[EM] Apportionment (biased?) let me add some more confusion to the mix :)

[Juho]

On Dec 11, 2006, at 12:38 , raphfrk at netscape.net wrote:

> > From: juho4880 at yahoo.co.uk
> >
> > One more tool that can be useful in some situations is the
> > hierarchical structure of the states/parties. To guarantee that
> > certain set of states/parties will not be underrepresented they  
> could
> > form a team/alliance. When seats are allocated to that team they
> > could lose (in typical allocation methods) only one seat to rounding
> > errors instead on many of them losing a seat. Geographic alliances
> > would maybe be more natural than e.g. an alliance of small states.
>
> What about sorting the States based on population and then splitting
> them into 2 groups such that the total population in each group is as
> equal as possible.
>
> The fractional seat is then split between the 2 groups based on  
> (Webster?)
> ... or maybe Webster should be used directly?
>
> This is then applied to each group recursively.

Ok. A binary tree like structure makes the division quite balanced  
(maybe even more than necessary for most practical needs).

> If any State ends up with zero seats, it is removed from the process
> and given a seat directly.  The process is then re-run, until it
> completes with all remaining States getting at least 1 seat.

Careful with this. There is a risk that the calculation rules steal  
seats from the states that have slightly more than one seat worth of  
inhabitants.

> This pretty much is forced to be unbiased between small and large  
> States
> size.  However, perhaps it would be biased in other ways.
>
> An additional rule could then be that States are allowed to form  
> groups
> 'manually', and manual groups cannot be split in two by the algorithm
> (until the group being processed is the manual group itself).

It is possible to support multiple "proportionalities". It is  
possible to make more than one of them "exact" (=all divisions  
followed to the accuracy of rounding errors that are smaller than one  
seat) at the same time or "approximate" (= one division based on one  
rule, then another rule applied in each group (of the first  
division), e.g. first the manual groups and then the automatic size  
based groups within the manual groups). A more typical situation  
would be to use some more orthogonal measures like party/ideology  
proportionality and regional proportionality.

The ideological and regional proportionality requirements are the  
most common ones. What others could there be? The state size based  
one was already discussed. Countries that have clear ethnical or  
religious division lines could use such additional proportionality  
rules. Maybe also different age or sex groups could be guaranteed a  
proportional share of the seats. It is quite straight forward to  
develop methods that respect such criteria either exactly or  
approximately in hierarchy. The number of seats should be large and  
the criteria should be as orthogonal as possible if we want to use  
several of them (to avoid situations where there for example are no  
female catholic candidates left in Hawaii when we would need one).  
Strong requirements on exact divisions also lead to pushing the  
rounding errors to some less critical areas but in a way that makes  
them very visible (e.g. (exact) ideological/party proportionality in  
50 states with (exactly) one seat in each state would probably lead  
to electing a green candidate in some state that has only a 5%  
minority of green votes).

> >
> > I already mentioned the different voting power. A simple method in
> > that direction would be to elect one representative from every state
> > and give her voting power in relation to the number of people she
> > represents. Or maybe large states would be given n seats with 1/n of
> > the voting power of the state etc. Maybe the building where these
> > representatives will work has a fixed number of physical seats =>
> > fill those seats and allocate voting power according to that.
>
> The logistics of this would make the legislature less efficient.  One
> possible rule would be that all Representatives must have voting
> strengths between 0.9 and 1.1 and a detailed count only happens if
> the vote is close (or if there is a motion demanding it).

I agree that some reasonable restrictions should be applied. Also my  
scenarios where the seats were divided in time may lead to too short  
times in office. If parties are allowed to fill the seats as they  
wish, one could also consider terms that last longer than one  
election period and terms that need not end and start at election  
time. Everything is ok as long as the party has exactly the agreed  
number of representatives active at any given time.

I however think that also a method that gives two votes to a  
candidate that got two quotas of votes and so on would be quite ok  
(i.e. the maximum number of votes could be infinite or some fixed  
limit instead of 1.1). Giving very long terms to candidates that get  
lots of votes is not as natural (since voters and candidates and the  
world change). Maybe they could keep some of their extra votes "in  
storage" for the next election but not more than some fixed amount.

One seat allocation method for different voting rights would  
(roughly) be to start from the root of the tree and allocate voting  
rights to each branch in proportion to the number of votes. The  
process would proceed always first in the largest still unallocated  
branch and would stop when all seats would be filled (= n branches  
have voting rights). After this the voting rights that were not  
allocated to individual candidates yet would all be given to the most  
popular sub-branch and finally the most popular candidate of a sub- 
branch. Additional rules on how to handle situations where one runs  
out of candidates or for maximum or minimum level of voting rights  
may be used.

A hierarchical structure may also lead to some natural arrangements.  
If one of the candidates in a small branch gets so many votes that  
also some other candidates will be elected from that branch, then  
that favourite candidate probably takes a leadership position within  
that branch even if the rules would not mandate that.

Juho Laatu

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