[EM] Stronger than LIIA
Forest W Simmons
fsimmons at pcc.edu
Thu Mar 8 14:01:03 PST 2007
1. Adding an alternative may not change the winner unless it pairwise
defeats the old winner.
2. Adding an alternative may not change the winner unless it is an
essential link in the strongest beatpath from the new winner to the old
As you mentioned , DMC satisfies (1). I think it also satisfies (2) if
you measure defeat strength by approval of the pairwise victor. In
fact, DMC is the version of Beatpath that measures defeat strength by
total approval of the victor of the pairwise contest.
I'm not a Forth programmer, but (in my day) I did a lot of programming
on the HP 48, which has a flexible stack based
language similar in spirit to a Forth.
>From: Matthijs van Duin <eme at nubz.org>
>Subject: [EM] Stronger than LIIA
>To: election-methods at electorama.com
>Message-ID: <20070306184236.GA8574 at cds.nl>
>Content-Type: text/plain; charset=us-ascii; format=flowed
>I came up with a criterion for ranked voting systems. I think it is
>new, though if it isn't I'm sure someone will point that out to me :-)
>Criterion: Adding a candidate who is pairwise defeated by the current
>winner may not cause a different winner to be chosen.
>Equivalently: If removing a candidate causes a different winner to be
>chosen, the new winner did not pairwise defeat the removed candidate.
>Intuitively the criterion feels right... if a new candidate shows up
>is immediately defeated by the current winner, it's "nice of you to
>come, and thank you for playing, but..."
>This criterion implies Local Independence of Irrelevant Alternatives,
>and hence Smith, Condorcet, Mutual Majority, etc. It appears stronger
>than LIIA though: if a new candidate is added who is defeated by the
>current winner, but itself defeats a candidate who defeats the current
>winner, then the new candidate is part of the smith set, so LIIA allows
>for a different outcome, but my criterion demands that the outcome
>remains the same.
>It's also attainable: Definite Majority Choice complies with this
>criterion, as do similar pairwise sorted methods. I haven't checked
>other methods yet, it would be interesting to see which ones comply,
>even more interesting to see a concrete case that complies with LIIA
>violates my criterion...
>Also, can anyone think of a good name for it? I think "Strong Local
>Independence of Irrelevant Alternatives" is getting a bit verbose ;-)
> - xmath
>Matthijs van Duin -- May the Forth be with you!
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