# [EM] IRV and Brown vs. Smallwood

Don & Cathy Hoffard dchoffard at verizon.net
Wed Apr 8 14:56:56 PDT 2009

```Thanks Ralph for pointing out my oversite.

>> The primary may be non-monotonic as well as the general election but
>> together they are monotonic.

>You presumably meant that the other way around.  Plurality is
>monotonic for both elections, but the 2 taken together result in
>strategy and a non-monotonic effect?

>Monotonic = voting for (or raising the preference of) a candidate
>cannot result in that candidate losing

SORRY, GOT IT BACKWARDS, MY FALUT.

Let's Look at the example in wikipedia
http://en.wikipedia.org/wiki/Monotonicity_criterion

Number of votes 1st Preference 2nd Preference
39 Andrea, Belinda
35 Belinda, Cynthia
26 Cynthia, Andrea

Using IRV "Cynthia is eliminated, thus transferring votes to Andrea, who is
elected with a majority."

In a primary Andrea and Belinda would be the top-two and would go to the
general election.
The Cynthia voters would now vote for Andrea in the general election (based
on their preference).
And the result would be the same as IRV.

Let us now assume Cynthia voters manage to "...persuades ten of Belinda's
supporters to change their votes to her at the next election." (or in this
election)

This election would look like this:
Number of votes 1st Preference 2nd Preference
49 Andrea Belinda
25 Belinda Cynthia
26 Cynthia Andrea

"Because of the votes Belinda loses, she is eliminated first this time, and
her second preferences are transferred to Cynthia, who now wins 51 to 49."
"In this case Andrea's preferential ranking increased between elections -
more electors put her first - but this increase in support appears to have
caused her to lose."
"Counterintuitively, it was the increase in support for Andrea (along with
the properties of IRV) that hurt her."

They could use the same strategy in a primary. Belinda would be eliminated
in the primary. Andrea and Cynthia would advance to the general election.
Assuming that the Belinda voters preferences remain the same then Cynthia
would win in the general election (51 to 49).
The strategy worked in a IRV election and in a top-two election.
It is clear that both voting SYSTEMS are non-monotonic.

In actual voting (IRV or Top-two) there is very little chance that Belinda
voters could be persuaded to vote for their third choice.
In order for this strategy to work you would have to have a precise
knowledge of all of the voters preferences (first and second).
In this example if you missed the 2nd preference by 2 (say it was really -
23 Belinda Cynthia and 2 Belinda Andrea) Andrea would win (51 to 49).
The 10 Belinda voters who switched would be very upset at the Cynthia voters
who convinced them to switch, now they have to settle for their third
choice, Andrea.

The argument some people are making is that IRV has a potential flaw.
Which I have pointed out, the top-two voting system has the same flaw.
I also pointed out that the top-two has more of a chance of voter
manipulation than IRV.
It would seem that those opposed to strategic voting and voter manipulation
are backing the wrong horse.

All of this is not relevant. The only way it would be relevant is if an
election method that is "non-monotonic" is unconstitutional.  Which would
rule out IRV and top-two.
However, the U.S. Supreme Court has already ruled that the top-two is
constitutional (see case below).

It is the responsibility of the legislature (or the voters in this case) to
decide on their election method, and it is the responsibility of the Supreme
Court to decide if it is Constitutional.  If you think that a voting method
is flawed you need to take that issue to the legislature (or voters) who
make the laws.  If the law (a voting method passed by the people) is full of
flaws and it passes the Equal Protection Clause (and other Constitutional
issues) then the "will of the people" shall prevail.

See Washington State Grange. v. Washington State Republican Party (2007)
"...they threaten to short circuit the democratic process by preventing laws
embodying the will of the people from being implemented consistent with the
Constitution."

Don Hoffard

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