IBIFA: Difference between revisions
m
fbc category
(add commentary -kv) |
m (fbc category) |
||
| (7 intermediate revisions by 3 users not shown) | |||
Line 1:
'''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
See also the full rules below.
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 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.▼
▲The weakness of MCA is that one's top-slot preference's security against one's middle-slot preference is based on the likelihood
Here is an example to illustrate the difference:
Line 9 ⟶ 11:
47 B
2 C
100 total
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.
Now add
51 A>C
Line 19 ⟶ 22:
2 C
5 D
105 total
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.
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.
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.▼
▲*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
▲>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:
▲
▲
▲>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▼
▲>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▼
▲*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.▼
▲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 97 ⟶ 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]]
| |||