# [EM] Two more 3-slot FBC/ABE solutions (not)

Chris Benham cbenhamau at yahoo.com.au
Tue Jan 24 16:48:54 PST 2012

```Jameson,

You're not missing anything.  You are right.  Thanks for pointing that out.

I should have thought more about those methods before suggesting them. I withdraw those suggestions.

I still stand by  APPMM as a good criterion. But the set can't be a component of a method algorithm that
meets the FBC.

Chris Benham

________________________________
From: Jameson Quinn <jameson.quinn at gmail.com>
To: C.Benham <cbenhamau at yahoo.com.au>
Cc: em <election-methods at electorama.com>
Sent: Wednesday, 25 January 2012 5:11 AM
Subject: Re: [EM] Two more 3-slot FBC/ABE solutions

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
>>
>>
>>
>>
>>----
>>Election-Methods mailing list - see http://electorama.com/em for list info
>>
>
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