[EM] Responses to some of Forest's ideas

[Forest Simmons]

In Craig's example below I agree that B is the best candidate in spite of
the fact that it is the IRV winner :-) 

However, it seems to me that B is the most likely Approval winner, too,
even under near zero information conditions [see explanation below]
although to be a good sport I have to admit that I left myself wide open
by saying "reasonable strategy". 

If I had required an air tight zero information strategy, only Richard
Moore could have responded :-) 

In any case, this example is not exactly what I was looking for since B is
not the only pairwise unbeaten candidate; nobody beats C pairwise, either.

In fact, if the minor modification that Craig suggested at the end of his
next posting is made (transferring one vote from the A faction to the C
faction) C becomes the only unbeaten candidate, though B is still the
obviously superior candidate, and most likely still the Approval winner.

So much for the superior stability of Condorcet.

Now here's why I think that B is the most likely zero information Approval
winner:

It seems to me that at least half of each of the two larger factions would
cut off their approval before A, because within each of those two factions
A is within human roundoff of the faction mean for utility, but below the
faction median.

Similarly, in the first faction B is not significantly below mean utility
but is above the median utility, so it is likely that at least one would
approve B. 

Note also that if the approval votes for A were so modified the results
would be B(51) > A(50) = C(50) = D(50). 

This shows the borderline nature of this example, hardly the definitive
example that I was hoping for.

Still, I have to admit that Craig's example came very close to satisfying
my stated conditions. Transferring one vote from the C faction to the B
faction would make B the CW, and given the leeway of "reasonable strategy"
Craig would have satisfied my stated challenge.

I think I should modify my challenge to ask for an example that has a
definite CW that is definitely better than a definite Approval winner.

Forest

On Fri, 20 Jul 2001, LAYTON Craig wrote:

> Forest wrote:
> 
> >Does anybody have an example in which reasonable strategy would tend to
> >make the Approval winner definitely less desirable than the Condorcet
> >Winner?
> 
> "Reasonable strategy" is a fairly loose term.  In an electorate with very
> innacurate polling information, reasonable strategy could result in a pretty
> bad outcome.  I can give you an example with zero info strategy;
> 
> 10 A>B>C>D : 100>30>1>0  Approval vote A
> 40 B>D>A>C : 100>52>51>0 Approval vote BDA
> 40 C>B>A>D : 100>95>66>0 Approval vote CBA
> 10 D>C>B>A : 100>60>50>0 Approval vote DC
> 
> A is the Approval winner with 90% approval (compared to 80% for B)
> B is the Condorcet, Borda, IRV and Cardinal Ratings winner, based on sincere
> ballots.
> B is the SU winner over A by 275 (av. 69) to 217 (av. 54).  90% of voters
> prefer B to A.
> 
> It would be difficult to argue that A is the deserving winner here.
> 
> The vague notion that attracts Condorcet advocates (what Rob termed
> "stability") is a consistency criterion. The idea being that, with the same
> group of voters with the same preferences, and the same field of candidates,
> the same candidate should win every time.  This will happen much more often
> in Condorcet than in any other method.  Rules should be generally designed
> to apply in every situation evenly.  It is arguable that this property is
> more important than what outcome the rules actually achieve.
> 
> Craig
> 
>