[Pnp-wg] Full IRV example, was Re: Interim report sections (fwd)

[Elizabeth Arnone]

Hence, my question to all was does everyone understand and agree with this?
My understanding of IRV was the vote was over in the first round since there
were no ties.
A total of 100 people made their 1st, 2nd and 3rd choice.  It is beyond me
why the rest of the process Steve describes is necessary, especially since
it complicates everything.

Thanks Steve for bringing this up because I think it needs clarification.
Liz

----- Original Message ----- 
From: "Steve Kramer" <scooter@guisarme.net>
To: <pnp-wg@gp-us.org>
Sent: Friday, April 15, 2005 1:23 AM
Subject: [Pnp-wg] Full IRV example, was Re: Interim report sections (fwd)


> Folks,
>
> Here is the full example that I sent to Elizabeth earlier.  It shows how
> IRV works, and it also shows that IRV fails the "monotonicity criterion"
> which I mentioned under "Mathematical Truths".  (Plurality/FPTP voting, by
> the way, *also* fails it.)
>
> *Please note* the point I make at the end of this exercise.
>
> -- 
>    Steve Kramer           ||         scooter (at) guisarme dot net
||
>    _____________________
===================================================
>   |  __/^\__        ,-^,|
>   |/~       \_     {  / |       "Power concedes nothing without a demand.
>               \/\   |!  |           It never has, and it never will."
>                 /  / )  |___
>                (_  \ \     /               Frederick Douglass
>                  ~v^  ?_,-'
>
> ---------- Forwarded message ----------
> Date: Sun, 10 Apr 2005 04:51:12 -0400 (EDT)
> From: Steve Kramer <scooter@guisarme.net>
> To: Elizabeth Arnone <elizarnone@comcast.net>
> Subject: Re: Interim report sections
>
> On Fri, 8 Apr 2005, Elizabeth Arnone wrote:
>
> > However, I don't understand #3 - which says,  "no winning candidate
should
> > ever lose as a result of being ranked *higher* by any voter.  How would
this
> > happen?  Same for #4.
> >
> Here's the example.  Let's say you hold an IRV election with three
candidates,
> and the following votes are counted:
>
>                            First         Second         Third
>    38 voters voted...      Smith          Allen        Johnson
>    25 voters voted...     Johnson         Allen         Smith
>    15 voters voted...      Allen          Smith        Johnson
>    15 voters voted...      Allen         Johnson        Smith
>     7 voters voted...      Smith         Johnson        Allen
>
> Here's how we count this in IRV:
>
> Smith has 45 first-place votes, Allen has 30, and Johnson has 25.  So
Johnson
> is eliminated.  *All* voters who listed Johnson first listed Allen second,
so
> every one transfers over to Allen.  Smith now has 45 votes, and Allen has
55
> votes (30, plus the 25 that were transferred over).
>
> Allen wins.
>
> Now let's consider if the votes had been slightly different.
>
>                            First         Second         Third
>    38 voters voted...      Smith          Allen        Johnson
>    25 voters voted...     Johnson         Allen         Smith
>    15 voters voted...      Allen          Smith        Johnson
>    15 voters voted...      Allen         Johnson        Smith
>     7 voters voted...     Johnson         Smith         Allen
>
> Look very carefully.  The **only** thing that changed is that the seven
voters
> at the bottom of the table decided to list Johnson first, *ahead* of
Smith.  In
> other words, these seven voters bumped Smith down a bit by not listing him
> first.  This should not help Smith in any way.
>
> But here's how it ends up happening in IRV:  Smith has 38 first-place
votes,
> Allen has 30, and Johnson now has 32.  So it's Allen who is eliminated,
and his
> votes are redistributed.  As it turns out, 15 of Allen's 30 go to Smith,
and 15
> go to Johnson as second-place choices. Smith now has 53 votes (38, plus
the 15
> he got being second to Allen), and Johnson has 47 votes (32, plus the 15
he got
> being second to Allen).
>
> Smith wins.
>
> So...when seven voters list Smith ahead of Johnson, Allen wins.  But when
those
> same seven voters switch, and list Johnson ahead of Smith - and nobody
else
> changes a single thing! - then suddenly *Smith* wins.
>
> This doesn't *precisely* prove what I wrote above...but it does show that
under
> IRV, a candidate can get a lower "score" and end up winning an election he
> otherwise would have lost with the *higher* score.
>
> And again, whatever method you choose, you'll end up with something weird
like
> this.  That's the point of that section.
>
> -- 
>    Steve Kramer           ||         scooter (at) guisarme dot net
||
>    _____________________
===================================================
>   |  __/^\__        ,-^,|
>   |/~       \_     {  / |     "Never was anything achieved without
danger."
>               \/\   |!  |
>                 /  / )  |___              Niccolo Machiavelli
>                (_  \ \     /
>                  ~v^  ?_,-'
> _______________________________________________
> Pnp-wg mailing list
> Pnp-wg@lists.gp-us.org
> http://lists.gp-us.org/mailman/listinfo/pnp-wg
>