# [EM] Consensus?: IRV vs. Primary w/Runoff

Steve Barney barnes992001 at yahoo.com
Wed Jan 30 13:01:02 PST 2002

```Forest:

Let me try to clarify what I meant in the previous message. First, here is a
definition.

Primary w/Runoff:
Elected candidate shall receive 50% plus one or more of the votes cast. If more
than two people are nominated, a run-off shall occur between the two people who
receive the most votes in the first round of voting if in that round one person
does not receive 50% plus one or more of the votes cast.

Now, here’s my argument:

If there are 3 candidates with the same voters, and the voters’ preferences
remain static between the first and second ballot, the two procedures are
mathematically identical, and will yield the same result.

If there are 4 or more candidates, the Instant Runoff voting procedure is less
manipulatable than the Plurality with a Runoff voting procedure, due to the
fact that voters cannot purposefully change their order of preference from one
balloting to the next.

Given the same voters and the same sincere preferences, the only mathematical
difference between these two procedures is that the IRV is less manipulatable
than the Primary w/Runoff procedure.

Therefore, IRV is better than the common Primary w/Runoff voting procedure in
the sense that it is either equally or less likely to violate any given
mathematically described fairness criteria, such as manipulability.

The reason I say “mathematically described” fairness criteria, is that I want
to exclude the political questions for the sake of the argument. For example,
some might argue that repeated balloting is better because the voters may be
according to that new information. I consider that to be a political question,
and I wish to leave that debate to others. Furthermore, that particular claim
seems to muddle the manipulation issue to the point where it becomes impossible
to prove (mathematically) one way or another. You have to hold certain things
constant to make the manipulation argument.

> Date: Tue, 29 Jan 2002 17:18:31 -0800 (PST)
> From: Forest Simmons <fsimmons at pcc.edu>
> To: Election_Methods-list <election-methods-list at eskimo.com>
> Subject: Re: [EM] Consensus?: IRV vs. Primary w/Runoff
>
> On Tue, 29 Jan 2002, Steve Barney wrote:
>
> > Do we have a consensus that the instant runoff vote (IRV) is MATHEMATICALLY
> > better than the common two step plurality vote (primary) with a follow-up
> > runoff between the 2 top plurality vote getters? It seems to me that it
> cannot
> > be worse, given that manipulation is bad. As far as I can see, the only
> > mathematically provable difference between them is that IRV is less
> > manipulatable. They share the same faults, including non-monotonicity. With
> 3
> > candidates, I believe they are mathematically identical.
> >
>
> I'm not sure what you are trying to say here. You conclude by saying that
> you "believe they are mathematically identical" immediately after opining
> that there is a "mathematically provable difference" between them. I
> suppose that's as good as any way of expressing confusion and bewilderment
> after being exposed to the stormy sea of opinion on the topic :-)
[...]

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"Democracy"?: