IBIFA: Difference between revisions
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'''Irrelevant Ballots Independent Fallback Approval''' ('''IBIFA''') is a method designed by Chris Benham.
In the three-slot case, IBIFA is like [[MCA]], except that in place of checking for a candidate (call him "A") with top-slot ratings from a majority of the ballots, one checks whether the quantity of top-slot ratings for A is sufficient to defeat the total approval (i.e. above-bottom ratings) of any other candidate, not including approval from the ballots that rate candidate A top. If any candidates pass this test, the one of them with the most top-slot ratings is elected. (If no voters tie multiple candidates at the top slot, a maximum of one candidate will be able to pass the test.)
See also the full rules below.
4-slot version:▼
The weakness of MCA is that one's top-slot preference's security against one's middle-slot preference is based on the likelihood that the top-slot preference will have a majority of top-slot preferences. However, narrow majorities can easily be eliminated by adding "irrelevant ballots" for minor candidates. Under IBIFA the top-slot preference's security is based on that candidate's likelihood of being able to beat any other single candidate. This may be more predictable and strategically useful than a majority-based rule.
Here is an example to illustrate the difference:
*Voters fill out 4-slot ratings ballots, rating each candidate as either Top, Middle1, Middle2▼
51 A>C
>or Bottom. Default rating is Bottom, signifying least preferred and unapproved.▼
47 B
2 C
>Any rating above Bottom is interpreted as Approval.▼
100 total
>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▼
>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.)▼
MCA and IBIFA both elect A. If B had received more votes than A, but not a majority, the A voters would be able to use their C preference to ensure that they got their second choice. Since A received a majority, the C preference is not needed.
The 3-slot version:▼
Now add 5 D ballots:
51 A>C
47 B
2 C
5 D
>Any rating above Bottom is interpreted as Approval.▼
105 total
>If any candidate/s X has a Top-Ratings score that is higher than any other candidate's approval▼
>Otherwise, elect the candidate with the highest Approval score.*▼
IBIFA still elects A, but MCA moves the win to C because A no longer has a majority. In IBIFA's view, the new D ballots are "irrelevant" and don't take the win away from A, because there is still no candidate who can compete with A's top-slot preference count. Tying the usage of the middle-slot preference to the actual viability of the top-slot preference means it is more safe to offer middle-slot preferences, with less fear that they will end up counting with as much weight as a top-slot preference.
It can also be adapted for use with ranked ballots:▼
IBIFA also does not sacrifice MCA's [[FBC]] compliance. If raising one's favorite candidate to equal-top doesn't make that candidate win, it also can't change the preexisting winner.
*Voters rank the candidates, beginning with those they most prefer. Equal-ranking and truncation▼
are allowed.▼
▲* 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.
Ranking above at least one other candidate is interpreted as Approval.▼
▲
▲
▲
▲The 3-slot version:
▲
▲
▲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
* An approved candidate ranked below
▲An approved candidate ranked below three other candidates is interpreted as being in the fourth-highest
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.
▲
that don't A-rate X, then elect the X with the greatest A score.
Line 71 ⟶ 73:
And so on as in the versions that use a fixed number of ratings slots, if necessary electing the most
approved candidate.
See also [[Relevant Rating]], a method which follows the same methodology as IBIFA but is intended to be more similar to Majority Judgment than MCA.
[[Category:Single-winner voting methods]]
[[Category:Graded Bucklin methods]]
[[Category:Irrelevant ballot immune methods]]
[[Category:No-favorite-betrayal electoral systems]]
[[Category:Monotonic electoral systems]]
[[Category:Single-winner voting methods]]
[[Category:Cardinal voting methods]]
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