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The USA Parliament How Pure Proportional Representation (PR) Works By James Ogle

YouTube Video "The Case for Proportional Representation" by John Cleese (1987)
An early post in Usenet in Februaru 1994 by joogle@cruzio.com

About Pure American Proportional Representation (PR)

1. Three Ways to Describe the Voting (Methods #1, #2, and #3)
2. Terms and Definitions
3. Commentary by James Ogle
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1. Three Ways to Describe the Voting (Methods #1, #2, and #3)

There are three ways to describe how to count votes in multi-winner districts which we are using on this site; Methods #1, #2 and #3:

Vote counting method #1, Calibrating: [1 / (number of seats +1)] X (+ or - .000N[N=adjusted number until all seats are filled]) plus one vote = threshold for being elected in multi-winner seat district
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Vote counting method #2, Count the tics: Description About James Ogle's Vote Counting by William Waugh on 12/3/2013 and Modified on 9/13/2015 by James Ogle

It begins with determining the Hagenbach-Bischoff quota.

Divide the election's total number of votes by the number of seats.

This is the 1st quota.

The candidates which make the quota with the lowest sum of the enumerated rankings marked on the ballots win in consecutive order from lowest sum to highest.

Once the open seats are filled, no more names are elected.

To start the process, the voters start ranking ballots. That is to say, each voter ranks the candidates.

The ranking on each ballot begins with enumerating names with marks of #1, #2, and so on.

On a ballot, the voter associates so many (or so few) candidates as she wishes with the rank numbers. Equal ranking is not allowed.

However, I repeat, the voter can rank _so few_ candidates as she wishes. She is allowed to leave a candidate out of the rankings on her ballot. This is significant in understanding how this system works.

So much for the balloting; now to explain how the tallying proceeds:The tallying process accumulates a pair of numbers for each candidate. The more important number is the count of occurrences where a ballot ranks the candidate at all, regardless of the rank number (James calls this a "tic").

The number of tics and the sum of those tics by each name are derived from the ranked numerals assigned to that candidate on ballots.

When the number of all the rankings for each candidate reaches the 1st quota, then that candidate gets top priority for being elected to the open seats.

Once these totals are accumulated, the process provides an overall ranking of the candidates based on the following procedure for comparing any two candidates: If candidate A has strictly more count of tics than candidate B, then A is ranked higher than B.

If A and B have exactly equal tic counts, they have to be compared with regard to the other number, the sums of their ranking tic numbers.

In that case, the one with the lower sum number of tics, ranks higher in the resulting overall rankings of the candidates produced by the system.

All the names which have accumulated a number of tics whose total is equal to or more than the Hagenbach-Bischoff 1st quota, are now to be considered elected in consecutive order until all the seats are filled.

The top of the order of those elected begins with the one name with the lowest sum of the minimum number of tics needed to reach the quota, followed by each numerically ranked name who reached the quota, from the sum of the lowest numerals of those votes/tics which are needed to reach the 1st quota.

All the consecutively ranked names from this step are elected until all the open seats are filled.

If this awards a number of seats different from the desired number of seats, then adjust the quota slightly up or down until it awards all the seats.

This comparison procedure is monotonic in the sense that it is mathematically impossible for it to lead to a rock-paper-scissors situation.

It will rank all the candidates if there are no ties. Ties are theoretically possible, but I think unlikely in practice, especially with a large electorate.

Ties are possible in all reasonable voting systems, and the USA and International Parliaments do not object to ties. * * *

Vote counting method #3, Ossipoff's writing: A Written Description by Mike Ossipoff from 1995

Also known as "Rule #4":

4. THE SAINTE-LAGUE PARLIAMENT SYSTEM for seat allocation in all multi-seat districts:

Divide the election's total number of votes by the number of seats. This is the 1st quota.

Divide this quota into each candidate's votes, and round off to the nearest whole number. That's that candidate's seat allocation.

