[EM] MDDA(symmetric completion example)

[Chris Benham]

On 11/23/2016 8:22 AM, Forest Simmons wrote:
>
> If the 44 buriers were more conservative in their burial by not 
> approving C …
>
>
> 43: A
>
> 03: A>B
>
> 44: B>>C(sincere is B or B>A)
>
> 10: C
>
> … then A would win without regard to the convention of the default 
> approval cutoff.
>

Forest,

By my calculation B wins if the default approval cutoff is just above 
equal bottom. With the symmetric completion
at the bottom all three candidates have majority-strength defeats (A>B 
51-49, B>C 68.5-31.5, C>A 54-46) and the
Approval scores are  B47 > A46 > C10.

So as in Smith//Approval  B wins.  This is a good example of why Kevin 
Venzke wasn't in favour of allowing voters
to rank among unapproved candidates (at least under Smith//Approval).

It's also a good advertisement for Approval Sorted Margins, which easily 
elects A.

And it leads me to think that in MDDA(SC) the default approval should 
only be for the top-voted candidates.

Chris Benham


On 11/23/2016 8:22 AM, Forest Simmons wrote:
>
> Chris,
>
> Here’s an example that you asked me to look at from last month.
>
> You wrote ….
>
> 43: A
>
> 03: A>B
>
> 44: B>C(sincere is B or B>A)
>
> 10: C
>
> C>A54-46,A>B46-44,B>C 47-10.
>
> Here A is the sincere CW and supported by the largest of the three
>
> factions of voters, but Winning Votes rewards the buriers by electing B.
>
> Benham andLV(erw)SMEeasily electA.Smith//Approval (equivalent
>
> here to Max Covered Approval) and Approval Sorted Margins elect C.
>
> [end quote]
>
> Let’s look at this example from the point of view MDDA(symmetric 
> completion):
>
>
> With symmetric completion every candidate is 50% plus defeated, so 
> nobody is disqualified, and the approval winner is elected.
>
>
> If the default is to approve only top, then A is elected.If the 
> default is to approve all ranked candidates, then C is elected.
>
>
> Neither case rewards the buriers.
>
>
> If the 44 buriers were more conservative in their burial by not 
> approving C …
>
>
> 43: A
>
> 03: A>B
>
> 44: B>>C(sincere is B or B>A)
>
> 10: C
>
> … then A would win without regard to the convention of the default 
> approval cutoff.
>
>
> So far so good!
>
>
> Forest
>
>
> P.S.
>
>
> Monkey Puzzle,
>
>
> I'll write a definition and brief explanation of MDDA(symmetric 
> completion) and its relation to MDDTR, ICA, and ICT tomorrow.  It 
> looks like I won't have enough time today.
>
>
> But briefly it is a cross between ICA and ICT, where the voters can 
> decide where the approval cutoff is on their ballot.  If they put it 
> just under Top, then their ballot is counted as in ICT.  If they put 
> it just above Bottom, then their ballot is counted as in ICA.
>
>
> MDDTR(pt/2) and ICT are the same.
>
>
> Gotta go!
>
>
> Forest
>
>
>
> ----
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>
>

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