Instant-runoff voting: Difference between revisions

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IRV can rather simply be thought of as a modification to [[Choose-one FPTP voting|choose-one FPTP voting]] to pass the [[Mutual majority criterion|mutual majority criterion]] (and further, always elect from the [[Dominant mutual third set|dominant mutual third set]]). This is because when all but one of the candidates in the mutual majority-preferred set of candidates is eliminated, the remaining candidate will guaranteeably be the majority's 1st choice among the remaining candidates and thus win.

~~The~~ ~~simplest~~ way to modify IRV to address many of the issues IRV opponents have without changing IRV fundamentally is to allow voters to approve candidates (using an [[approval threshold]]). If there are any majority-approved candidates, elect the most-approved of them, otherwise run IRV. Even if voters [[Favorite Betrayal|Favorite Betray]], they can still approve their honest favorite, giving that candidate a chance to still win. In addition, this allows voters to better avert the [[center squeeze effect]]. The standard argument made by IRV advocates against [[Approval voting]], that it fails [[later-no-harm]], has little to no relevance to this modification, since voters seeking to avoid hurting their favorite candidates' chances of winning in the approval round can simply refrain from approving anyone, forcing the election to run under IRV rules.

One simple way to modify IRV to address many of the issues IRV opponents have without changing IRV fundamentally is to allow voters to approve candidates (using an [[approval threshold]]). If there are any majority-approved candidates, elect the most-approved of them, otherwise run IRV. Even if voters [[Favorite Betrayal|Favorite Betray]], they can still approve their honest favorite, giving that candidate a chance to still win. In addition, this allows voters to better avert the [[center squeeze effect]]. The standard argument made by IRV advocates against [[Approval voting]], that it fails [[later-no-harm]], has little to no relevance to this modification, since voters seeking to avoid hurting their favorite candidates' chances of winning in the approval round can simply refrain from approving anyone, forcing the election to run under IRV rules.

Though IRV is often praised for passing [[later-no-harm]], which is claimed to encourage voters to rank all of their preferences, it doesn't tend to use as much of the information provided by the voters as other ranked methods, such as [[Condorcet methods]]. This is a less extreme analog to how [[First Past the Post electoral system|first past the post]] technically passes [[later-no-harm]] by ignoring later preferences altogether. So IRV's [[later-no-harm]] compliance has to be evaluated in context of the other criteria it fails due to using less information than other methods - that is, there may be ambiguity to how much IRV is truly protecting a voter's interests by not using their later-preference information at all.

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Votes in the 1st round are 45 A 35 B 65 C.

If you elect a candidate the moment they have a majority, C would win, making the strategy backfire. But if you keep eliminating until you have only two candidates, then B is eliminated first, and then A wins with 80 votes.<ref>https://www.reddit.com/r/EndFPTP/comments/f7daa0/key_details_emerge_for_how_rankedchoice_in_nyc/fib0pgd?utm_source=share&utm_medium=web2x</ref></blockquote>~~Several~~ ~~variations~~ of IRV ~~have~~ ~~been~~ ~~proposed~~ to ~~meet~~ the [[~~Condorcet~~]] ~~and~~ [[~~Smith~~ ~~criterion|Smith~~]] ~~criteria.~~ ~~The~~ ~~simplest~~ of ~~these~~ ~~are~~ to ~~either~~ ~~(elect~~ ~~the~~ [[~~Condorcet~~ ~~winner~~]] if ~~one~~ ~~exists),~~ or ~~(eliminate~~ ~~all~~ ~~candidates~~ ~~not~~ in the [[~~Smith//IRV|Smith~~ ~~set~~]])~~, and then run IRV~~.

