Approval scored voting

Approval Scored Voting (ApSV) is an electoral system promoted by Acadia Smith

Method
The system is a combination of scored ballots, approval voting, and instant run off voting. It has both single winner assignment and multi seat assignment which can be found in the following description:


 * Voters score the candidates on a preset scale (I'd suggest 0-10 with 0 meaning they refuse to give that candidate a vote, 1 meaning horrible, and 10 meaning absolutely amazing) any candidate not scored or that received a 0 score is crossed off a voters ballot to signify the fact they will not receive a vote from said voter.


 * The candidates that received the highest score from a voter then receive 1 vote each.


 * These votes are then tallied up and the candidate with the least amount of votes is eliminated.


 * The only time candidates may receive new votes is if a voter's highest scored candidates on a voters ballot are all eliminated and the next best scored candidates then all receive a vote.


 * This process is repeated until 2 candidates are left, the candidate with the most votes wins.

Usage
In the case of picking multiple seats you calculate the initial votes as if you were picking a candidate to fill one seat

you then take the candidate with the most votes and assign them a seat, this candidate is now considered safe (equal to eliminated in the 1 seat election system but with the bonus of the candidate that is safe has a seat).

The votes are redistributed just as if the safe candidate was a candidate in a one seat election that was eliminated but with the add-on that any ballot that gave a vote to this newly elected candidate has the weight of their ballot divided by 0.5 in the recounting (the weight of the ballot is equal to how much 1 vote from that ballot is worth, each ballot starts with a weight of one).

the candidate to receive the least amount of votes is then eliminated (their voters ballot weight is not changed) and their votes are redistributed as normal.

The election continues until all seats are filled or the number of candidates remaining/safe are equal to that of the total number of seats.

If the case of a tie in which no candidate can be chosen to be eliminated then the tied candidates enter their own tiebreaker in which the ballots are looked at to see which candidate was scored higher the least compared to the other candidates in the tie breaker, if this ties then the double tied candidates enter a 2nd tie breaker in which a separated scored voting system is used to find a looser, if this ties then the tripled tied candidates are all eliminated.

This tie breaker system is also used if there is a tie for 1st place when picking a single winner in which instead of triple tied candidates being eliminated they enter a new election using a non scored voting system"

the system was developed to create a mix between cardinal and ranked systems while using a ballot system that Acadia Smith commonly deemed better at projecting a voters preferences.

History
ApSV was developed in 2020 by Maine native Acadia Smith.

Discussions
Below is a set of links to discussions about ApSV, in reverse-chronological order from when the discussions began. Dates are UTC:


 * 2020
 * 2020-06-11 - Talk:Approval_scored_voting - asking whether ApSV is IRV (with whole-votes equal-ranking) or is a truly a new system?
 * 2020-06-09 - Talk:Approval_scored_voting - initial suggestions that ApSV might be a variant of STV (or more specifically, IRV)
 * 2020-05-?? - (reddit discussion: fill me in)