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Sorry if this just me being dumb, but does "if one candidate (X) wins the election, and a new alternative (Y) is added, only X or Y will win the election." make sense? Shouldn't it be "if one candidate (X) is running for election,..."? Or do I just not get it?
—The preceding unsigned comment was added by 72.138.193.74 ( talk) 00:52, 26 April 2007 (UTC).
Is this finally a demand were Approval Voting works better than any Condorcet method (besides simplicity)?
Jack Rudd ( talk) 20:58, 22 May 2008 (UTC)
LIIA implies Condorcet (and Smith), but Condorcet (and even Smith) doesn't imply LIIA. KVenzke 03:21, 20 June 2006 (UTC)
I edited the beginning of the LIIA section, because it seemed to give the impression that LIIA is practically original research, and that it doesn't even have an agreed-upon name. Also, it seemed to be POV to mention Condorcet methods here, as more specifically it is Smith methods that may satisfy it. I'm not sure about the rest of the section: It seems to be a general argument against the utility of IIA rather than an argument in favor of LIIA. KVenzke 20:14, 25 June 2006 (UTC)
I deleted the piggybacking addition on my own parenthetical comment on the Morgenbesser anecdote because if it is correct (and I'm not convinced it is -- it needs at the least more exposition) it should be a separate "technical" paragraph on its own, not overloading what is meant to be an illustrative non-technical comment on an illustrative anecdote. The meaning of the addition is also not clear to me -- that the analogy is imperfect because the preference rankings could shift non-transitively with a new option even *after* the choices have been frozen? This seems meaningless to me -- how can one take account of the new option at all if the choices are already frozen? 142.103.168.33 04:19, 12 July 2006 (UTC)
I don't understand why LIIAC is considered a weaker version of IIAC. IIAC doesn't imply LIIAC, does it? We should mention this if that's the case, or include a short proof if it isn't. Also, does someone have a reference to the Young & Levenglick paper introducing LIIAC? CRGreathouse 22:33, 13 July 2006 (UTC)
A recent edit deleted references in the article to Arrow (1951), b/c his usage of 'IIA' is different from the usage of 'IIA' in the rest of the article. One way of handling the ambiguity is with a Wikipedia:Disambiguation page and separate articles for each page. Another way is to define and discuss each uaage within the article itself (as was done in the article Qualitative economics). (This has already been done with the section IIA in econometrics.) Then the fact of different usages should be noted in the lead section. Arrow's usage of the same term is spelled out in the link to Arrow in the article. There's also a nice intuitive statement in Kenneth Arrow. The current intro to the article is
In Arrow's usage, the second sentence could be rephrased as:
Example (adapted from Sen, Collective Choice and Social Welfare, 1970, p. 37): the choice between Hillary and McCain, given preferences of voters for each relative to the other in 2008, is not to be affected by their preferences for say George Allen (who by hypothesis is not on the ballot) in 2008. Thomasmeeks 15:59, 2 December 2006 (UTC) (spelling typo fixed) Thomasmeeks 12:29, 3 December 2006 (UTC)
(New left margin to respond directly to CRG's points above). I thank CRG for prompting a more careful response. I've had a chance to look at Ray (1973) (thx JSTOR), cited above and in IIA. Arrow (1950 JPE, 1951) does use an example that equates removing X or adding X back as affecting the choice between A & B (the spoiler effect), just as CRG suggests. But, Ray (1973, pp. 989-90), cited above, demonstrates that that Arrow's own formal statement of IIA (called IIA(A) by Ray), is inapplicable to the example he cites ("Clearly, this [Arrow's example] is a violation of IIA(R[adner]-M[arshak]], not IIA(A)." p. 990). So, the distinction of Arrow's IIA condition from other uses does matter. Thomasmeeks 15:48, 6 December 2006 (UTC) (p. numbers above corrected Thomasmeeks 02:09, 7 December 2006 (UTC))
Just state Arrow's definition here, which from Social Choice and Individual Values seems to be:
-- Henrygb 00:02, 3 December 2006 (UTC)
Maybe it's just me, but it seems like the example is flawed. "Note that the social choice ranking of [A, B] is dependent on preferences over the irrelevant alternatives [B, C]." How can B be considered irrelevant when it is the winning candidate when it is switched? It's just like saying: There are three parties, 5 voted A, 3 voted B, 3 voted C. Because B and C lost, giving the voted from C to B shouldn't matter. (which is illogical)
I'm trying to think of a better example here.. 203.116.243.1 ( talk) 03:17, 27 September 2010 (UTC)
I don't think the example adduced here is a clear example of IIA; I'm not sure I even think it's a flaw. One intent of Borda voting is to give "partial credit", as it were, for preferred also-rans. If enough credit is added to an also-ran who's already close to winning, it can push them over the top.
