[Election-Methods] RE : Corrected "strategy in Condorcet" section

[Chris Benham]

Juho wrote:

> If the ballots are considered to hold both approval and ranking  
> information (maybe even giving higher weight to approval) then also I  
> have some sympathy towards D. But if we compare this kind of combined  
> ballots to pure ranking ballots then probably also the votes would be  
> different. 

I classify ballot-types purely by the type of information they collect 
(allow the voters to specify) and not by what the algorithm does with 
that information.

> I mean e.g. that since the 1000 A>B voters seemed to have a uniform  
> and therefore maybe strong opinion A>B that might mean that if they  
> were told to give votes where also approval would be counted then the  
> vote could have been closer to (but maybe not all the way) 1000 A,  
> 1000 B, 1 D>B.

But yes.  (But shouldn't  your "1000B"  read  *1000C*?)

> I read you comments so that winning votes was not very good.

On balance better than Margins, just not one of my favourites.  I agree 
that the Margins algorithm idea is more intuitive, and I like the fact 
that in common with IRV
the best zero-info strategy is to simply rank sincerely regardless of  
ratings.  I like methods that are either like this or have 0-info 
incentive to truncate disapproved
candidates (for voters with a big gap in their sincere ratings).  I 
don't  WV's random-fill incentive.

> Combining approval and margins would be better. And pure margins  
> would be worse than approval + margins. 

By itself  I consider that the word "margins" refers to the margins in 
the pairwise ranking comparison. "Approval-Margins" ignores this (only 
noting the win/lose/draw result)
so isn't the same thing as "approval + margins".

> I assumed also that D would  be a good winner with approval + margins 
> but I'm not sure you stated  anything on if D should win if the 
> ballots were purely ranking based  (1000 A>B>C=D>E, 1000 C>D>A=B>E, 1 
> D>B>A=C>E to "fool" your method :-). 

This could arise if  the votes are sincere and/or in a 0-info election 
where the voters all wish to express their rejection of  E. To cope with 
this I suggested as my current
favourite algorithm for plain ranked ballots "ASM(R) Elimination".  That 
would eliminate E, and then ballots like A>B>C=D>E would be interpreted 
as only approving
A and B.

> The comparison is of course a bit tricky since approval + margins has  
> more data available, although it also limits the expressiveness  
> somewhat since the approval cutoff is at a fixed position. A free  
> cutoff location would allow the voter to express also preferences  
> between the non-approved candidates. Maybe you didn't allow that for  
> some strategy resistance reasons (as usual :-).


No, the original version of  AM was for ballots  that allows voters to 
specify an approval cutoff. Notice that in this discussion I specified 
algorithms I like "if we are using plain ranked ballots".
But this can only make a difference if  voters want to use some 
strategy  (or non-strategy?) other than approving all but one of  the 
Smith set members. I doubt that is sufficient to justify
a more complex ballot and giving the voters an extra perhaps-difficult 
decision.

But I think that is an interesting and legitimate  ballot-style. Perhaps 
my favourite method using this type of ballot is a version ASM 
Elimination where at each stage ballots that specify
some approval distinction among remaining candidates are "interpreted" 
as approving that way, but ballots that don't make any explicit approval 
distinction among remaining candidates
are interpreted as approving the remain g candidates they rank (among 
remaining candidates) above bottom or equal-bottom.

This somewhat undermines the "real meaning" of  expressed approval, but 
limits the disappointment of voters who make the mistake of not making 
approval distinction among the members
of the Smith set (and so I regard as more fair).

Chris Benham