[EM] P.R. with districts

[DEMOREP1 at aol.com]

Proportional representation variants with districts guaranteed to elect zero, 
1 or 2 or more per district.

1.  The number of seats equals the number of districts (S=D). Each party 
getting a quota (Hare or Droop) of the total votes in all districts has its 
highest vote receivers elected.  Likely that some districts may not elect 
anyone (SMD zero per district variant)  (Possible to have S<D).

2.  The number of seats is more than the number of districts (S>D). 

A. zero per district variant

Each party getting a quota (Hare or Droop) of the total votes in all 
districts has its highest vote receivers elected.   Less likely that some 
districts may not elect anyone.

B. 1 per district variant 

The plurality winner or majority winner (preferably - using a single winner 
method) in each district is elected.  The overall p.r. seats for each party 
are adjusted by removing the votes for the district winners (above the Hare 
or Droop votes/seats ratio).    

Possible that some parties may get an excess percentage of the seats compared 
to their votes (with plurality especially). 

C.  2 or more per district variant

2 or more in each district are elected (using Hare or Droop quotas).  The 
overall p.r. seats for each party are adjusted by removing the votes for the 
district winners (above the Hare or Droop votes/seats ratio).    Possible 
that some parties may get an excess percentage of the seats compared to their 
votes.

The objective of all of the above is to get (as close as possible) ---

Party seats = Total Seats x Party Votes/ Total votes

I suggest that the Method of Equal Proportions (MEP) be used to apportion 
seats.  MEP uses the square root of S x (S+1) as divisors where S is the 
number of seats (so as to produce as nearly equal as possible votes/ seats 
ratios for different parties) (e.g. square roots of 2, 6, 12, 20, etc. - with 
large S amounts the square root fractions approach 0.5 (such as s.r. of 50 x 
51 = approx 50.5)).

For exact results each elected candidate would have a voting power equal to 
the number of votes received (since party votes/ party seats ratios for 
different parties are almost never equal -- especially with lower numbers of 
votes and/or seats) (i.e. Party voting power = Party votes).

If number voting (1, 2, etc.) is not used by the voters, then candidates can 
transfer their surplus or losing votes (within or outside of their districts)

The 2A variant is one way to do away with primaries (district ballot access 
by nominating petitions), have districts (with a limited number of candidates 
on the ballots) and permit small parties to win 1 or more seats overall.    

The purist party list- one district (at large) systems produce an excessive 
number of parties (causing p.r. to be severely attacked - as in Israel or 
South Africa).   

I mention again that about 5 parties can adequately represent the major left 
to right (or circular) political factions (i.e. number of seats = 5 x the 
number of districts).