# [EM] I need an example of Condorcet method being subjected

Kathy Dopp kathy.dopp at gmail.com
Fri Jan 22 21:07:50 PST 2010

```> From: Jonathan Lundell <jlundell at pobox.com>
> To: "Terry Bouricius" <terryb at burlingtontelecom.net>
> Cc: kathy.dopp at gmail.com, election-methods at lists.electorama.com
> Subject: Re: [EM] I need an example of Condorcet method being
>        subjected
> Message-ID: <ACF2480E-5C32-4678-8E29-500F743F598A at pobox.com>
> Content-Type: text/plain; charset=us-ascii
>
> On Jan 22, 2010, at 10:30 AM, Terry Bouricius wrote:
>
>> Jonathan,
>>
>> Yes and no...You are correct that Arrow never uses the term
>> "monotonicity," but the concept is embodied in his second condition,
>> called "positive association."
>
> Yes--I'm talking about terminology merely (that, and that "monotonicity" itself needs definition in a particular context).
>

Jonathan,

Monotonicity is a mathematical concept that is fairly simple to
describe. There is non-decreasing monotonicity, strictly increasing
monotonicity, non-increasing monotonicity, etc.  Arrow describes the
concept re. elections fairly well in one of his fairness conditions.

IRV/STV are the only alternative voting methods I am aware of that
fail this monotonicity condition that Arrow's fairness condition
requires but I have not studied all alternative methods so there must
be others that fail Arrow's monotonicity criteria.  Plurality
elections do *not* fail this criteria which is why IRV/STV fail more
of Arrow's fairness criteria than plurality does.

The simplest way to state it in English is that the act of voting in
any one election should be monotonically increasing by giving the
voter the right to know that voting for a candidate always increases
that candidate's chances of winning holding all other things constant
(given the votes of other voters).  In other words, mathematically,
increasing the input or x value, always increases the output or y
value in a monotonically increasing function.

IRV/STV are the only methods I know that fail the monotonicity test
and thus deprive the voters the right to know what effect, positive or
negative, their ballot will have on the candidates the voter votes
for, but I'm sure there must be others.

because you incorrectly think of general and primary elections as
being one election, because in each plurality election the voter
retains the right to help the candidates of their choosing to win each
election, so a voter can knowingly strategize effectively if the voter
chooses to, unlike with IRV/STV where, for instance in the recent
Aspen election if 75 fewer voters had voted for one of the city
council members, he would have won instead of losing.  What an insane
voting method!

--

Kathy Dopp

Town of Colonie, NY 12304
phone 518-952-4030
cell 518-505-0220

http://electionmathematics.org
http://kathydopp.com/serendipity/

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

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