Talk:Independence of irrelevant alternatives

Is this finally a demand were Approval Voting works better than any Condorcet method (besides simplicity)?

Yeah, Approval does satisfy IIA. Of course, it doesn't satisfy the Condorcet criterion -- Arrow showed that no method can satisfy both the Condorcet criterion and IIA. This is easy enough to see. If you have a race that includes a cycle of A > B > C > A, and your method currently selects A, then if B drops out, you'll now have C > A, and C will win. So the race is between A and C, under the control of B (an "irrelevant alternative" -- he is not the winner in either case). This is why many analysts consider the IIA criterion flawed, and instead say that meeting Condorcet is good, and meeting the local IIA criterion is good, but total IIA is not important as long as those other two are met. I'm not clear why another editor considered the example of how the existence of cycles trivially implies IIA failure a "special pleading" for Condorcet. It seems, to me, critical to understanding Arrow's theorem and IIA's role in it. Rmharman 17:45, 14 June 2006 (UTC)[reply]

Local IIA is clearly special pleading since it is designed to say "Condorcet methods satisfy IIA (except when they do not in which case it doesn't really matter)". The role I see of IIA in Arrow's theorem is to show that democracy is complicated, and is vulnerable to tactical behaviour, and that there is no objectively optimal solution to the questions which result. I see nothing special about the Condorcet criterion compared with many other criteria, and if you do then that is your point of view. --Henrygb 22:39, 14 June 2006 (UTC)[reply]

The point of LIIA is that there are some sets of preferences (cyclic ones) under which no method can satisfy IIA. Satisfying IIA under all possible scenarios in which it is possible to satisfy it is not meaningless. Saying that it's "special pleading" is like saying that building a "divide by 0" exception into a programming language is special pleading -- "your math program can solve all divisions, except the ones it can't, which don't really matter." Well, yes, exactly. We don't need to provide an "answer" to a divide by 0 request, other than, "that's meaningless." In the context of cyclic preferences, IIA is meaningless. Saying that "democracy is complicated" and all systems are vulnerable to tactical manipulation under some circumstances, doesn't mean it's impossible to make meaningful comparisons about how vulnerable a given electoral system is -- under what conditions odd behaviors might emerge, and how likely those conditions are in the real world. As for whether Condorcet is special -- that depends on whether you think that majoritarianism is, in general, a good thing; Condorcet/Smith is the clearest majoritarian criterion, though note that even the most basic version, "a candidate with a majority of first choice votes must win," is contradictory to IIA, as I showed in the example in the article. The only way to satisfy IIA is to have an "election" that doesn't actually consider the will of the voters -- either have it be dictatorial, or random, or something silly like that. In any case, I don't privilege Condorcet above all other concerns -- I'm fine with the variety of Condorcet failure that can occur under Approval Voting, for example, as long as voters have access to good polling information and can make choices with some understanding of the consequences -- but in general, a Condorcet-winner seems to have a pretty strong argument that they're the majority choice. Rmharman 21:13, 23 June 2006 (UTC)[reply]

There are plenty of methods that satisfy IIA. Not only are there dictatorial methods, random methods, and others, but the cardinal methods (such as Approval voting and Range voting) have a particular attractiveness. But they have other issues. Condorcet methods and the criterion tend to presume one-dimensional politics and often lead to the election of inoffensive candidates rather than contraversial ones. You may like that, but it is still a POV. --Henrygb 01:37, 24 June 2006 (UTC)[reply]

LIIA implies Condorcet (and Smith), but Condorcet (and even Smith) doesn't imply LIIA. KVenzke 03:21, 20 June 2006 (UTC)[reply]

Is there a name for the subset of Condorcet methods that satisfies LIIA? Rmharman 21:13, 23 June 2006 (UTC)[reply]

I don't know of a name for this subset of methods. I would have to just call them "methods which satisfy LIIA." KVenzke 19:41, 25 June 2006 (UTC)[reply]

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)[reply]

Preferences set

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)[reply]

I think that the comment was useful, although you're probably right in that it didn't belong in your parenthetical. The comment seemed to discuss the fact that preferences are taken as given for voting systems---anything that acts to change that is, strictly speaking, outside of the scope of the field. This is why there is a difference between runoff elections and IRV: preferences can only be stated once, frozen, for IRV, while they can change for various reasons in a true runoff election. See, for example, Corks' "Evaluating Voting Methods" (p. 3) CRGreathouse 03:12, 14 July 2006 (UTC)[reply]

LIIAC

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)[reply]

You are correct. It is easy enough to produce a range voting example (so meeting IIA) where the new candidate wins despite not being in the Smith set. --Henrygb 09:45, 14 July 2006 (UTC)[reply]

Are there any methods that adhere to both IIAC and LIIAC? CRGreathouse 23:28, 14 July 2006 (UTC)[reply]