[EM] MCA on electowiki (re " Later-no-help" and "Favorite Betrayal" criteria)

[C.Benham]

http://wiki.electorama.com/wiki/Majority_Choice_Approval#Criteria_compliance

> The Later-no-help criterion </wiki/Later-no-help_criterion> and the 
> Favorite Betrayal criterion </wiki/Favorite_Betrayal_criterion> are 
> satisfied by MCA-P


They are also met by  "MCA-A",  "MCA-M" and "MCA-S".

I consider it desirable that methods should have  Later-no-Harm and 
Later-no-Help in at
least approximate probabilistic balance. These methods all (badly) fail 
Later-no-Harm, so meeting
LNHelp contributes to the strong truncation incentive.

> They're also satisfied by MCA-AR if MCA-P is used to pick the two 
> finalists


That method does not meet the Favourite Betrayal criterion.

25: A
24: A>C
02: B>A
22: B
25: C>B
02: C=B (sincere is C>B)

No candidates' TR (or "P") score reaches the majority threshold of 51 
and all their Approval
scores exceed it, so a resolution method is needed.

Of the candidates that reached a majority score, I gather the method 
selects the two with the
highest TR scores for a runoff.

TR scores:  A49,    B26,    C27.

The method selects A and C for the runoff, which A wins 51-27.

If the 2 C=B voters vote sincerely C>B the result is the same.

But if they  change to B>C the TR scores change to A49,  B26,  C25 and 
the method
then selects  A and B for the runoff which B wins 51-49, a result those 
two voters prefer.

25: A
24: A>C
02: B>A
22: B
25: C>B
02: B>C   (was C=B, sincere is C>B)


Chris Benham





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