[EM] 04/02/02 - We have No Evil of Non-Monotonicity:

[Donald Davison]

04/02/02 - We have No Evil of Non-Monotonicity:

Alex,

Your first example of 3/29/02 does not exactly prove non-monotonicity, but
that is not important.  What is important is that you are showing that a
small change can trigger a larger change and maybe change the final
results.  This is normal because after any change an election is not the
same election.  We must accept that we may get different results after we
make any change.

All examples that are suppose to show non-monotonicity are concocted such
that a small change will trigger the elimination of a different candidate
that may result in another candidate being elected.  This elimination of a
different candidate not only brings a new set of `choices as votes' into
the math of the election, but it also repeals the old set of `choices as
votes' that were used from the first candidate to be eliminated.  This is a
very big net change in the election.

Concocted examples are very close to the Candidate Withdrawl method.  Your
example at first eliminated Ross, then it starts over and eliminates George
instead.  That is how Candidate Withdrawl works.

All you need to do is to start over `one more time' and eliminate Bill,
that will give us three sets of pairs for a pairwise election known as
Condorcet, but I digress.

It must be accepted by all of us that the two elections of a concocted
example are not the same elections, they are two seperate elections and it
follows that the results may be different.
    Suppose there was a real election with results like your first election
in your first example in which George Bush is the winner.  Further suppose
that four years later in the next real election we have the same candidates
and the results are almost the same except for the two percent difference
that you have shown in your second election of your first example.  In
other words, I have asked you to suppose that the two elections of your
first example happened four years apart.  Where's the evil.

We have no evil - there is No Evil!

Any change in an election makes it a different election.  You may as well
mark them number one and number two.  It's like comparing DNA, the two must
be exactly the same, if not, they are not the same, there is no DNA match
of your two elections in your first example.

Consider the case of filling a vacancy in Preference Voting/STV using the
data from the last election.  The dropping of the now vacant candidate
releases an entire quota of next `choices as votes' that were not in the
math of the original election.  This will not be the same election, it's a
new ballgame.  Other things can happen, `shit happens', one of the
remaining sitting members could be eliminated (if it were not for a rule
that guards the remaining sitting members).

Monotonicity is not a valid concept.


As a side note:  If we tally your first example as an Approval Voting
election each candidate will receive the same number of votes as follows:
                100 Bill,  100 George,  100 Ross

Bucklin yields:  68 Bill,   87 George,   45 Ross

While Bucklin is able to make a decision,
       Approval has no clue as to who should be the winner.

Your second example of 3/29/02 tells me that IRVing is the better method
for the voter than Approval Voting.

Your second example is too close to call, but it is safe for all the voters
to make a second choice in an IRVing election.  Their second choice will
not be used unless their candidate happens to be last in the first count of
the ballots.  Most voters prefer to rank choices instead of making them
equal.

On the other hand it will not be safe for the voters to make a second
choice if the method is Approval Voting.  That second choice just might
cause the first choice to lose, but then if the voters do not make a second
choice they may not have a vote when the final decision is made between the
last two candidates.  Under Approval Voting the voters are damned if they
do and they are damned if they don't.


Regards,
   Donald Davison, host of New Democracy at http://www.mich.com/~donald

   +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+
   |                        Q U O T A T I O N                          |
   |  "Democracy is a beautiful thing,                                 |
   |        except that part about letting just any old yokel vote."   |
   |                           - Age 10 -                              |
   +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+
    APV   Approval Voting
    ATV   Alternative Vote  aka  IRV Instant Runoff Voting  aka  IRVing
    FPTP  First Past The Post  aka  Plurality
    NOTA  None of the Above  aka  RON Re-Open Nominations
    STV   Single Transferable Vote  aka  Preference Voting  aka  Choice Voting
          aka  Hare Clarke  aka  Hare Preferential Voting

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