IBIFA

Irrelevant Ballots Independent Fallback Approval (IBIFA)

4-slot version:

• Voters fill out 4-slot ratings ballots, rating each candidate as either Top, Middle1, Middle2

>or Bottom. Default rating is Bottom, signifying least preferred and unapproved. > > >Any rating above Bottom is interpreted as Approval. > > >If any candidate/s X has a Top-Ratings score that is higher than any other candidate's approval >score on ballots that don't top-rate X, elect the X with the highest TR score. > > >Otherwise, if any candidate/s X has a Top+Middle1 score that is higher than any other candidate's >approval score on ballots that don't give X a Top or Middle1 rating, elect the X with the highest >Top+Middle1 score. > > >Otherwise, elect the candidate with the highest Approval score.*(Obviously other slot names are possible, such as 3 2 1 0 or A B C D or Top, High Middle, Low Middle, Bottom.)

The 3-slot version:

• Voters fill out 3-slot ratings ballots, rating each candidate as either Top, Middle

>or Bottom. Default rating is Bottom, signifying least preferred and unapproved. > >Any rating above Bottom is interpreted as Approval. > >If any candidate/s X has a Top-Ratings score that is higher than any other candidate's approval >score on ballots that don't top-rate X, elect the X with the highest TR score. > >Otherwise, elect the candidate with the highest Approval score.* >

It can also be adapted for use with ranked ballots:

• Voters rank the candidates, beginning with those they most prefer. Equal-ranking and truncation

are allowed.

Ranking above at least one other candidate is interpreted as Approval.

The ballots are interpreted as multi-slot ratings ballots thus: An approved candidate ranked below zero other candidates is interpreted as Top-Rated. An approved candidate ranked below one other candidate is interpreted as being in the second-highest ratings slot. An approved candidate ranked below two other candidates is interpreted as being in the third-highest ratings slot (even if this means the second-highest ratings slot is left empty). An approved candidate ranked below three other candidates is interpreted as being in the fourth-highest ratings slot (even if this means that a higher ratings slot is left empty).

And so on.

Say we label these ratings slot from the top A B C D etc. A candidate X's A score is the number of ballots on which it is A rated. A candidate X's A+B score is the number of ballots on which it is rated A or B. A candidate X's A+B+C score is the number of ballots on which it is rated A or B or C. And so on.

If any candidate X has an A score that is greater than any other candidate's approval score on ballots that don't A-rate X, then elect the X with the greatest A score.

Otherwise, if any candidate X has an A+B score that is greater than any other candidate's approval score on ballots that don't A-rate of B-rate X, then elect the X with the greatest A+B score.

And so on as in the versions that use a fixed number of ratings slots, if necessary electing the most approved candidate.*

This is analogous with ER-Bucklin(whole) on ranked ballots: