[EM]Definite Majority Choice, AWP, AM

[James Green-Armytage]

Hi Juho,
	Some replies follow, on the subject of voter strategy and
approval-weighted pairwise. These comments should also be helpful for
others who don't understand why I consider AWP to be clearly better than
DMC and AM.
>
>The voting method sees only the altered votes. Although the sincere CW 
>would be K, a voting method that elects K is not necessarily good. In 
>this case votes "4: B>D>>K" were altered. But as well it could have 
>been that those votes were sincere and for example votes "4: K>>B>D" 
>were altered. Lets say that the sincere votes of those K supporters are 
>"4: K>>D>B". If that was the case, then the sincere CW would have been 
>D.

	Yes, but you've not yet understood the virtue of cardinal-weighted
pairwise and approval-weighted pairwise. I request that you read my
cardinal pairwise paper, as most of the arguments used therein apply to
AWP as well. 
http://fc.antioch.edu/~james_green-armytage/cwp13.htm
	No Condorcet method can escape the possibility of the burying strategy,
but CWP and AWP make it so that you can't change the result from a sincere
CW to someone who is very *different* from the sincere CW (except by large
cycle strategies that are probably to complex to be realistic). 
	In this example, Kerry is similar to Dean, while Kerry and Dean are
different from Bush. How do I define "similar" and "different"? The
average rating differentials on preferences between two candidates. This
is straight out of my cardinal pairwise paper, section 7.a.
	Changing the winner from Kerry to Bush is what I call a "flagrant"
incursion ("one that causes a very high-priority defeat to be overruled by
a false defeat"). Changing the winner from Dean to Kerry (as in your
scenario) does not fit this definition. A flagrant incursion undermines
the intent of the voters much more severely than a non-flagrant incursion.
	Furthermore, Kerry voters planning a burying strategy against Dean risk
much more than Bush voters planning a burying strategy against Kerry. This
is in part because Dean cannot possibly stand a chance of being elected
without the help of Kerry supporters; if the Kerry supporters get wind of
the strategy ahead of time and respond in kind, Bush's victory is assured.
Bush, on the other hand, has no similar allegiance with Kerry or Dean, and
Bush supporters on the whole have less to lose if Dean and Kerry
supporters get alienated from them (because, for the most part, they
already are). It is in this way that CWP and AWP distribute strategic
incentive in roughly inverse proportion to strategic ability. Section 7.b.
This is perhaps the best possible anti-strategic property to have; if we
accept that at least some group of voters is likely to have a burying
opportunity against the sincere CW, it is much better for this group to
consist of voters who don't prefer some candidate on the opposite side of
the political spectrum to the CW.
>
>So, it looks to me that in the example above the voting methods should 
>behave as if there was a sincere cycle and not favour K any more than 
>the others.

	First of all, as Mike said, ignoring voter strategy won't make it go
away. 
	However, I can make a very strong argument for CWP and AWP in "sincere
voting" scenarios as well. Let's say that second set of votes are sincere,
as you suggest. Bush beats Dean, and most of the B>D voters feel strongly
about that preference (44 out of 52 place their cutoff between Bush and
Dean). Kerry beats Bush, and most of the K>B voters feel strongly about
that preference (46 out of 51 place their cutoff between Kerry and Bush).
Dean beats Kerry, but only a small portion of the voters feel strongly
about the D>K preference. Hence, if you have to overrule one defeat, I
argue that the D>K defeat is the most appropriate one to overrule.
	Do you see how this makes common sense?
>
>The best voting methods or voting organizers can do in this situation 
>is to try to discourage strategic voting.
>
	If the reward-strength/probability of a given strategy obviously
outweighs the risk strength/probability, then we should assume that voters
will tend to use the strategy. Perhaps they won't, but we should err on
the side of caution, especially where flagrant incursions are concerned.
Anything else would be naive and dangerous.

Sincerely,
James Green-Armytage
http://fc.antioch.edu/~james_green-armytage/voting.htm

+++++++++++++++++++++++++++++++++
APPENDIX: My example from 9/22/04
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-September/013936.html

3 candidates: Kerry, Dean, and Bush. 100 voters.
	Sincere preferences
19: K>D>>B
5: K>>D>B
4: K>>B>D
18: D>K>>B
5: D>>K>B
1: D>>B>K
25: B>>K>D
23: B>>D>K
	Kerry is a Condorcet winner.

	Altered preferences
19: K>D>>B
5: K>>D>B
4: K>>B>D
18: D>K>>B
5: D>>K>B
1: D>>B>K
21: B>>K>D
23: B>>D>K
4: B>D>>K (these are sincerely B>>K>D)
	There is a cycle now, K>B>D>K



happy birthday to me ... happy birthday to me ...... *sigh* ......