I think a better example is as follows. Let's suppose that five voters rank alternatives {A, B}; three prefer A to B and two prefer B to A. If we score two points for a first choice and one point for a second choice, A wins over B, 8 points to 7.
Suppose a third alternative C is introduced. Suppose also that the three voters who preferred A find C the worst of the three (A, B, C), but the two voters who preferred B put C in second place (B, C, A). If we score three points for a first choice, two points for a second choice, and one point for a third choice, we now find that B wins with 12 points, A is second with 11 points, and C brings up the rear with 7 points. In short, introducing a third option that did not affect the individual relative rankings of A and B nevertheless influenced the overall result of the vote. BrianTung ( talk) 18:58, 1 February 2011 (UTC)
The definition of Local Independence of Irrelevant Alternatives (LIIA) in the article does not at all match the definition provided by Peyton Young in his 1993 book Equity in Theory and Practice.
Here are two equivalent ways to express the real LIIA: (1) If the alternative that won or the alternative that finished last is deleted from all the votes, then the relative order of finish of the remaining alternatives must not change. (2) If a subset S of the alternatives are together in the order of finish--in other words, no alternative outside S finishes between or tied with any alternatives in S--then the relative order of finish of the alternatives in S must not change if all alternatives outside S are deleted from the votes.
Young's LIIA is much stronger than the criterion listed in the article, and it's failed by one of the two voting methods that the article mentions as satisfying LIIA, Schulze's method. (Ranked Pairs satisfies it, as does Peyton Young's method. Young's method also satisfies a weak reinforcement criterion--if two collections of votes separately produce the identical order of finish, then the combined votes must produce that same order of finish. Young's method fails independence of clone alternatives, however, which is much more important than reinforcement since it is fairly easy for a minority to nominate slightly inferior clones but hard or impossible for a minority to partition the voters.)
Depending on the comments, I intend to correct the article. SEppley ( talk) 17:08, 27 February 2012 (UTC)
The article now reads (in "Criticism of IIA")...
"IIA is too strong to be satisfied by any voting method...These include Approval and Range Voting"
Why are there no failure examples in the article?
Shall I add them?
Filingpro ( talk) 07:53, 23 May 2013 (UTC)
PROPOSAL: It seems that the criticism of IIA section shows that when there is a cycle in the aggregate of voter preferences, then it is trivial to show how any plausible voting method will fail IIA. Therefore, I suggest that when considering showing examples of failure by voting methods, we include examples of failure for any method that can fail IIA when there is no cycle.
For example, Approval voting fails IIA even when there is no aggregate voter cycle because it is vulnerable to simple spoilers just as Plurality is.
APPROVAL FAILURE IIA:
Filingpro ( talk) 02:32, 5 October 2013 (UTC)
Here are the problems addressed in the edit:
The former paragraph reads:
"
IIA is too strong to be satisfied by any voting method that reduces to majority rule when there are only two alternatives. Most ranked ballot rules do so, while Approval and Range can pass IIA because they do not necessarily reduce to majority rule.[5] Any comprehensive use of strategy that makes Approval or Range reduce to majority rule when there are only two candidates will make those methods fail IIA as well. (Even if only one voter is an optimizing voter, it is possible to construct a tied or nearly-tied example to show IIA can be violated.)
"
Problem #1: To comply with IIA, a method must pass every case. Any failure case results in non-compliance. Therefore, there is a problem with the rhetorical structure: "Approval and Range can pass IIA because they don't necessarily reduce to majority rule". This does not logically follow they pass IIA because all that is needed is one case of reducing to majority rule that causes failure.
