# [EM] IRV and Brown vs. Smallwood

Don & Cathy Hoffard dchoffard at verizon.net
Tue Apr 7 23:54:21 PDT 2009

```Thanks Peter for your comments

>400: Smith, Jones, Johnson
>300: Jones, Smith, Johnson
>600: Johnson, Jones, Smith

Johnson loses regardless as to whether Smith or Jones is eliminated
Normal IRV with no strategy:
Jones is eliminated in the first round and Smith wins in the second round.

IRV with a strategy, of 101 vote switch, from Johnson voters to Jones
Smith is eliminated in the first round and Jones wins in the second round.
The Johnson voters would have to except Jones as their second best choice.

A more realistic example is the following:

340: Smith, Jones, Johnson
40  Smith, Johnson, Jones
280: Jones, Smith, Johnson
20: Jones, Johnson, Smith
620: Johnson, Jones, Smith

First let's look at a primary with a top two general election:
Smith (380) and Johnson (620) advance and Jones is eliminated (with 300)
Assume the Jones voters vote their same preference in the general election.
Smith wins (660) and Johnson loses (640)

Assume that 100 of the Johnson voters vote for Jones in the primary
Jones (400) and Johnson (520) advance to the general election, and Smith is
eliminate (380)
Assume the Smith voters vote the same preference in the general election.
Also assume the 100 who voted for Jones in the primary switch back to
Johnson in the general election.
Johnson wins (with 660) and Jones loses (with 640).
The Strategy worked.

It is clear that a primary (a plurality election) and a top two run-off
general election taken together is subject to Strategic voting.
The primary may be non-monotonic as well as the general election but
together they are monotonic.

Next let's look at an IRV election:
In the first round Smith (380) and Johnson (620) and Jones is eliminated
(with 300)
Assume the Jones voters vote the same preference in the general election.
Then in the second round Smith wins (660) and Johnson loses (640)

Assume that 100 of the 620 Johnson voters change their preference to the
following
100: Jones, Johnson, Smith
520: Johnson, Jones, Smith

Jones (400) and Johnson (520) advance to the second round, and Smith is
eliminate (380)
Now under IRV rules the 100 who voted for Jones continue to vote for Jones.
Jones wins (with 740) and Johnson loses (with 560).
The Strategy did not get Johnson elected but Johnson votes would be happier
it Jones than Smith.

IRV elections are LESS subject of strategic voting than a primary and a
top-two run-off.
Both voting systems are clearly monotonic.

Why is Monotonicity an issue, if they are both systems are monotonic and
monotonic is not ever a constitution requirement.

```