# [Election-Methods] apportionment and unequal voting strengths

raphfrk at netscape.net raphfrk at netscape.net
Fri Dec 7 19:03:57 PST 2007

```I was looking at the seats in the EU parliament.? One of the issues is that there is a great variation in the sizes of the various (27) countries.

4 countries with 55 million+
3 countries with 20-40 million
5 countries with 10-16 million
7 countries with 5-10 million
5 countries with 1-5 million
3 countries with <1 million

Most of the countries are small (74% are less than 20 million).

The way they allocate seats is that the larger countries get more seats but it isn't quite proportional, larger countries get fewer seats than they would get if it was perfectly proportional..

Also, the seats are only indirectly based on population, as they are fixed by the various treaties.? This means that a country with a good negotiating team can get more seats than its fair share.

An approx formula for the current arrangement is that the seats are proportional to

(P + 1 million)^(0.8)

and

countries with a population below 2 million are considered to have 2 million.

The problem is that if the small countries are to get a reasonable number of MEPs (say 5+), then this requires that the larger countries get a very large number of seats (the largest 6 get more than 50 each and Germany gets 99).

One solution that I was thinking about was to allow MEPs to have different voting strengths.? This means that a large country could be given a smaller number of MEPs than currently but each would have a larger voting strength.? This leads to a smaller parliament but still gives all countries reasonable representation.

There was a discussion on this list a while back about Webster's method being unbiased and I wonder if a system for allocating variable strength seats would also be unbiased.

A seat total (S) is valid if

S/(round up(S/N))

is an integer

A valid seat total is one that can be divided by an integer to give an integer that is slightly less than N.? I have given a list of the valid seat totals from 1-200 at the end of the post.? N represents the max number of MEPs a country is allowed.

For example, assuming N=20, from 20-40 all
the valid totals will be even and from 40-60, all the valid totals would be divisible by 3 and so on.? This allows easy dividing so that if the voting power of the MEPs from that country are set to an integer amount, the seats can be divided to give an integer.

Define increment (Inc) as the smallest increment of S required to bring it to the next valid seat total.

Define effective population (Pe) as the population after the re-balancing has occurred.

Allocate seats to the country with the highest

Pe/(S+Inc/2)

excluding countries where Inc is greater than the number of seats left.

The country's total is then increased by Inc.

Once all the seats have been allocated.? Determine the voting strength for each country's MEPs needed to bring the total seats less than or equal to 20 and divide the number of seats allocated to that country by that amount.?? This will give an integer number of seats for each of the countries due to the way the increment works.

One issue is that the total number of seats would not be known in advance so the parliament would have to be large enough to handle a variable number of seats being required.? This is probably not a big issue as if N is small enough (say 10), each country will get around 9 seats each anyway.

However, it has the potential to reduce the size of the parliament.? Using 20 as the limit would reduce the size of the parliament from 782 to around 350.? Using 10 as the limit would reduce it to 214.

Using 10 as the limit, the following are the valid values from 1-200

MEPs get 1 vote
? 1 =? 1*1
? 2 =? 2*1
? 3 =? 3*1
? 4 =? 4*1
? 5 =? 5*1
? 6 =? 6*1
? 7 =? 7*1
? 8 =? 8*1
? 9 =? 9*1
?10 = 10*1

?12 =? 6*2
?14 =? 7*2
?16 =? 8*2
?18 =? 9*2
?20 = 10*2

?21 =? 7*3
?24 =? 8*3
?27 =? 9*3
?30 = 10*3

?32 =? 8*4
?36 =? 9*4
?40 = 10*4

?45 =? 9*5
?50 = 10*5

?54 =? 9*6
?60 = 10*6

?63 =? 9*7
?70 = 10*7

?72 =? 9*8
?80 = 10*8

?81 =? 9*9
?90 = 10*9

Always 10 MEPs just their vote totals change
100 = 10*10
110 = 10*11
120 = 10*12
130 = 10*13
140 = 10*14
150 = 10*15

Raphfrk
--------------------
Interesting site
"what if anyone could modify the laws"

www.wikocracy.com

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