Majority Support?

Tue Nov 12 23:35:48 PST 1996

Mr. Eppley's comments bring up the elementary point that every voter will
apparently will have to made aware that if he/she fails to rank a
possibility, then any ranking that they do make ranks over any such

A modified Condorcet is included as part of my 1.
Limited approval in included as part of my 2. 

Plain Condorcet has the chance of picking a majority disapproved candidate
and plain approval have the chance of picking a wrong head to head candidate
as I have repeatedly stated.
Mr. Eppley wrote:
You [D] misunderstood the question.  I'm basically asking: why would good
candidates choose not to compete in the original election if they're able to
win the re-election?
D- I continue to not understand your question. If such "good" candidates do
not run in the election, then how can they run for re-election ?
>[D] All 3 do not have majority approval.

E- Right, that's the problem I'm pointing out, but you didn't answer the
question.  The question I asked was: ARE YOU CONCERNED that this can be the
outcome even when the compromise candidate is really okay?

D- I AM CONCERNED about electing majority approved candidates and not
electing minority approved candidates (and especially about not electing
majority disapproved candidates).
E--Can you construct a realistic example where the winner by plain Condorcet
could become majority-disapproved if some | dividing lines are inserted into
the rankings, without making all the candidates become majority-disapproved?

Here's an attempt to meet this "example spec":
   45: Washington Hitler Stalin
   20: Hitler
   35: Stalin Hitler Washington
    ==> Hitler wins by plain Condorcet.
   Could Washington have been elected if voters had also been able to express
disapproval of Hitler?  Insert some disapproval
dividing lines:
   35: Washington | Hitler Stalin
   10: Washington Hitler Stalin
   20: Hitler
   15: Stalin Hitler Washington
   20: Stalin | Hitler Washington
    ==> 55 voters now disapprove Hitler, but Washington is only
        disapproved by 20.
So the question is, is this scenario realistic enough to be of 
concern?  If so, it meets the spec.  If not, can you construct 
a realistic example so we have something to really be worried 
D- Votes to the left of the / symbol are approval votes.
                  H      S      W
35W/HS                      35
10WSH       10     10    10
20H            20
15SHW       15     15    15
20S/HW               20
100            45     45    60
Only W is majority approved. Thank you for the example. It will be used by
the opponents of plain Condorcet along with the supposedly unrealistic
standard circular tie example (as if there was W>S>H>W in head to head
pairings) in which all the candidates are defeated by a majority.
E- There's a lesser of evils dilemma in approval voting
which can distort approvals: should I approve a compromise candidate and risk
defeating my true favorite, or should I disapprove the compromise candidate
and risk electing the greater evil?  
D- Approve both your compromise candidate and your true favorite candidate
and rank your true favorite candidate ahead of the compromise candidate. 
If either or both fail to get majority approval, then either or both lose.
If either or both gets majority approval, then either or both go head to head
against each other and other majority approved candidates, if any.
E-This can result, for example, in the disapproval of a candidate who would
have been approved had s/he been the only candidate running.  
And it can result in the disapproval of all candidates even though there's
one who would have been approved if all voters had voted sincerely.
D-Plain approval voting picks too many candidates having majorities (or high
minorities) based on later ranked choices (if there were ranked choices in
plain approval which by definition are not allowed in "plain" approval

For new folk- In plain approval voting, a voter votes for one or more
candidates. The candidate with the most votes wins. Such "most votes" would
generally be a combination of 1st, 2nd, etc. choice votes if (repeat, if) the
voters could vote 1, 2, etc. 
Example-- Using approval---
                   W        H        S
4 W              4
30 WH         30       30
11 WS         11                 11
1 S                                     1
16 SW         16                 16
18 SH                     18      18
9 H                           9
5 HS                         5       5
6 HW             6         6
Tots           67        68      51
H wins using approval. Note that the WH votes defeated W.
Using head to head
                     W          H
4 W[H=S]        4
30 WH[S]       30
11 WS[H]       11
1 S[H=W]
16 SW [H]      16
18 SH[W]                  18
9 H[S=W]                    9
5 HS[W]                      5               
6 HW[S]          6
Tot              67         32, W beats H
                      H           S
4 W[H=S]
30 WH[S]        30
11 WS[H]                    11
1 S[H=W]                       1
16 SW [H]                    16
18 SH[W]                     18
9 H[S=W]         9
5 HS[W]           5
6 HW[S]           6
Tots             50          46, H beats S
                      S            W
4 W[H=S]                      4
30 WH[S]                     30
11 WS[H]                      11
1 S[H=W]          1
16 SW [H]        16
18 SH[W]         18
9 H[S=W]
5 HS[W]             5
6 HW[S]                         6
Tots                40        51, W beats S
W beats both H and S using head to head.

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