Talk:Kemeny-Young method
From Wikipedia, the free encyclopedia
Contents |
[edit] Example
This needs an example. I am not certain how this works so let's try:
- 5 voters prefer A then B then C
- 4 voters prefer B then C then A
- 2 voters prefer C then A then B
So the A/B tally is 7/4, the B/C tally is 9/2, and C/A tally is 6/5. So:
- ABC gets 7+9+5=21
- BCA gets 4+9+6=19
- BAC gets 4+9+5=18
- CAB gets 7+2+6=15
- ACB gets 7+2+5=14
- CBA gets 4+2+6=12
So ABC wins, so A is preferred to B and to C. This fails the independence of irrelevant alternatives criterion since if B was not a candidate, C would be preferred to A. So the article is wrong when it says "A voting theory named Arrow's impossibility theorem is commonly misinterpreted to imply that a fair and full order-of-preference result cannot be achieved, but this theorem only applies to vote-aggregation methods (how vote counts are distributed), so it does not apply to VoteFair ranking nor the Condorcet method". Asumming I have understood. --Henrygb 23:09, 29 May 2006 (UTC)
[edit] Reply to Henrygb
You interpreted the method correctly. Here are the calculation details for your example.
You are correct in saying that VoteFair ranking does not achieve independence of irrelevant alternatives for the example you present, and this is a significant point, so I will edit the entry to make this clarification.
However, your example does not contradict my statement that Arrow's impossibility theorem does not apply to VoteFair ranking nor the Condorcet method. Do you agree? (The qualification that limits Arrow's theorem is expressed with the words "which aggregates voters' preferences" in the WikiPedia formal statement of the theorem.)
Based on your insightful feedback I have revised the paragraph to say:
A voting theory named Arrow's impossibility theorem is commonly misinterpreted to imply that a fair and full order-of-preference result cannot be achieved, but this theorem only applies to vote-aggregation methods (how vote counts are distributed), so it does not apply to VoteFair ranking nor the Condorcet method. VoteFair ranking achieves all the desired criteria that Arrow's theorem proves are simultaneously unavailable to vote-aggregation voting methods, except that VoteFair ranking can fail to achieve independence of irrelevant alternatives when a circular ambiguity is involved. (Note that this rare unfairness is not due to Arrow's theorem.)
VoteFair 06:40, 30 May 2006 (UTC)
- I would not agree that it is "misinterpreted". Arrow's theorem does apply to Condorcet methods (of which this is one particular type). And with several candidates and multi-dimensional issues, circular ambiguities are not rare. The only cases where I think Arrow's theorem is not really meaningful are approval voting and range voting. --Henrygb 13:21, 30 May 2006 (UTC)
- And something is wrong with your link at [1] as the IRV result should be a win for A, by 7 votes against 4 for B in the second round. --Henrygb 13:26, 30 May 2006 (UTC)
You are right that my software's IRV calculations produce the wrong result for your example, so I will find and fix that bug.
Speaking of examples, I will convert one of the VoteFair ranking examples from my book into HTML and add it to the VoteFair ranking page.
Although I do not believe that Arrow's theorem applies to either VoteFair ranking or the Condorcet method, I will adjust the wording to accommodate your objections.
My statement that Arrow's theorem is "commonly misinterpreted" refers to the mistaken belief that Arrow's theorem applies to all possible voting methods. In turn, this leads to the mistaken belief that all voting methods -- including VoteFair ranking and every future method that will ever be created -- have to be limited in their ability to satisfy all the desired criteria (unrestricted domain, non-imposition, non-dictatorship, monotonicity, and independence of irrelevant alternatives).
I'll expand the explanation of VoteFair ranking to include a section that explicitly addresses each of the following criteria: unrestricted domain, non-imposition, non-dictatorship, monotonicity, and independence of irrelevant alternatives. After all, that's what's really important.
I agree that circular ambiguities are not rare. My statement is intended to say that the occurrence of an irrelevant alternative altering the ranking is rare, and that (as far as I know) such an alteration only occurs when a circular ambiguity is involved. I'll improve the wording to make this clearer.
Thank you for your valuable feedback. I appreciate finally getting to communicate with someone who really understands voting!
VoteFair 19:33, 30 May 2006 (UTC)
[edit] VoteFair ranking moved to Kemeny-Young method
I moved the article "VoteFair ranking" to "Kemeny-Young method" because this is the name which is used in the literature for this method. Actually, already in 2004, I have told the author of this article that this method is usually known as "Kemeny-Young method". Markus Schulze 11:04, 3 June 2006 (UTC)
[edit] Relationship between VoteFair ranking and Kemeny-Young method
I am the person who created the VoteFair ranking page. The contents of the VoteFair ranking page (and its discussion) was moved (and tagged as a "minor edit"!) without first discussing the change, so this is my opportunity to explain why I created a new page, and how this change might be accommodated.