Problem #2: “Comprehensive use of strategy” by voters is not required to make Approval and Range fail IIA. Nor is it required that any voter is an “optimizing voter”. It only requires that a voter might be minimally rational – i.e. that it is at least possible they do not vote against their interest – i.e. abstain from voting. As long as we do not assume that certain voters will necessarily abstain – i.e. we do not necessarily exclude them from representation, then all rating methods fail IIA. Specifically we are just allowing even the possibility that a voter having meaningful preferences for A>B, might cast a positive vote for A in a two candidate election (rather than abstain), and thus allowing Approval and Range to fail IIA. This failure is trivially shown just as Plurality voting fails to resolve common vote splits. Making clear the minimum requirement for failure of IIA is editorially vital to the thesis of this section, that IIA is too strong.
PS last two paragraphs of this section may require editing or removal, or moving to Majority Criterion
Filingpro (
talk) 15:45, 5 May 2015 (UTC)
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This section contains the wonderful sentence:
"Arrow's IIA does not imply an IIA similar to those different from this at the top of this article nor conversely.[7]"
...
What?
"does not imply": ok, se we're a no
"similar to": um, like
"those different from": wait, unlike
"this at the top": ok, I think this is actually "those at the top" or referring to the other IIA definition above
"nor conversely": .. wait, the opposite? Is this logical converse? Wait, let me rewrite:
not like those unlike to the other defintion, or the other way
not unlike the other definition, and not like?
like the other def, and also not?
I really feel this is saying that "Arrow's IIA is different from the earlier definition, and it doesn't imply the earlier definition. Also the earlier definition does not imply Arrow's definition of IIA. But they have similar intuitions." But this is I think reading a lot into it and prognosticating meaning where I feel it is very confused. I actually don't know which implication directions hold, if any. I came here to find out. — Preceding unsigned comment added by Ex0du5 5utu7e ( talk • contribs) 06:04, 20 August 2020 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Sorry if this just me being dumb, but does "if one candidate (X) wins the election, and a new alternative (Y) is added, only X or Y will win the election." make sense? Shouldn't it be "if one candidate (X) is running for election,..."? Or do I just not get it?
—The preceding unsigned comment was added by 72.138.193.74 ( talk) 00:52, 26 April 2007 (UTC).
Is this finally a demand were Approval Voting works better than any Condorcet method (besides simplicity)?
Jack Rudd ( talk) 20:58, 22 May 2008 (UTC)
LIIA implies Condorcet (and Smith), but Condorcet (and even Smith) doesn't imply LIIA. KVenzke 03:21, 20 June 2006 (UTC)
I edited the beginning of the LIIA section, because it seemed to give the impression that LIIA is practically original research, and that it doesn't even have an agreed-upon name. Also, it seemed to be POV to mention Condorcet methods here, as more specifically it is Smith methods that may satisfy it. I'm not sure about the rest of the section: It seems to be a general argument against the utility of IIA rather than an argument in favor of LIIA. KVenzke 20:14, 25 June 2006 (UTC)
I deleted the piggybacking addition on my own parenthetical comment on the Morgenbesser anecdote because if it is correct (and I'm not convinced it is -- it needs at the least more exposition) it should be a separate "technical" paragraph on its own, not overloading what is meant to be an illustrative non-technical comment on an illustrative anecdote. The meaning of the addition is also not clear to me -- that the analogy is imperfect because the preference rankings could shift non-transitively with a new option even *after* the choices have been frozen? This seems meaningless to me -- how can one take account of the new option at all if the choices are already frozen? 142.103.168.33 04:19, 12 July 2006 (UTC)
I don't understand why LIIAC is considered a weaker version of IIAC. IIAC doesn't imply LIIAC, does it? We should mention this if that's the case, or include a short proof if it isn't. Also, does someone have a reference to the Young & Levenglick paper introducing LIIAC? CRGreathouse 22:33, 13 July 2006 (UTC)
A recent edit deleted references in the article to Arrow (1951), b/c his usage of 'IIA' is different from the usage of 'IIA' in the rest of the article. One way of handling the ambiguity is with a Wikipedia:Disambiguation page and separate articles for each page. Another way is to define and discuss each uaage within the article itself (as was done in the article Qualitative economics). (This has already been done with the section IIA in econometrics.) Then the fact of different usages should be noted in the lead section. Arrow's usage of the same term is spelled out in the link to Arrow in the article. There's also a nice intuitive statement in Kenneth Arrow. The current intro to the article is
