit R equals the maximum weit fIv, in the weiting row, for fIv tIms as many maximum konstituensys ( shown in the far rIt kolum ) as minimum konstituensys ( shown in the far left colum of numbers ).
In terms of the previus sektion's diskusion of R, for representativs, it is simplest to asum that the uniform-member system, in this exampl is a fIv-member system.
( Nout that a simpl adaptation of tabl uon also shows how a non-uniform system of konstituensys is distributed. The weiting row kud be re-designated as the number of representativs per konstituensy. The binomial distribution then shows how sixtyn konstituensys wud be either uon-, tw-, thry-, for- or fIv-member konstituensys. The averaj number of representativs per konstituensy is thry. )
| Number of konstituensys klas'd from under-sIz to over-sIz: |
1 | 4 | 6 | 4 | 1 |
| Weiting to mak-up for konstituensys being mor under-sIz than over-sIz: |
1 | 2 | 3 | 4 | 5 |
| Totals of under-sIz to over-sIz ( about 18 averaj ) konstituensys: |
1 | 8 | 18 | 16 | 5 |
J F S Ross pointed out that elektoral lejislation ignor'd the natural law ( wich I kal the Ross quota ) for konstituensy variations in a singl member system. This shud be a variation of uon-third or 33 1/3 per-sent about the norm. I belyv Canada alows a 30 per-sent variation about the requir'd averaj sIz singl member konstituensy. That may not be tu far out. But Ross said that Britain's lejislation, in 1944, for a 25 per-sent variation, was found to be unworkabl.
In 1979, the viktorius Torys trI'd to impos as equal konstituensys as posibl. As a result, limits even below the 25 per-sent limit wer impos'd on unwiling lokalitys, after being over-rul'd in a hyring. Suksesful lokal oposition no dout depended on how much klout the lokal komunity had, rather than on the inherent justis of the kais.
Tak the exampl of tw Yorkshir konstituensys. The Boundary Komision desided to tak tw wards out of York, rather than lyv the sity as uon konstituensy. Thys tw wards wer aded to a rural konstituensy inkluding the smal town of Selby. York's lokal Labor and Tory asociations wer both opos'd to this taking out a slIs of the York 'kaik'. The pepl of York suksesfuly opos'd the plan.
But the Boundary Komision got away with a similar sort of plan for the Yorkshir town of Scarborough and distrikt. Ther tw wards, that sher'd the town's sy-sId interests, wer put in the agrikultural konstituensy of Ryedale. The juj admited the lokal oposition's kais was just but said he had to defer to the government's wish to equalis konstituensys as much as posibl.
The government had not set a definit limit to konstituensy variations. So,
with respekt to the boundary chanjes, som komunitys wer bound to be
tryted as 'mor equal than others'. This 'Orwellian' government gav
inequitabl gId-lIns, in its komand of equal konstituensys.
Uon must remember that by equalising the singl member konstituensys, the
Tory party in power inkrys'd its majority by about a hundred syts without
inkrysing its vot. Thus mor aparent equality was a stalking hors for even
mor inequality.
The singl member system is the most proun to jerymandering. For exampl, the Boundary Komision propos'd that Colchester's tw singl member konstituensys shud hav boundarys with uon sub-urban konstituensy shap'd lIk a do-nut and an other urban konstituensy shap'd lIk the hol in the midl. The later wud most lIkly hav gon to Labor.
The Town Klerk was ask'd if he wud hav objekted to this, if the Torys
had not kontrol'd the lokal kounsil. He wud not anser the question til he
had retIr'd. The hyring found against the do-nut as spliting town and
kuntry.
Beyond spliting a komunity on iner versus outer sity lIns, the mor basik
objektion is to spliting a town at al with singl member konstituensys.
Dr J F S Ross, MC, BSc, PhD, sivil enjinyr, army ofiser and kolej prinsipal, turn'd frylans rIter on demokratik elektions. Parliamentary Representation, in 1943, was the first bwk to revyl the bak-grounds of MPs. Nowadays such work givs akademiks a job. Ross did the reserch in his own tIm and found konsiderabl difikultys in his way. Indyd, a kopy of the bwk found its way into the Hous of Komons library, as esential ryding.
Ross' motivation was not an in-kom. He show'd how unrepresentativ
suposedly representativ demokrasy was. ( Ross' bwk inkluded a Tory MP's
dokument on parliment as a plutokrasy. ) This serv'd as evidens for a
representativ elektoral system, naimly the singl transferabl vot ( STV ).
Leiter statistiks on MPs rutynly stil show striking deficiensys, such as in
siens and teknolojy -- Ross' own kompetans.
In 1955, an other substantial work, Elections and Electors, kontinu'd Ross's aims. ( This was the bwk that konverted this rIter, wen a student. Leiter, I ask'd for a kopy from the sekretary of the Electoral Reform Society, in charj of its vital balot servises. LIk Ross, he had byn a military man, Major Frank Britton. He had a military MBE. )
In 1959, Ross publish'd a short bwk, The Irish Electoral System, to present the kais for retaining STV in the Irish referendum.
In 1955, Ross rout a pointed pre-fas to the first edition of Voting in Democracies, by J Lambert and Enid Lakeman. In leiter editions this bekaim Lakeman's standard work, How Democracies Vote. LIk Ross, she bekaim rekognis'd as a lyding expert on voting method.
Ross, Lakeman and Britton belong'd to wat mIt be kal'd the old gard of elektoral reform, hw belyv'd that the singl transferabl vot was rItly the demokratik method and wudnt suport expedients lIk the alternativ vot or party lists.
Richard Lung.
25 november; 14 desember 2002.