[EM] Two more 3-slot FBC/ABE solutions

[Jameson Quinn]

In fact, that would seem to be a pretty strong argument that these methods
don't meet the FBC. What am I missing?

2012/1/24 Jameson Quinn <jameson.quinn at gmail.com>

> The problem with these methods is that you can't afford to vote for the
> marginal candidate whom only you have heard of, because that candidate will
> not be part of any S, and so your ballot will count against any S, even an
> S that you otherwise like.
>
> Jameson
>
> 2012/1/24 C.Benham <cbenhamau at yahoo.com.au>
>
> Following on from my recent definition of  the APPMM criterion/set, I'd
>> like to propose two not bad 3-slot methods that meet the FBC..
>>
>> Recall that I defined the APPMM criterion thus:
>>
>>  *If the number of ballots on which some set S of candidates is voted
>>> strictly above all the candidates outside S is greater than the number of
>>> ballots on which any outside-S candidate is voted strictly above any member
>>> of S, then the winner must come from S.*
>>>
>>
>>
>> The APPMM set is the set of candidates not disqualified by the APPMM
>> criterion.
>>
>> APMM//TR:
>>
>> * Voters fill out 3-slot ratings ballots. Default rating is Bottom
>> (signifying least preferred and not approved.) The other slots are Top
>> (signifying most preferred) and Middle.
>>
>> From the set of candidates not disqualified by the APPMM criterion, elect
>> the one with the most Top ratings.*
>>
>>
>> APMM//CR:
>>
>> * Voters fill out 3-slot ratings ballots. Default rating is Bottom
>> (signifying least preferred and not approved.) The other slots are Top
>> (signifying most preferred) and Middle.
>>
>> From the set of candidates not disqualified by the APPMM criterion, elect
>> the one with the highest  Top minus Bottom ratings score.*
>>
>>
>> So far I can't see that these are technically any better  than my earlier
>> suggestion of  TTPBA//TR, and unlike that method they fail the "Tied at the
>> Top Pairwise Beats All" criterion.
>>
>> But like that method they meet the Plurality and  Mono-add-Plump
>> criteria, and also have no problem with Kevin's bad MMPO example.
>>
>> I'm happy for APMM//CR to be also called APMM//Range. This method is more
>> Condorcetish than APMM//TR, for example:
>>
>> 49: C>B
>> 27: A>B
>> 24: B>A
>>
>> B>A 73-27,  B>C 51-49,  A>C 51-49.
>>
>> APMM//TR elects A, while  APMM//CR elects B (like TTPBA//TR).
>>
>> I am sure that APMM//TR has no defection incentive in the "Approval Bad
>> Example", and the other method also does in the example normally given.
>>
>> Of course some other points-score scheme (perhaps giving greater weight
>> to to Top Ratings) is possible.
>>
>> Chris Benham
>>
>>
>>
>>
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>>
>
>
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