Legislative Elections with Accumulated Choices

[DEMOREP1 at aol.com]

The Accumulated Choices Tie Breaker for executive and judicial offices can be
modified for proxy type legislative elections (with some major complexity-
especially in computer programming)---

N legislative seats to be filled
Droop quota is used-- Quota (Q) = 1 + (Total Voters/(N+1))

Example for new folk-- Total voters= 700, Seats= 5, Q= 117
(Only 5 candidates can get 117 votes. 5 x 117= 585, 700-585= 115 maximum for
a sixth candidate)

The voters vote the standard 1, 2, 3, etc. for their first, second, third,
etc. choices. When any candidate is elected in any step, the ballots that
produced his/her election are removed. Transferred ballots are removed.

Step 1. (a) If the same N candidates get more votes than each other candidate
(in rotation), then such N candidates shall be elected.
(b) For such comparison purposes, the choice on each ballot that ranks one of
the N candidates or for such other candidate shall count as one vote for such
candidate.
(c) The following steps occur if (a) does not happen.

[Step 1(a) is the single winner equivalent to seeing if a single candidate
can beat each other candidate head to head. With many candidates there is a
very high probability that there will not be such a set of N candidates.]

Step 2. If a candidate gets a quota of first choice votes, then he/she is
elected.

[Example- Candidates C and E get more than 117 first choice votes and so are
elected]

Step 3. (a) If a candidate gets a quota of first plus second choice votes
from the remaining votes, then he/she shall be elected. 
(b) If 2 or more candidates get such quota, then the candidate with the
highest number of first plus second choice votes shall be elected (with (a)
repeated, if necessary).
(c) If a voter's first choice does not get a quota and the voter's second
choice is elected in Step 1, then such vote shall be transferred to the such
elected candidate.

[Example- Candidates A and F respectively get 125 and 120 first and second
choice votes. A is elected. F then gets less than 117 first and second choice
votes from the remaining votes (due to the crossovers of A and F second
choices). Some of the F first choice voters voted for C or E for second
choice. Such votes are transferred to C or E -- the logic being that their
first choice (F) did not make a quota so their second choice should be made
effective as soon as possible.]

Step 4. (a) If a candidate gets a quota of first plus second plus third
choice votes from the remaining votes, then he/she shall be elected.
(b) If 2 or more candidates get such quota, then the candidate with the
highest number of first plus second plus third choice votes shall be elected
(with (a) repeated, if necessary).
(c) If a voter's first or second choice does not get a quota and the voter's
third choice is elected in Steps 1 or 2, then such vote shall be transferred
to such elected candidate. 

[Example- Candidates B and F respectively get 120 and 118 first plus second
plus third choice votes from the remaining votes. B is elected. F again gets
less than 117 votes. Some of the voters voted for C, E or A for third choice.
Their votes are transferred to C, E or A.]

Step 5. Later steps
5(a) For each later step add another choice level and step level. 
5(b) Repeat until all seats are filled or until all votes are transferred.
5(c) If the preceding does not happen due to a failure of any remaining
candidate to get a quota, then the remaining candidate with the highest
accumulated votes from all choice levels from the remaining votes shall be
elected. 
5(d) Repeat 5(c) if necessary until all the seats are filled or until all
votes are transferred. 
5(e) If ballots remain, then transfer them to the highest choice on each
ballot who is elected, if any. 

[Example of 5(c)-- Candidates F, K and M respectively get 110, 112 and 105
accumulated choices for the last remaining seat. K is elected. All remaining
votes are transferred to C, E, A or B (whichever is the highest choice on
each ballot, if any).]

Ties
Step 6. If ties occur at any step, then use a lottery.

Voting Power
Step 7. Each member of the legislative body shall have a voting in the
legislative body, in person or by written proxy, equal to the votes that the
member finally receives in the election.

[Example- Final results C-157, E-151, A-145, B-135,  K-112, Total 700]
-----
The simpler proxy p.r. system eliminates the candidate with the least number
of first choice (plus transferred votes) repeatedly until only N candidates
remain. See Subj:  Condorcet Math in all Elections, Date:  Sat, Apr 13, 1996
4:16 PM EDT. In other words, the simpler system works from bottom up versus
top down in the above.

If the number of seats and the number of voters is large enough, then the
results of both methods would likely be the same (especially with partisan
candidate groupings and high voter rankings within each group by the party's
supporters -- e.g. if a party had three candidates, then the party's
supporters would generally vote 1, 2 and 3 in some combination for such 3
candidates. If the number of party supporters was large enough, then at least
1 of the 3 candidates would be elected early on.

Note- For legislative elections the quota for accumulated choices is the
Droop quota. For executive and judicial elections the quota for accumulated
choices is a majority of the total votes. With accumulated choices, the votes
of the voters should be seen as a giant matrix----     
                         Voters
Choice (Level)
1              F    A    C    G   A   More ballots right
2              A    F    D    B   H
3              C    B    B    F    K
4              D    K    A    K    B
More choices down

If the first choices do not produce winners, then the second choices are
added. If the first plus second choices do not produce winners, then the
third choices are added. And so forth.