If, due to rounding, this awards a number of seats different from the desired number of seats, then adjust the quota slightly up or down until when paragraph two is carried out, it will award all seats.
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2. Terms and Definitions

Tic

A tic is a numeral, i.e. #1, #2, #3 etc. (or 1, 2, 3). Tics are required in all cases in USA Parliament voting and any character other than a numeral in voting on USA Parliament matters is considered not legitimate. Additionally, when more than one tic is used, the next tics must be consecutive numbers and no number may be skipped or used more than once or the entire marked ballot is marked "spoiled", or no good.

Parliamentary Go-Ahead

The parliamentary go-ahead means that the executives in an elected entity give the approval in advance in the election of all new nominees who are nominated by the other executives on the committee. Once the majority (50% plus one) of the executives give the go-ahead to elect all new nominees with their own #1 ranking (tic), then when any executives nominates a new name, the name is automatically elected. That's because the majority of execs had all agreed to give the new nominee a #1 tic.

Once the parliamentary go-ahead is given, then the execs can take turns nominating new names, and as all new names get elected in consecutive order, the top name (#1) on the list is moved down one spot to #2 and the new name is at the top. As each new name is elected, the process continues.

One executive may also elect two or more names in consecutive order as long as the parliamentary go-ahead is in effect.

This way, one executive can do all the nominating, and there is no slow down awaiting for approvals of the nominee being elected. The executive may still withdraw the parliamentary go-ahead and/or give the new nominee(s) a different tic besides a #1, but they may only use consecutively ranked numbers in their own column of rankings. The #1 across the board gives top nominee the #1 spot, but when numbers other than #1 are awarded, the rankings (tics) of all executives are averaged and the order of the name is affected accordingly. Then, the list of names is re-organized, the names with the most tics and lowest sums in ties are set in order, all the list's names are ranked with consecutive numbers from top to bottom and the process begins all over again.

Ranked Choice Voting (RCV)

Ranked choice voting is a system based on algebra where the voter ranks one or more choices beginning with the number one, followed by consecutive numbers, where no same number can be used more than once or the ballot is marked spoiled. The strict compliance to the consecutively ranked numbers enables a perfect vote count by all vote counters. The number one choice is the top preference of the voter, represented by the numeral 1.

Single-winner Districts Under RCV

When the marked ballots are counted, there is a minimum threshold for the name or item to win in a single winner district of 50% plus one vote, under RCV. Everyone's vote goes initially to his or her 1st choice. If no alternative has a majority, then the alternative with fewest votes is eliminated, and each of its ballots goes to voter's next choice. This process of elimination & re-distribution continues until 1 alternative has a majority of the ballots. RCV in single winner districts is known as Instant Runoff Voting (IRV).

Pure Proportional Representation (PR) In Multi-winner Districts Only (more per district = more exact representation)

In a two member district under RCV the threshold is 33.33% (closest the name/item can come to a three-way tie, or 1/3) plus one vote, and after each round of elimination under RCV, the first item/name to garner an additional vote (33.33% plus one vote) breaks the tie and is elected. The second item/name to reach 33.33% plus one vote is the second item elected in consecutive order.

In other words, three names received 33.33% of the votes cast, and two of the names received an additional vote and they win in consecutive order with 33.33% plus one vote each.

Each additional seat/item elected, lowers the threshold proportionately.

In a three member district, closest to four-way tie, 1/4th (or 25%), plus one vote, breaks the tie. The first three names to garner 25% of the votes (plus one vote) are elected, and the forth also received 25%, but no additional vote so that name did not win.

In a four member district, closest to a five-way tie, 1/5th (or 20%), plus one vote, breaks the tie and so the first four names to garner 20% plus one vote win in consecutive order.

In a five member district, closest to a six-way tie, 1/6th (or 16.66%), plus one vote, breaks the tie.

In a nine member district, closest to a ten-way tie, 1/10th (or 10%), plus one vote, breaks the tie.

In a 100 member district, closest to a 101-way tie, 1/101th (or .99%), plus one vote, breaks the tie.

In a 1000 member district (like the 8th USA Parliament Election of 2012), it's the closest we can come to a 1001-way tie (or .0999%), plus one vote, breaks the tie.
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Guaranteed Minimum Voter Satisfaction Level

Note: When 100 names win with .99% plus one vote each, a minimum total of 99% plus 100 votes counted to elect the 100 names.

