Reveling the Majority Winner

[Blake Cretney]

---
Blake


On Fri, 30 Oct 1998 20:11:17   Bart Ingles wrote:
>Blake Cretney wrote:
>> 
>> On Sun, 18 Oct 1998 11:25:14   New Democracy wrote:
>> > [...]
>> >     I like to think of my first choice as being my Plan A and I wish to
>> >stay with my Plan A as long as possible. Plans B and C etc are there in the
>> >event Plan A does not work out.
>> >
>> I think you're right that on average peoples rankings towards the end
>> of the ballot will be less considered than those at the beginning.
>> They may not have even heard of some of the candidates they rank last.
>
>> But, what if a voter's ballot starts with a large number of weaker
>> candidates.  In IRO, these candidates are likely to be all eliminated
>> and the voter is likely to have a fully weighted vote between the two
>> final candidates, even though this preference may appear far down on
>> his ballot, and therefore, we might conclude, is less meaningful.
>> Do you see this as a good thing, or a bad thing?
>> 
>
>I would expect many third-party supporters to do just that -- i.e. vote
>for a large number of weaker candidates before including a "lesser evil"
>major candidate.  In this case, the major candidate would be fairly
>well-considered.  Maybe even more so than some of the minor candidates,
>which the voter wouldn't expect to win anyway.
>
>When the voter expects his top choice to win, his lower choices will be
>less considered (and probably not counted under IRO).
>
>

There is an apparent conflict between my belief that on average
preferences towards the end of the ballot are less meaningful, and
my support of a method that counts a preference between two
candidates independently of where in the ballot the preference is
expressed.  That is, if a voter ranks A over B at the beginning of
the ballot, the method does not differentiate this from voting
A over B at the end of the ballot.

Let me first state that although I have never participated in an
election where rankings are allowed, I know I would have trouble
ranking many of the lowest candidates.  Elections tend to have
a number of fringe or protest candidates who receive little
publicity and have little chance of election.  For most voters,
a preference between these candidates is likely to be arbitrary.

However, this doesn't matter.  The method I advocate passes 
MIIAC (Modified Independence from Irrelevant Alternative Criterion).
What this states is that any expressed preference between two
candidates who are not in the Smith set has no effect.

Smith Set-  The smallest non-empty set of candidates where every
candidate in the Smith set beats every candidate outside the Smith
set.

Fringe candidates will not be in the Smith set.  This is because
to be in the Smith set, a fringe candidate would have to actually
be majority preferred to a main-stream candidate who IS in the
Smith set.  It is unlikely that all the main-stream candidates 
will be in the Smith set, let alone fringe candidates.

Furthermore, MIIAC means that if I try to hurt a main-stream
candidate by ranking it lower than a fringe candidate, this
won't have any effect either.  Not unless so many people do
this that the fringe candidate becomes a likely contender
and member of the Smith set.

There is another reason I am not concerned about ill thought-out
preferences at the end of the ballot.  Arbitrary preferences
will tend to cancel each other out because they get subtracted
from each other.  This is different from AV/IRO, where arbitrary 
preferences can sometimes cause clone problems.  If you missed
my example of this, I can send it to you.

It is often suggested that AV focuses on results that are more 
meaningful.  To question whether this is true, I have provided an 
example with 4 groups of voters.

1. 40 A B C
2. 12 B A C
3. 13 B C A
4. 35 C B A

AV uses group 2 and 3's second preferences.  However, group 1 and
4's are locked away.  It is important to notice that AV's ignoring
of preferences is not only something that happens between fringe
candidates at the lower end of the ballot.  It also occurs between
major contenders at the top of the ballot.  The decision that group
2 and 3's second preferences are somehow more meaningful seems like
an entirely arbitrary decision to me.

In fact, AV's process is hard to reconcile with the goal of using
meaningful results.  This is because a result that is not used at
a particular round of AV, and therefore one would hope is not 
meaningful, may be used at a later round as if the vote suddenly
became more considered.  

So how DOES AV decide what information is meaningful for a given
round?  It all depends on the decisions it made in the previous
round based on the information it allowed then.  So, a change
in a previous round can have wild and unexpected consequences
down the line.  This is why AV can do things like violate
monotonicity.

1. 34 A B C
2. 6  A C B
3. 13 B A C
4. 12 B C A
5. 20 C B A
--
Winner B

1. 34 A B C
2. 6  C B A -- change by A becoming last choice of group 2
3. 13 B A C
4. 12 B C A
5. 20 C B A
--
Winner A

In the first example, only the first choices and group 5's second
choice are considered meaningful.  But in the second example, because
A has annoyed a small group of people, group 5's second choice is
not considered meaningful.  Instead, only group 3 and 4's second
choice is meaningful.  AV's decisions about what is and what is not
meaningful seem to be rather arbitrary.

---
Blake



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