In Arrow's usage, the second sentence could be rephrased as:
Example (adapted from Sen, Collective Choice and Social Welfare, 1970, p. 37): the choice between Hillary and McCain, given preferences of voters for each relative to the other in 2008, is not to be affected by their preferences for say George Allen (who by hypothesis is not on the ballot) in 2008. Thomasmeeks 15:59, 2 December 2006 (UTC) (spelling typo fixed) Thomasmeeks 12:29, 3 December 2006 (UTC)
(New left margin to respond directly to CRG's points above). I thank CRG for prompting a more careful response. I've had a chance to look at Ray (1973) (thx JSTOR), cited above and in IIA. Arrow (1950 JPE, 1951) does use an example that equates removing X or adding X back as affecting the choice between A & B (the spoiler effect), just as CRG suggests. But, Ray (1973, pp. 989-90), cited above, demonstrates that that Arrow's own formal statement of IIA (called IIA(A) by Ray), is inapplicable to the example he cites ("Clearly, this [Arrow's example] is a violation of IIA(R[adner]-M[arshak]], not IIA(A)." p. 990). So, the distinction of Arrow's IIA condition from other uses does matter. Thomasmeeks 15:48, 6 December 2006 (UTC) (p. numbers above corrected Thomasmeeks 02:09, 7 December 2006 (UTC))
Just state Arrow's definition here, which from Social Choice and Individual Values seems to be:
-- Henrygb 00:02, 3 December 2006 (UTC)
Maybe it's just me, but it seems like the example is flawed. "Note that the social choice ranking of [A, B] is dependent on preferences over the irrelevant alternatives [B, C]." How can B be considered irrelevant when it is the winning candidate when it is switched? It's just like saying: There are three parties, 5 voted A, 3 voted B, 3 voted C. Because B and C lost, giving the voted from C to B shouldn't matter. (which is illogical)
I'm trying to think of a better example here.. 203.116.243.1 ( talk) 03:17, 27 September 2010 (UTC)
I don't think the example adduced here is a clear example of IIA; I'm not sure I even think it's a flaw. One intent of Borda voting is to give "partial credit", as it were, for preferred also-rans. If enough credit is added to an also-ran who's already close to winning, it can push them over the top.
I think a better example is as follows. Let's suppose that five voters rank alternatives {A, B}; three prefer A to B and two prefer B to A. If we score two points for a first choice and one point for a second choice, A wins over B, 8 points to 7.
Suppose a third alternative C is introduced. Suppose also that the three voters who preferred A find C the worst of the three (A, B, C), but the two voters who preferred B put C in second place (B, C, A). If we score three points for a first choice, two points for a second choice, and one point for a third choice, we now find that B wins with 12 points, A is second with 11 points, and C brings up the rear with 7 points. In short, introducing a third option that did not affect the individual relative rankings of A and B nevertheless influenced the overall result of the vote. BrianTung ( talk) 18:58, 1 February 2011 (UTC)
The definition of Local Independence of Irrelevant Alternatives (LIIA) in the article does not at all match the definition provided by Peyton Young in his 1993 book Equity in Theory and Practice.
Here are two equivalent ways to express the real LIIA: (1) If the alternative that won or the alternative that finished last is deleted from all the votes, then the relative order of finish of the remaining alternatives must not change. (2) If a subset S of the alternatives are together in the order of finish--in other words, no alternative outside S finishes between or tied with any alternatives in S--then the relative order of finish of the alternatives in S must not change if all alternatives outside S are deleted from the votes.
Young's LIIA is much stronger than the criterion listed in the article, and it's failed by one of the two voting methods that the article mentions as satisfying LIIA, Schulze's method. (Ranked Pairs satisfies it, as does Peyton Young's method. Young's method also satisfies a weak reinforcement criterion--if two collections of votes separately produce the identical order of finish, then the combined votes must produce that same order of finish. Young's method fails independence of clone alternatives, however, which is much more important than reinforcement since it is fairly easy for a minority to nominate slightly inferior clones but hard or impossible for a minority to partition the voters.)
