re: [EM] 03/29/02 - Rob Richie Letter and Non-Monotonicity

Alex Small asmall at
Fri Mar 29 00:55:08 PST 2002

Donald wrote:

>why would every A voter rank C second, but no C voters rank A second?

Substitute "almost every" for every and I can give plausible example.

Imagine a candidate, call him Crazy Ross, with niche appeal.  Say his main
issue is cutting taxes while balancing budgets.  If you trust his data and
charts, and believe him to be sane, then he's an excellent candidate.
However, many people doubt his sanity.

The other two candidates are Papa George and Slick Bill.  Papa George does
not have all of Crazy Ross's detailed plans and charts, but he seems more
committed to fiscal restraint than Slick Bill, who has several large
spending proposals.

It is reasonable to assume that most people who rank Crazy Ross first will
rank Papa George second.  It is also reasonable to assume that most people
who rank Papa George or Slick Bill first rank Crazy Ross last, because they
don't think anybody with the title "Crazy" should have nuclear launch codes.

It is not unreasonable to assume this profile:

30% Bill > George > Ross
 7% Bill > Ross > George
25% Ross > George > Bill
 6% Ross > Bill > George
25% George > Bill > Ross
 7% George > Ross > Bill

The runoff is between Slick Bill and Papa George.  25% of the electorate
defects to Papa George, and Papa George wins.  Note that Papa George is in
fact the Condorcet winner, and Crazy Ross is the Condorcet loser.

Now, suppose that 2% of the electorate, all from the Bill>George>Ross camp,
votes strategically and lists Ross>Bill>George.  Slick Bill now has 35%
first place votes, Crazy Ross has 33% first place votes, and Papa George
has 32% first place votes.  The runoff is Crazy Ross vs. Slick Bill, and
Slick Bill wins.

I don't know if those were the actual poll numbers in 1992.  Point is, in
1992 we had a candidate whom many perceived to be insane, and because of
his economic stances it is reasonable to assume that many of his supporters
would have taken the incumbent over the other challenger.  It's a very
reasonable scenario.

Anyway, using reasonable numbers, inspired by an actual election, I've
constructed a non-monotonic scenario.


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