If you elect a candidate the moment they have a majority, C would win, making the strategy backfire. But if you keep eliminating until you have only two candidates, then B is eliminated first, and then A wins with 80 votes.<ref>https://www.reddit.com/r/EndFPTP/comments/f7daa0/key_details_emerge_for_how_rankedchoice_in_nyc/fib0pgd?utm_source=share&utm_medium=web2x</ref></blockquote>The main criticism of IRV is essentially that it determines who the worst candidate is using 1st choices, rather than by, say, [[Approval voting|approvals]]. This ignores most of a voter's ballot. [[Instant Pairwise Elimination]] is an example of an IRV-like method that attempts to use all available ballot information and [[pairwise counting]] information to determine who the worst candidate is (usually by eliminating the [[Condorcet loser]]).

Several variations of IRV have been proposed to meet the [[Condorcet]] and [[Smith criterion|Smith]] criteria. The simplest of these are to either (elect the [[Condorcet winner]] if one exists), or (eliminate all candidates not in the [[Smith//IRV|Smith set]]), and then run IRV.

Here is a visualization example of IRV (it should be read as "Voter 1 ranks Candidate A 1 i.e. 1st, etc.):

{| class="wikitable"

|+Rankings of the candidates

!Number of voters to the right

Candidates below

!2

!4

!5

!6

|-

|A

|5

|'''<big>1</big>'''

|3

|2

|3

|-

|B

|2

|5

|4

|5

|'''<big>1</big>'''

|-

|C

|4

|3

|'''<big>1</big>'''

|3

|4

|-

|D

|3

|2

|'''<big>1</big>'''

|2

|-

|E

|'''<big>1</big>'''

|4

|5

|4

|5

|}

This can be converted into:

{| class="wikitable"

|+Rankings of the candidates

!Number of voters to the right

Rankings below

!2

!4

!5

!6

|-

|1st

|'''<big>E</big>'''

|'''<big>A</big>'''

|'''<big>C</big>'''

|'''<big>D</big>'''

|'''<big>B</big>'''

|-

|2nd

|B

|D

|A

|D

|-

|3rd

|D

|C

|A

|C

|A

|-

|4th

|C

|E

|B

|E

|C

|-

|5th

|A

|B

|E

|B

|E

|}

Because the smallest number in favor of any candidate is 2 for E, E is eliminated. This yields:

{| class="wikitable"

|+Rankings of the candidates

!Number of voters to the right

Rankings below

!2

!4

!5

!6

|-

|1st

|'''<big>B</big>'''

|'''<big>A</big>'''

|'''<big>C</big>'''

|'''<big>D</big>'''

|'''<big>B</big>'''

|-

|2nd

|D

|A

|D

|-

|3rd

|C

|A

|C

|A

|-

|4th

|A

|B

|C

|}

Now A has the smallest coalition in favor of them (4 votes), so they are eliminated. Then:

{| class="wikitable"

|+Rankings of the candidates

!Number of voters to the right

Rankings below

!8 (2 + 6)

!9 (4 + 5)

!5

!<s>0 (5 - 5)</s>

!<s>0 (6 - 6)</s>

|-

|1st

|'''<big>B</big>'''

|'''<big>D</big>'''

|'''<big>C</big>'''

|'''<s>D</s>'''

|'''<s>B</s>'''

|-

|2nd

|D

|C

|D

|<s>C</s>

|<s>D</s>

|-

|3rd

|C

|B

|<s>B</s>

|<s>C</s>

|}

Two columns can be merged because, with all of the eliminated candidates, they now are identical in their rankings of the remaining candidates. Now C has the fewest votes (5), so they are eliminated. Since there are only two candidates remaining after this elimination, the result is guaranteed to be known, so this is the final round:

{| class="wikitable"

|+Rankings of the candidates

!Number of voters to the right

Rankings below

!8 (2 + 6)

!<big>14 (4 + 5 + 5)</big>

!<s>0 (5 - 5)</s>

!<s>0 (6 - 6)</s>

|-

|1st

|'''<big>B</big>'''

|'''<big>D</big>'''

|'''<s>D</s>'''

|'''<s>B</s>'''

|-

|2nd

|D

|<big>B</big>

|<s>B</s>

|<s>D</s>

|}

D wins with 14 votes to B's 8.

==See also==

*[[Australian electoral system]]

*[[Electoral systems of the Australian states and territories]]