Depending on the comments, I intend to correct the article. SEppley ( talk) 17:08, 27 February 2012 (UTC)
The article now reads (in "Criticism of IIA")...
"IIA is too strong to be satisfied by any voting method...These include Approval and Range Voting"
Why are there no failure examples in the article?
Shall I add them?
Filingpro ( talk) 07:53, 23 May 2013 (UTC)
PROPOSAL: It seems that the criticism of IIA section shows that when there is a cycle in the aggregate of voter preferences, then it is trivial to show how any plausible voting method will fail IIA. Therefore, I suggest that when considering showing examples of failure by voting methods, we include examples of failure for any method that can fail IIA when there is no cycle.
For example, Approval voting fails IIA even when there is no aggregate voter cycle because it is vulnerable to simple spoilers just as Plurality is.
APPROVAL FAILURE IIA:
Filingpro ( talk) 02:32, 5 October 2013 (UTC)
Here are the problems addressed in the edit:
The former paragraph reads:
"
IIA is too strong to be satisfied by any voting method that reduces to majority rule when there are only two alternatives. Most ranked ballot rules do so, while Approval and Range can pass IIA because they do not necessarily reduce to majority rule.[5] Any comprehensive use of strategy that makes Approval or Range reduce to majority rule when there are only two candidates will make those methods fail IIA as well. (Even if only one voter is an optimizing voter, it is possible to construct a tied or nearly-tied example to show IIA can be violated.)
"
Problem #1: To comply with IIA, a method must pass every case. Any failure case results in non-compliance. Therefore, there is a problem with the rhetorical structure: "Approval and Range can pass IIA because they don't necessarily reduce to majority rule". This does not logically follow they pass IIA because all that is needed is one case of reducing to majority rule that causes failure.
Problem #2: “Comprehensive use of strategy” by voters is not required to make Approval and Range fail IIA. Nor is it required that any voter is an “optimizing voter”. It only requires that a voter might be minimally rational – i.e. that it is at least possible they do not vote against their interest – i.e. abstain from voting. As long as we do not assume that certain voters will necessarily abstain – i.e. we do not necessarily exclude them from representation, then all rating methods fail IIA. Specifically we are just allowing even the possibility that a voter having meaningful preferences for A>B, might cast a positive vote for A in a two candidate election (rather than abstain), and thus allowing Approval and Range to fail IIA. This failure is trivially shown just as Plurality voting fails to resolve common vote splits. Making clear the minimum requirement for failure of IIA is editorially vital to the thesis of this section, that IIA is too strong.
PS last two paragraphs of this section may require editing or removal, or moving to Majority Criterion
Filingpro (
talk) 15:45, 5 May 2015 (UTC)
Hello fellow Wikipedians,
I have just modified one external link on Independence of irrelevant alternatives. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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This message was posted before February 2018.
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regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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source check}}
(last update: 5 June 2024).
Cheers.— InternetArchiveBot ( Report bug) 22:35, 9 December 2017 (UTC)
This section contains the wonderful sentence:
"Arrow's IIA does not imply an IIA similar to those different from this at the top of this article nor conversely.[7]"
...
What?
"does not imply": ok, se we're a no
"similar to": um, like
"those different from": wait, unlike
"this at the top": ok, I think this is actually "those at the top" or referring to the other IIA definition above
"nor conversely": .. wait, the opposite? Is this logical converse? Wait, let me rewrite:
not like those unlike to the other defintion, or the other way
not unlike the other definition, and not like?
like the other def, and also not?
I really feel this is saying that "Arrow's IIA is different from the earlier definition, and it doesn't imply the earlier definition. Also the earlier definition does not imply Arrow's definition of IIA. But they have similar intuitions." But this is I think reading a lot into it and prognosticating meaning where I feel it is very confused. I actually don't know which implication directions hold, if any. I came here to find out. — Preceding unsigned comment added by Ex0du5 5utu7e ( talk • contribs) 06:04, 20 August 2020 (UTC)