When 1000 names win with .0999% plus one vote each, a minimum total of 99.9% plus 1000 votes counted to elect the 1000 names.

That's known as the "guaranteed minimum voter satisfaction level".
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ROUNDS

The first vote count of the items/names described above are elected is known as "round one", and round one is followed by round two, three, etc., until all the items/seats are elected.
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Commentary by Tory Mast
The History of Single Member Districts for Congress

Single Transferrable Vote (STV)

Should the threshold not be broken by any of the fractions (or percentages) listed above, then the name/item with the fewest #1 votes is eliminated because they have the least likely chance of winning the threshold.

Each marked ballot from the first eliminated name/item's stack of ballots is transferred to the voter's next highest ranked choice, being a #2. This is known as the single transferrable vote (STV).
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There are two variations ranked choice voting in the parliament's rules; instant runoff voting (IRV) used to elect one item with a guaranteed majority (50% plus one vote), and the Sainte-Lague parliament seat distribution system which is used for electing two or more items/names per election.
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Sainte-Lague Parliament Seat Distribution System

When electing two or more items/names per election or district in the Sainte-Lague parliament seat distribution system which is pretty much the only system the USA Parliament uses, rule #3 was written by mathematician Mike Ossipoff in 1995 and it reads;

THE SAINTE-LAGUE PARLIAMENT SYSTEM for seat allocation in all multi-seat districts: 1. Divide the election's total number of votes by the number of seats. This is the 1st quota. 2. Divide this quota into each candidate's votes, and round off to the nearest whole number. That's that candidate's seat allocation. 3. If, due to rounding, this awards a number of seats different from the desired number of seats, then adjust the quota slightly up or down, till, when paragraph 2 is carried out, it will award all seats.
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The Hagenbach-Bischoff Quota

The USA Parliament uses the Hagenbach-Bischoff method, since it is the most exact
formula known for STV in the Sainte-Lague.
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Ranked Choice Consensus Voting

Ranked choice consensus voting is like consensus, where all items/names being
voted upon that receive rankings or tics cast by all the participating
voting members are considered approved by consensus. Using the STV system,
consecutive numbers beginning with the number "1" must be used, or the ballot
is marked spoiled and considered democratically illegitimate.
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3. Commentary by James Ogle

After conducting the USA Parliament elections for 17 consecutive years, it turns out that the IRV system (for single winners only) was never used in a single winner district election in the USA Parliament's elections. Only multi-winner districts of two or more have been used, under the Sainte-Lague parliament seat distribution system.

There is currently a split in the voting reform movement in the USA. Most reformers in the national voting reform movement are trying to implement single winner district IRV systems in many state, county and city elections. The USA Parliament never uses IRV and supports only the Sainte-Lague parliament seat distribution system in all cases over IRV with no exceptions.
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Ties

The way I have been making the vote count over the years, is the names/items are elected in consecutive order, based on the number of rankings (or tics) each name/item garners until all the names/items are elected in consecutive order. In case there is a tie for the list between names that garner the same number of tics, then the lowest sum of the total tics breaks the tie.

Example of a Tie

Say the first 999 names with the most votes (or tics) were elected in consecutive order without a tie in the number of tics received per name. And a tie of two tics occurs while trying to elect the 1000th name. The tie is broken by simply adding the sum of the tics. For example, say both names received two tics, and all the other remaining names received one or zero tics. Of the two names in a tie with two tics, one name garnered a #665 and a #3 tic while the second name in the tie garnered a #665 and a #2 tic. The vote counter simply adds the sum of the two tics, and name with lowest sum breaks the tie and is elected as the 1000th spot. The name with the higher sum is not elected, but is elected as #1001 which is the first name of all consecutively ranked names as back-ups. All other names recieving one tic are elected as consecutively ranked names as back-ups, starting with #1002. The names with zero tics are not elected as back-ups.

The system described here will give us the same results that the Hagenbach-Bischoff method will give us.