CIFeR stands for Candidate Initiated Free Riding.
How it works:
Each voter approves of any number of candidates.
The outcome with the combination of candidates in which the most voters approve of at least one of those candidates is the leading outcome.
But wait? Wouldn’t such a voting method be highly vulnerable to free riding? That’s where the candidate initiated free riding comes in.
Each candidate has the ability to remove any approval any voter gives them. (They also have the ability to undo a removal of one of their own approvals in case they mess up)
After a predetermined period of time in which candidates can decide which of their own approvals they want to remove from the ballots in order to give similar candidates a chance at winning seats, the current leading outcome becomes the winning outcome.
It passes the anti-favorite betrayal criterion.
Under the assumption that a voter’s favorite candidate has the same wits and intentions as that voter, it passes the favorite betrayal criterion.
In both Monroe’s method and Elbert’s method as well as virtually any method that uses hard quotas (such as @Ciaran’s apportioned methods) adding ballots that approve of every candidate can change the election result. However, like harmonic voting, adding both ballots that approve of every candidate and ballots that approve of no candidate cannot affect the election result. This is because candidates don’t have any incentive to remove their own approval off of a ballot that approves of every candidate, because doing so would just help every other candidate equally. This is good because a vote that does not give a distinction between any candidate being able to influence the election result seems a bit strange to me.
Advantages over asset voting:
One of the criticisms with asset voting is that it gives slimy politicians too much power. While candidates are still a player in the election result under CIFeR voting, the power politicians have to influence the election result is greatly reduced. Under asset voting it is theoretically possible for a unanimously unpopular least favorite candidate to win if he makes enough backroom deals with the other candidates. Under CIFeR voting, this is impossible since candidates can only remove their own approval marks from ballots and cannot alter the approvals of any other candidate on the ballot, thus they can’t make a voter approve of a candidate they didn’t approve of.
Asset voting is does not necessarily reduce to approval voting in the single winner case, it’s single winner version is viewed as inferior to other single winner voting methods. Unlike asset voting, CIFeR is a multi-winner adaption of approval voting because it actually reduces to approval voting in the single winner case. When electing a single winner, the only candidate whom has the ability to alter the election result after the votes have been cast is the approval voting winner, and there is no rational reason for the approval voting winner to remove his own approvals making him no longer the winner. But because the winning candidate technically has the ability to do this in the single winner case, CIFeR technically reduces to approval voting in which the winning candidate has the ability to resign and pass the contested seat to the next most approved candidate.
Disadvantages over asset voting:
Running a CIFeR voting election requires tallying up every possible combination in which a voter can rate all the candidates. That means, in order to run a CIFeR election, you need to tally each of the 2^C possible ballot combinations where C is the number of candidates in the race.