[EM] Discussion about majority complaints

[James Green-Armytage]

Hi Jobst,
	Thanks for your thoughtful post. I don't have tons of time in the next
couple of weeks, so sorry in advance if I don't reply so quickly, but
anyway, here's my first reaction to your issue.

>1. How "serious" are majority complaints? 

	Mathematically, they are the thorn in the paw of majority rule."Minority"
complaints can be serious as well, but I won't get into the tyranny of the
majority issue here.

>Are there more and less
>serious ones? 

	Yes, I think so. I think that it has to do with intensity of the
preference for someone else and the size of the group complaining.

>Can we measure the "seriousness" of a complaint
>quantitatively? 

	Ultimately, no, but we can try to find an approximate measurement.

>2. What possibilities to rebut such a majority complaint should we
>expect our election method to provide us with? In particular, when we
>use a method which provides us with a beatpath from W to X (a "rebutting
>beatpath"), should we design our method so that the rebutting beatpaths
>are as strong as possible or as short as possible?

	Usually, we deal with strength and ignore length.
>
>3. When rebutting a majority complaint X>W by pointing at a beatpath
>W>A>...>B>X, should we take into account that these people constituting
>these "rebutting defeats" may belong to the complaining group? In
>particular, when we argue that the rebutting beatpath is "stronger" than
>the complaint, shouldn't we then try to measure "strength" in a way
>which avoids counting the same voter towards both the strength of the
>complaint and to the strengths of the defeats we use to rebut the
>complaint?

	It's an interesting idea. Note that cardinal pairwise does this to some
degree. Let's say that the pairwise comparisons are Dean>Kerry,
Kerry>Bush, Bush>Dean, as in my original cardinal pairwise example.
http://fc.antioch.edu/~james_green-armytage/voting_methods/altweighted_pairwise.htm
	Let's say that I am a Dean>Kerry>Bush voter, and Kerry wins. If the
intensities of my preference were Dean>Kerry>>>>>>Bush, and I voted Dean
100 > Kerry 99 > Bush 0, then I am consciously choosing to invest more in
the path that eventually serves as the rebuttal to the complaint, than to
the complaint itself. Or, perhaps my intensities are Dean>>Kerry>>Bush,
and my ratings were 100, 50, 0. Or, maybe Dean>>>>Kerry>>Bush, and 100,
15, 0. The idea is, I'm given a choice as to how much of the preference
gets distributed to a given preference as opposed to something that could
be the rebuttal to that preference.
>
>4. For methods which construct a complete social ordering of all
>candidates, should we even be prepared to rebut *all* complaints of the
>type "Y is placed higher than X but we prefer X to Y", or should we only
> care if Y is the winner?

	The question isn't whether the method *produces* a complete ordering, but
whether the later places really matter. If so, it would be more important
to justify the later orderings.
>
>
>ad 1. I think all majority complaints are so serious that we should be
>prepared to rebut them in some way.

	Okay.

>  I also think that some types of complaints are so serious that they
>should be avoided completely. If, for example, X covers Y or dominates Y
>in some other strong sense

	like if every voter prefers X>Y

>, Y should not win (the corresponding criteria
>are usually called "efficiencies").

	Okay.
>
>ad 2. The rebuttal may be of different type:
>  a) We may just point out that also the proposed exchange X would be
>subject to a similar complaint, and we may try to design the method so
>that this rebutting defeat is as "strong" as possible. For example, we
>could elect the candidate W for which the minimum strength of all
>strongest defeats against those candidates defeating W is as large as
>possible.

	hmm... that's new, isn't it? Don't know how that will play out...
>
>  b) We may point at some beatpath W>...>X and design our method so that
>this rebutting beatpath is as strong or as short as possible, or optimal
>in some other sense.
>  c) We may point out that W is "better" than X as measured by some
>score like the Copeland score, or as indicated by some binary relation
>like the Covering relation or any other type of "domination".
>  Personally, I think we should use type b and look for short rebutting
>beatpaths. 

	Why short rather than strong? This idea seems both new and controversial
to me. Do you prefer short over strong on purely aesthetic grounds, or is
there some practical reason for doing it this way?

>More precisely, I think we should require (since it is
>possible!) that there always be a beatpath of the form W>A>X whenever
>X>W. Only as a second criterion we should try to have these rebutting
>defeats as "strong" (see below) as possible .

	How would you deal with a situation with pairwise defeats and ties as
follows: A>B, B>C, C>D, D>A, A=C, B=D ?
>
>ad 3. Assume that we argue that the two defeats W>A>X are both
>"stronger" than the complaint X>W, and that we define "strength" as the
>number of voters having the corresponding preference. Then those members
>of the complaining majority which have X>W>A or A>X>W may not accept our
>rebuttal but may point out that their other preferences shall not be
>counted against their main preference X>W. Hence I think we should try
>to measure defeat strength in a more sophisticated way, perhaps using
>cardinal weights as James suggests. Or perhaps only by using an approval
>cutoff and counting how often X is above and W is below the cutoff like
>I suggested in the proposal named "grand compromise". When using the
>latter measure of strength, it is never possible for some voter to be
>counted towards both the strength of W>X and that of X>A.
>
	Yes, it looks like this is basically what I was talking about above.

my best,
James