I created VoteFair ranking back in 1991 or 1992, without any knowledge of the Kemeny-Young method. After creating VoteFair ranking, but before I gave it a name, I looked for descriptions of such a voting method. I found none.
An e-mail message from Markus Schulze in 2004 claimed that VoteFair ranking overlapped the Kemeny-Young method. I could not find any indication as to when the Kemeny-Young method was created, so as far as I knew that method was derived from VoteFair ranking. The only description of the method I found made it clear that the Kemeny-Young calculations differ from VoteFair ranking calculations. Specifically, VoteFair ranking seeks to maximize a function, whereas Kemeny-Young seeks to minimize the inverse function.
Markus Schulze and Henrygb are two voting-method experts who agree that my VoteFair ranking description is suitable as a description of the Kemeny-Young method, so I am willing to trust their judgment regarding the suitability of my description for the Kemeny-Young method. Note that I still haven't yet found a full description of the method. The move of the VoteFair ranking page wiped out the previous contents for the Kemeny-Young method page, but as I recall the description was the same brief four-sentence paragraph I've seen elsewhere.
The existing Kemeny-Young method page clearly did not apply to the method used for VoteFair calculations. That's why I created the VoteFair ranking page.
Another reason I created a new page is that the important information about which voting criteria is met by the Kemeny-Young method does not apply to the VoteFair ranking method. As an example, VoteFair ranking meets the Condorcet criteria, but descriptions of the Kemeny-Young method indicate that it does not meet the Condorcet criteria. Rather than assume the methods were equivalent, and make corrections on that basis, I created the new page with VoteFair-ranking-specific information.
The fact that the pre-existing Kemeny-Young-method description is now gone suggests that we can expand the information to account for any differences between VoteFair ranking and the Kemeny-Young method.
VoteFair 07:21, 5 June 2006 (UTC)
[edit] Cleanup
I did a major cleanup on this page today, changing "VoteFair" to "Kemeny-Young" when it was used to refer to the system in general. The Kemeny-Young method, as such, has no implementation details; the two implementations are the classic Kemeny-Young implementation and the VoteFair method. I distinguish between these in the text -- for example, the VoteFair method advocates (correctly!) treating unranked alternatives as tied for last place; this is not a part of the general Kemeny-Young method, so stays "VoteFair".
I also removed many POV/advocacy phrases. I like Kemeny-Young, but this isn't the place for that.
I added a Dodgson matrix for the example. Here, again, I distinguish between the "tally table" implementation of VoteFair and the matrix, which is pretty standard in voting methods. (The tally table has length n(n-1) for n candidates, and this is prohibitively long for more than, ay, five candidates.)
Most importantly, I changed the table. Claiming it meets all criteria (except when there's a circular ambiguity) is POV; other methods describe this as not meeting criteria. Still, I kept the comment that it meets the criteria when there is a Condorcet winner in a * comment. While this may seem harsh, I actually strengthened the claims of the table -- I changed a "yes, but" answer on the Majority Criterion to a "Yes", since as a Condorcet method Kemeny-Young cannot fail to elect a majoriy winner. CRGreathouse (talk • contribs) 18:09, 28 July 2006 (UTC)
[edit] Arrow's Theorem
Kemeny-Young is subject to Arrow's Theorem, there's no doubt. It is a SWF and meets Pareto and non-dictatorship, so it doesn't meet IIA. No Condorcet method is IIA. CRGreathouse (talk • contribs) 18:09, 28 July 2006 (UTC)
[edit] Corrections
Thank you CRGreathouse for the clarifications about the origins of the Kemeny-Young method. Now I finally know that the Kemeny-Young method predates VoteFair ranking, and by how much. Also thank you for making other improvements.
I suggest that someone knowledgeable add to the John George Kemeny and Peyton Young pages a link to this Kemeny-Young page. (I'm an expert about VoteFair ranking, but I know nothing about the Kemeny-Young origins beyond what is here.)
Today I improved the correctness and clarity of this article. I also corrected grammar mistakes and improved the formatting.
Here are clarifications about changes that might be questioned:
- Please note that "VoteFair" is an adjective, not a noun.
- I reinserted the phrase "In all cases that do not involve circular ambiguity" into the appropriate "comments" entries (in the "criterion" table). Without this qualification those statements were not valid. The fact that this qualification appears in a footnote was not sufficient to clarify that the unqualified statements described the ideal criterion. Now the statements describe the Kemeny-Young/VoteFair characteristics.
- Based on the information in List of matrices I removed the word "Dodgson" for referring to the (square) matrix.
- I removed references to a "tally table" where it was more appropriate to refer to pairwise comparison counts. This way the wording fits both the Kemeny-Young method and VoteFair ranking. (Note: If sequence scores were not involved there would be no need to even mention tally tables.)
VoteFair 07:25, 3 December 2006 (UTC)
