[EM] MCA on electowiki

[Kathy Dopp]

On Mon, Oct 18, 2010 at 8:24 PM, Jameson Quinn <jameson.quinn at gmail.com> wrote:
>
>
> 2010/10/18 Kathy Dopp <kathy.dopp at gmail.com>
>>
>> On Mon, Oct 18, 2010 at 7:06 PM, Jameson Quinn <jameson.quinn at gmail.com>
>> wrote:
>> > Because by simply voting (participation), you change the threshold
>> > needed
>> > for an absolute majority, and thus for certain kinds of wins. You cannot
>> > do
>> > this by changing your vote (monotonicity).
>>
>> But  Statement of Participation Criterion that you linked to says:
>>
>> Adding one or more ballots that vote X over Y should never change the
>> winner from X to Y.
>>
>> so failing the criteria means adding more votes having X > Y would
>> change the winner from X to Y.  i.e. failing monotonicity.
>>
>> Kathy
>
> This is not the definition of monotonicity. Monotonicity states that
> changing an existing vote from X≤Y to X>Y should not change the winner from
> X to Y. It says nothing about adding new X>Y votes.


The mathematical definition of increasing monotonicity says when I
increase the independent variable, the dependent variable likewise
increases (for voting, when I increase votes for a candidate, that
candidate's chance of winning increases.)  Or the mathematical
definition of nondecreasing monotonicity says, when I increase the
independent variable, the dependent variable never decreases (for
voting when I increase votes for a candidate, the candidate's chances
of winning never decreases.)

I would say by any standard normal mathematical definition of
monotonicity, if a voting method fails the Participation Criterion you
linked to, it also fails to be monotonic.

Adding votes or increasing ranking for a candidate, should not cause
that candidate to lose whereas he otherwise might have won.  To me,
that is just another way of stating nonmonotonicity.

Kathy

> Clearly, the two ideas are related. However, MCA's failures of the "Combined
> Monotonicity and Participation Criterion" are limited to the rare
> "participation-type" failures, not the potentially more common
> "monotonicity-type" failures. (This goes for all stated versions of MCA)
>
> JQ



-- 

Kathy Dopp
http://electionmathematics.org
Town of Colonie, NY 12304
"One of the best ways to keep any conversation civil is to support the
discussion with true facts."

Fundamentals of Verifiable Elections
http://kathydopp.com/wordpress/?p=174

Realities Mar Instant Runoff Voting
http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf

View some of my research on my SSRN Author page:
http://ssrn.com/author=1451051