I'd certainly say that IIA is worth achieving if it can be done. But while I imagine that LIIA is supposed to go some way towards full IIA, I think that this is an illusion. Let's say we have an A>B>C>A cycle. If A wins, then the result order under an LIIA compliant system must be:
-
A2. B3. C
Adjacent candidates in the order will never swap over if other candidates are removed. If A is removed, B wins. If C is removed, A wins. But the question is: what is so special about adjacent candidates? This simply means that if B is removed, then C wins. This is arguably worse than adjacent candidates swapping because a candidate has gone above a candidate that was originally two places above them.
Failure of IIA means that there is the possibility that a pair of candidates will swap their order with the removal of a third candidate. Passing LIIA simply determines which candidates might swap over, but without any justification of why these swaps are better than other swaps.
Toby
From: Rob Lanphier robla@robla.net
To: "tdp201b@yahoo.co.uk" tdp201b@yahoo.co.uk
Cc: "rahyman@sbcglobal.net" rahyman@sbcglobal.net; Kristofer Munsterhjelm km_elmet@t-online.de; "election-methods@lists.electorama.com" election-methods@lists.electorama.com
Sent: Sunday, 8 October 2017, 17:41
Subject: Re: [EM] Let's play Jenga!
On Sun, Oct 8, 2017 at 6:44 AM, Toby Pereira tdp201b@yahoo.co.uk wrote:
I've never seen an explanation of why LIIA [(Local Independence from Irrelevant Alternatives)] is something you'd want to achieve in a method. It seems to be a criterion for the sake of it.
Do you believe standard IIA[1] is something worth achieving?
Rob
[1]: https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives
I'd certainly say that IIA is worth achieving if it can be done. But while I imagine that LIIA is supposed to go some way towards full IIA, I think that this is an illusion. Let's say we have an A>B>C>A cycle. If A wins, then the result order under an LIIA compliant system must be:
1. A2. B3. C
Adjacent candidates in the order will never swap over if other candidates are removed. If A is removed, B wins. If C is removed, A wins. But the question is: what is so special about adjacent candidates? This simply means that if B is removed, then C wins. This is arguably worse than adjacent candidates swapping because a candidate has gone above a candidate that was originally two places above them.
Failure of IIA means that there is the possibility that a pair of candidates will swap their order with the removal of a third candidate. Passing LIIA simply determines which candidates might swap over, but without any justification of why these swaps are better than other swaps.
Toby
From: Rob Lanphier <robla@robla.net>
To: "tdp201b@yahoo.co.uk" <tdp201b@yahoo.co.uk>
Cc: "rahyman@sbcglobal.net" <rahyman@sbcglobal.net>; Kristofer Munsterhjelm <km_elmet@t-online.de>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com>
Sent: Sunday, 8 October 2017, 17:41
Subject: Re: [EM] Let's play Jenga!
On Sun, Oct 8, 2017 at 6:44 AM, Toby Pereira <tdp201b@yahoo.co.uk> wrote:
I've never seen an explanation of why LIIA [(Local Independence from Irrelevant Alternatives)] is something you'd want to achieve in a method. It seems to be a criterion for the sake of it.
Do you believe standard IIA[1] is something worth achieving?
Rob
[1]: https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives
