In discussion of the merits and demerits of various methods of achieving integer proportional mapping of a spectrum of votes (these, single choice votes as in FPTP or classic party vote PR–MMP using both in two votes) with Jefferson’s method, much promoted on this site especially, versus Hamilton’s, by far my favorite for the purpose of forming multi-member bodies as it is most inclusive, I stumbled upon what as far as I know is a new procedure.
For a capsule description:
Dividing the total of all ballots cast by the number of seats to be assigned, the total of ballots cast for each party in the election shall be divided by that quota, and the set of all parties and independent candidates (henceforth referred to simply as parties, independents being regarded as parties of one candidate) that thus would obtain at least one quota seat determined and totaled; the remainder of votes cast for parties shall also be noted.
These two subtotals shall be divided by the quota and the portion with greatest remainder beyond integer quota seats shall receive the remaining seat.
Using the Huntington-Hill method of proportional seat allocation, all parties included in the quota set shall be apportioned seats out of the share assigned in step 2 to the quota parties.
The subquota parties shall be ranked in accordance to votes received, and in default of actions described below in step 5, the top ranked ones totaling to the share of seats for subquota parties determined in step 2 shall also be elected.
However, the multiple of apportioned seats for the quota parties shall be subtracted from the total votes each party received, and any party having a positive balance remaining (and thus underrepresented) shall be able to participate in asset voting with the subquota parties, able to transfer any part of this excess to any party of their choice that agrees to accept them, as the subquota parties shall also be able to transfer their received ballots in the same manner. These transfers will reorder the list, and any consolidation that exceeds the quota shall upon final confirmation entitle that party to a seat, which shall be subtracted from the available seats allocated to the subquota share of seats. Any seats remaining shall go to the parties with positive outstanding shares in the largest number per the criteria in step 4. This process shall occur in a stipulated time frame and upon the end of the time frame any tentative assignments of votes not rescinded shall be locked in place and any votes not consolidated in parties winning seats shall be deemed suspended, subject to procedures in step 6.
Majority guarantee and ngoing operation of asset votes cast by parties not represented directly:
a) Upon completion of step 5 the body composition shall be set and no seats shall be added or lost to any party by the processes here, but;
b) All votes toward any party winning one or more seat shall be divided by the number of seats that party wins and this shall be divided by the quota, for an index of actual vote based representativeness of that party’s seats, and the entire set of all votes effectively assigned to seated parties shall be divided by total seat numbers, and multiplied by the seat majority of the body to determine a majority quota for the body.
c) At any time during the period after the election closes until the body finally adjourns for the last time prior to the next election, any party that assigned asset votes to any other party without itself holding any seats when the process of step 5 is complete can, by default by the individual candidate not seated of such a party, or whatever party authority this candidate may have delegated this power to, withdraw them, or parties that did not assign asset votes toward any party holding one or more seat can by mutual agreement with the party add them. These subtractions and additions change the majority vote quota for the body and the indices of any seated parties affected for all matters subsequent to the change being recorded.
d) By default all body business is conducted on the basis of one member having one unitary vote, but any majority claimed for any purpose including supermajorities of specified scale must, in the members counted toward that majority, actually exceed the majority threshold as adjusted by the members’ summed indices to be unchallengable. The body shall in its administration determine whether any votes that were close enough to the appropriate minimum threshold to be at risk of falling below that threshold and note those that might fail to meet this target. If this should happen, any member in the member count majority can protest the passage and a reasonable time limit in context shall be set for the member count majority to in some fashion raise the count above the actual majority threshold relative to represented public popular vote in the body. These shortfalls shall not be created retroactively by changes in part c that happen after the vote in question, but such changes can if they result in raising the recorded share of members above the threshold will settle the issue. Upon expiration of the deadline set failure to meet the majority criterion shall be deemed a failure of the original vote.
As laid out, these procedures are for a classic proportionally elected body such as say the legislature of the kingdom of Denmark. But they can with suitable adjustment apply more broadly, as to say my proposal to achieve PR in a body primarily elected by FPTP in single member districts via evaluation of the need for top off seats to counter overhangs. More on that, with mention of the problems of generalizing the concept of proportionality beyond single choice simple voting, in the next post.