[EM] DH3 pathology, margins, and winning votes

[Chris Benham]

Warren,
There are some desirable election method properties I insist on in part 
because they are so "cheap".
Two of these are  Douglas Woodall's  "mono-add-plump" and "mono-append".
The first says that if x wins and we add some ballots that plump (bullet 
vote) for x, then x must still win.
The second says that if x wins, and then on some ballots that didn't 
rank x  we rank x immediately below
the previously lowest ranked (above equal-bottom) candidate; x must 
still win.

Woodall demonstrates that Smith//IRV, unlike Smith,IRV  fails both these 
criteria.
(He calls the latter "CNTT,AV" standing for "Condorcet(Net)Top 
Tier,Alternative Vote.")

>abcd 10
>bcda  6
>c     2
>dcab  5
>
>All the candidates are in the top tier, and the AV winner is a.  But
>if you add two extra ballots that plump for a, or append a to the two
>c ballots, then the CNTT becomes {a,b,c}, and if you delete d from all
>the ballots before applying AV then c wins.
>

So what is a good argument "in the other direction"?


>But I guess this is an argument "for" BTR-IRV;
>
I strongly suspect that BTR-IRV also fails these criteria, and I know 
that unlike Smith(Schwartz),IRV
it fails Clone Independence.

 From an August 2004 message I sent to the instantrunoff-freewheeling 
Yahoo group:


> CB: Standard  IRV  has some good properties, some of which I regard as 
> essential. One of these is Independence of  Clones.
> Douglas Woodall  splits this into two.
> "Clone-Winner: cloning a candidate who has a positive probability of 
>  election should not help any other candidate."
> "Clone-Loser: cloning a candidate who has a zero probability of 
> election should not change the result of  the election."
> (To  "clone"  candidate x is to add one or more extra candidates, 
> which are all ranked adjacently with  x  and each other  by  all
> the voters.)
>
> Take this example:
> 25:Brown>Jones>Davis>Smith
> 26:Davis>Smith>Brown>Jones
> 49:Jones>Smith>Brown>Davis
>
> First-preference totals: Jones49,  Davis26, Brown25,  Smith0. 
>  "LeGrand IRV"/Bottom-2 Runoffs (BTR) proceeds  thus.
> Smith  pairwise beats Brown, so Brown is eliminated. (Jones now has an 
> unassailable 76 top-preferences).
> Davis > Smith, so Smith is eliminated.  Then Jones > Davis, so  Jones 
> wins.
>
> Now lets clone Davis:
> 25:Brown>Jones>Davis1>Davis2>Smith
> 24:Davis1>Davis2>Smith>Brown>Jones
> 02:Davis2>Davis1>Smith>Brown>Jones
> 49:Jones>Smith>Brown>Davis2>Davis1
>
> First-preference totals: Jones49, Brown25, Davis(1) 24, Davis(2) 2, 
>  Smith 0.
> Davis2 > Smith, so Smith is eliminated
> Davis2 > Davis1, so Davis1 is eliminated. Top-prefernce totals are 
> now: Jones49, Davis(2) 26, Brown25.
> Brown > Davis2, so Davis2 is eliminated.
> Then Brown > Jones, so Brown wins.
>
> Cloning the loser Davis changed the result, so "LeGrand IRV"/BTR  
> fails  Clone-Loser. 

As I understand it, BTR-IRV was invented by Rob Le Grand purely as a 
gimmick to try to sell Condorcet
to IRV supporters. I don't think he ever seriously suggested  it was 
good, and I don't know how anyone
else got that idea.


Chris Benham



Warren Smith wrote:

>I'm not sure your IRV restricted to Smith set BUT do NOT eliminate the 
>non-Smith candidates,  is better than the pre-elimination.   
>
>Think you could make arguments either direction.   
>But I guess this is an argument "for" BTR-IRV;  with BTR-IRV you do
>not have to worry about that issue, since you get the same result either way.
>
>wds
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