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

[James M Leas]

Steve Kramer,
Did you see the article in Scientific American last year on majority
voting methods? IRV was mentioned but not given much space because,
according to the article, it did not necessarily provide the outcome
desired by a majority of the voters, as your example below illustrates.
The article actually focused on another system that it said was better at
providing majority rule. I think that system looked at more than just the
first place choices, as IRV does. 

I wonder whether anyone in the Greens has expertise in this important
area? Burlington, Vermont voted for a charter amendment to implement IRV
in the future mayoral elections. If the state legislature and the
governor approve it could happen next year. But if there is a better
system we should know about it and consider an amendment for future
elections. 

I would ask, do you only have this problem with IRV if all three have
lots of votes? If all three candidates have a similar number of votes
maybe dropping the one with the fewest first place is inappropriate and
the rankings should all be considered to determine who got the majority. 
Jimmy

On Fri, 15 Apr 2005 01:23:18 -0400 (EDT) Steve Kramer
<scooter@guisarme.net> writes:
> 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^  ?_,-'
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