MDDA(symmetric completion example)
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>A 54-46, A>B 46-44, 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 and LV(erw)SME easily elect A. 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
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
Election-Methods mailing list - see http://electorama.com/em for list info
I might be missing something but since C is ranked above bottom in the last
two factions, which add up to 54% of the electorate, candidate C would have
more implicit approval than candidate B.
On Tue, Nov 22, 2016 at 5:19 PM, Chris Benham cbenhamau@yahoo.com.au
wrote:
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>A 54-46, A>B 46-44, 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 and LV(erw)SME easily elect A. 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
Election-Methods mailing list - see http://electorama.com/em for list info