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.)
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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.
 
Here is an example to illustrate the difference:
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47 B
2 C
100
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.
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2 C
5 D
105
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.
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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:
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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.
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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:Median rating 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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