Re:[EM] We have No Evil of Non-Monotonicity:

[Alex Small]

Donald wrote:

>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.

Back to my previous example:

19% Bill > George > Ross
18% Bill > Ross > George
19% Ross > George > Bill
12% Ross > Bill > George
16% George > Bill > Ross
16% George > Ross > Bill

Right now the runoff will be Bill vs. George, and George will win.

Now let's say that some of the people (2% of population) from the
Bill>Ross>George camp change their minds, and join the Ross>George>Bill
camp.  They have moved Bill to last place, and improved their rankings of
both George and Ross.  However, neither George nor Ross (both of whom they
have enhanced their support for) wins.  Bill, the person they moved to last
place, now wins.

What is unrealistic or concocted about this?  I show a closely divided
electorate, the sign of a strong race.  In August of 1992 the three
Presidential candidates on whom this example is modeled were running neck-
and-neck in 1st place votes.  This is a completely realistic situation.

The second-place breakdowns are also reasonable:  George's and Bills camps
are divided over Ross's sanity, and Ross's camp shows a slight preference
for George because of his fiscal positions, but the preference is not
strong because they're deeply dissatisfied with the incumbent George.

What would it take for you to say that these numbers are not concocted?
Sure, I came up with them, but I came up with them as a plausible model of
a real-world case, not as a knife-edge, unstable, rare example to prove an
arcane point.

Also, you can say there is no monotonicity on the grounds that the whole
electorate is changed, but then you abuse the language.  Point is, a
segment of the electorate gained respect for the winner, lost respect for
their first choice, and ranked the winner higher and their first choice
lower.  The man that they demoted then won as a result.  State the
monotonicity criterion however you wish, but this is a messed-up (and very
realistic) situation that can occur with IRV.

More generally, for any 3-candidate race we can always say that A beats B
and B beats C (barring ties).  If the runoff is between A and B, and B has
the most first-place votes, as long as the margin (in first-place votes)
between A and B is greater than the margin between A and C, some of B's
supporters can rank C as their first choice and help B win.  The
possibility of helping somebody by ranking him lower is a messed-up
situation, whatever you want to call it in technical terms.

We can debate whether this alone is a sufficient criticism of IRV, or at
least sufficient reason to prefer some other method over IRV.  As Arrow
reminds us, no method is perfect, even if some are better than others, so a
criticism of IRV is not sufficient grounds to support another method.
However, it is absurd to deny that this is a valid criticism of IRV.  The
only debatable point is whether this flaw is out-weighed by other merits
when comparing IRV with a particular system.

Interestingly, under Condorcet George still would have won after people
rated Bill lower.  Perhaps there's a lesson in that...

Nah, couldn't be....

Alex