[EM] summary of Condorcet anti-strategy measures

[James Green-Armytage]

>For the time being I'll just say that my observation
>is borne out by a lot of examples. In all your
>excellent examples given to demonstrate AWP's
>resistance to Burying, AM  also frustrates the
>Buriers; except in one where AWP "cheated"  by
>electing a "strongly defeated" candidate
>(pairwise beaten by a candidate with a higher
>approval score). 

	I'm sorry, but I don't think that this definition of "strongly defeated"
is especially useful. Nor do I think that it is "cheating" to drop such a
defeat in the event of a majority rule cycle. An example:

Preferences
26: B>>D>K
22: B>>K>D
19: D>K>>B
6: D>>K>B
22: K>D>>B
5: K>>B>D

Direction of defeats
B>D 52-48
D>K 51-49
K>B 52-48

Strong preferences on either side of defeats
B>D 48-47
D>K 6-5
K>B 46-48

	By your definition, the D>K defeat is a "strong defeat", but by my
definition, it is a very weak defeat. 48 voters have a strong B>D
preference. 46 voters have a strong K>B preference. On the other hand,
only 6 voters have a strong D>K preference. Hence I say that D>K is the
weakest defeat. D and K are obviously very similar candidates in this
example, and most of the D voters (19: D>K>>B) will be deeply upset if
their preference for D changes the winner to B. (On the other hand, if K
wins, it is unlikely that many of the B>>D>K voters will deeply regret not
helping D more, as D is below their cutoff.) I see this as the last
frontier for reducing the spoiler effect: making it so that the entry of a
similar candidate to the original winner will not throw the race to an
opposite candidate. And then there are all the strategy arguments, which I
hope you are familiar with... 
	I really don't care that Kerry is the "least approved candidate" in this
example, because of the reasons stated above, and because I think that
methods that place a very high importance on the approval score of
candidates tend to be strategically unstable.

>For the time being I'll just say that my observation
>is borne out by a lot of examples. 
...
>
>Here is an example in which they both fail:
>49: A>>C>B   (sincere is A>B>>C)
>03: B>>A>C
>48: C>>B>A

	Individual examples are very helpful when one is trying to get an
intuitive sense of how methods respond to various scenarios, but it is
also important to draw general conclusions about methods that are based on
analytical reasoning, rather than just one's impression after working
through several examples. 
	I have done this with CWP and AWP: I have stated general reasons why AWP
and CWP are unusually resistant to the burying strategy, I have written up
these reasons in my paper and repeated them in various posts. I find it
frustrating that, while no one has contradicted my arguments, few people
if any show evidence of understanding them in full. I think that the
arguments in favor of CWP and AWP are very strong, and yet people seem to
go on ignoring them and promoting methods that do not share the same
benefits. Please forgive me if all of this sounds egotistical and
self-serving, but this is honestly my perception of things.
	In your example above, it is perfectly logical that supporters of A
should be able to advantageously bury B in AWP and CWP. That is because
only 3 voters express a strong B>A preference. The average B>A rating
differential is 3/52 = .06, while the average A>B rating differential is
0/49 = 0. Here are the rest of the average rating differentials:
A>B = 0/49 = 0
B>A = 3/52 = .06
A>C = 49/52 = .94
C>A = 48/48 = 1
B>C = 52/52 = 1
C>B = 48/48 = 1
	What does this tell us? It tells us that A and B are very similar
candidates (according to my definition of a similar candidate, stated in
my paper as the average rating differentials on both sides of the
preference), whereas they are both very different from C. AWP and CWP do
not protect sincere-winner candidates against burying strategies on behalf
of similar candidates. Vulnerability to the burying strategy in general
can't be avoided, but CWP and AWP place this important limit on it:
burying via a 3 candidate cycle can only succeed for a similar candidate X
to the sincere CW, never for a candidate Y with a CW>Y average rating
differential of .34 or more (according to cast ballots).
 	I have already stated the reasons why this is important many times over,
so put it in a very small nutshell that probably leaves a lot out. One,
stealing the election from a highly different candidate from the sincere
CW is more of a severe violation of the integrity of the system and the
will of the voters. Two, supporters of a highly different candidate have
less to lose and more to gain by burying the CW, while supporters of a
similar candidate have more to lose and less to gain... hence supporters
of a highly different candidate are much more likely to try the strategy.
	Coming back to your example, there are plenty of reasons why it is not
damaging to AWP. First of all, it is not extremely damaging if it does
succeed, because A and B are highly similar candidates. However, it's
success is unlikely, for the following reasons. First, the A>B>>C faction,
while they don't stand to gain a great deal by having B instead of A,
stand to lose quite a lot if they are wrong about the direction of the A-C
pairwise comparison. Hence, the risk/reward ratio of the strategy is
highly questionable. 
	Second, to have the entire A>B>>C faction reversing their preference
would probably require at least enough coordination to get the C>>B>A
faction suspicious. They have the option of voting C>B>>A. If at least 23
of them do this, the A strategy fails as is. If at least 31 of them do
this, the A strategy becomes utterly impossible. This is a pretty natural
thing for the C voters to do. Consider that if C probably only wins the
election under the condition that C wins the A-C pairwise contest. (Any
A>C defeat will be too heavy to overrule.) If that's the case, then the
only possible cycle that C can win is a C>A>B>C cycle, and in a C>A>B>C
cycle, it doesn't matter where C>B>A voters place their approval cutoff,
because there is no C>B defeat or B>A defeat. Hence, C>B>>A is a logical
vote even if the C voters do not anticipate the A voters' strategy.
	Finally, if the sincere votes in your example were 49 A>>B>C; 3 B>>A>C;
48 C>>B>A, the A voters decided to bury B and the C voters didn't care
enough to save him (even though there isn't much reason not to do so), B
would be a sufficiently low utility CW that some might argue that it makes
sense for the election to boil down to the A-C comparison.

	Conclusion: Come on, Chris! How can you go on denying CWP and AWP? Help
me spread the gospel! ;-)

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