[EM] Irrelevant Ballots Independent Fallback Approval (IBIFA)

[Chris Benham]

 "Irrelevant Ballots Independent Fallback Approval" (IBIFA) is the name I've settled on for the method I proposed
in a May 2010 EM post titled "Bucklin-like method meeting Favorite Betrayal and Irrelevant Ballots".

http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html

In that post I wrote that it uses multi-slot ratings ballots, and defined the 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:
http://wiki.electorama.com/wiki/ER-Bucklin





Chris Benham