[EM] Dual Dropping method and "Preference Approval" ballot ideas

[matt at tidalwave.net]

On 11 Sep 2002 at 11:25, Markus Schulze threw a strike or two against DD:

Thank you for these insights.  Joining this group was another good idea.

> in so far as the way DD chooses between the SSD winner
> and the RP winner isn't clone-proof DD isn't clone-proof.

Strike one against DD.
 
> It isn't clear whether DD meets monotonicity. Consider the
> following scenario:
>   Candidate A is the SSD winner. Candidate B is the RP winner.
>   DD chooses candidate A.
>   Suppose, some voters improve their opinion about candidate A.
>   Then, as SSD meets monotonicity, candidate A is still the SSD
>   winner. However, it is possible that, by ranking candidate A
>   higher, the RP winner is changed from candidate B to candidate
>   C. When now DD chooses candidate C, then DD violates monotonicity.

If margin is used to determine dropping cost then a higher ranking for candidate A 
will tend to decrease 
the SSD dropping cost (because candidate A will be the losing candidate of at least 
one dropped pair). 
There is no such correlation with magnitude based dropping cost.  Since I am a 
person who likes to 
combine alternatives when I don't know enough to choose one over the other, I 
have been combining 
margin and magnitude when ranking pairs and evaluating dropping cost.  Now I  
believe I have found a rationale for using just margin for dropping cost.

If, as appears to be the case, the monotonicity violation only occurs when 
        1) the two method's winning candidates differ and 
        2) a gain for the DD winning candidate also changes the DD losing method's 
winning candidate 
	and 
        3) a resulting drop in dropping costs convert the DD losing candidate into the 
DD winning 
	candidate
then in the absence of lower dropping cost there will be no monotonicity violation.  
So we are talking 
about a trade-off of lower dropping cost in exchange for some low probability of 
monotonicity violation.  

> Therefore, I suggest that pure RP or pure SSD should be used instead of DD.

Is the empire calling three strikes? I counted only 1 and 1/2 :)
 
> By the way, the reason why I have proposed SSD (aka beatpath
> method, aka path voting, aka Schulze method) as an alternative
> to RP is that the SSD winner differs from the MinMax winner
> significantly less frequently than the RP winner differs from
> the MinMax winner. The MinMax method is the best Condorcet
> method when strategical nomination is not an issue.
> 
> Markus Schulze

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