[EM] New criterion: Independence Of Weakly Defeating Alternatives (IWDA)

[Jobst Heitzig]

Inspired by the example I posted recently, I suggest to discuss a new
independence criterion. It is in the same spirit as IPDA and ISDA in
that it requires the winner to stay the same when an alternative is
added which is very weak in a sense. More precisely, the new alternative
is considered weak when the new defeats it brings are too weak to be
considered essential new information. Here's the definition:


INDEPENDENCE OF WEAKLY DEFEATING ALTERNATIVES (IWDA):
The winner must not change when an alternative X is added but for each
option Y which is defeated by X, already some stronger defeat against Y
is affirmed/undropped by the method.


In the current wording, IWDA only applies to methods which affirm
defeats (like Ranked Pairs, River, Kemeny) or drop defeats (like PC, SD,
SSD).

Ranked Pairs and Kemeny fail IWDA, as can be seen from the example I
posted recently. In that example, C is the "weakly defeating alternative".

Does SSD (Beatpath) fulfil IWDA?

And how does IWDA relate to IPDA and ISDA?

Jobst