[EM] IRV vs Plurality vs. Condorcet (point for Kathy at bottom, in case she's not reading)

[robert bristow-johnson]

On Jan 14, 2010, at 4:24 PM, Terry Bouricius wrote:

> Response to Robert's statement...
> "I guess I still haven't heard a good justification for why the  
> Condorcet winner, if one exists, should *ever* be rejected as the  
> elected winner."
> ...
>
> Imagine this scenario. ..

sure, but i have a less imaginative scenario for you, Terry.

> A highly polarized electorate with a three candidate race. Only two  
> candidates are seen by the media and the public as viable, with 49%  
> favoring candidate A and 46% favoring B, and 5% favoring C slightly  
> over A. Most voters don't know much about C, but C has carefully  
> avoided alienating any constituency by only stressing his  
> likeability, rather than issues. However while the supporters of  
> both A and B don't think much of C they rank C second because they  
> subscribe to the "anybody but X" notion.

they evidently think more of C than they do of B or A (their least  
preferred choice).

> The A supporters all rank A>C>B, while the B supporters all rank  
> B>C>A and the C voters all rank C>A>B
>
> 49 A>C>B
> 46 B>C>A
>  5 C>A>B
>
> In a traditional runoff or IRV, A would win over B, after C's  
> elimination by 54 to 46. I think that is a reasonable expression of  
> "the public will" though not the only possible one.
>
> With Condorcet,
> C would defeat A by 51 to 49
> and C would defeat B by 54 to 46
>
> Thus C is the Condorcet winner.
>
> It is certainly justifiable to argue that C is the "rightful" winner.

consider the justifiability without consideration of your pre- 
election polling data that concludes that nobody really (well,  
perhaps 5%) wants Candidate C elected to office.

> But it is not unreasonable to say that C is not the "rightful"  
> winner, since 95% of the voters are highly dissatisfied with C  
> being elected.

from simply what the ballots say, you cannot deduce that 95% are  
"highly" dissatisfied.  perhaps many (but not all) of the A  
supporters view C as alright, just not as good as their guy.  same  
for the B supporters.   i realize that this is not consistent to the  
premise in which you built this scenario, but in the past on this  
mailing list, i find the construction of these scenarios not so  
persuasive.  they're good for counter-examples if someone is  
*proving* that something always is the case.

but, i believe that we should take what the ballots say at face value  
and not read into them anything more than what they say.  they say  
that 49% like A better than C and they like C better than B.  the  
ballots themselves do not say how much more they like A over B than  
they like A over C and we should not assume any quantitative amount.   
we should just say that they like A over either B or C and they like  
C better than B.  ballots have more authority than unofficial  
partisan or media polls.

so, how 'bout this scenario:

what is more likely (and in fact is confirmed in the town we live in  
this last year) is that A gets 33%, B gets 38% and C gets 29%, but C  
is the Condorcet winner.  so, specifically, it would look like


    6  A          (no preference between B and C)
   23  A>C>B
    4  A>B>C

   15  B
   17  B>C>A
    6  B>A>C

    5  C
   15  C>A>B
    9  C>B>A

the mano-a-mano is:

      48 A>B   47 B>A
      39 A>C   46 C>A
      42 B>C   52 C>B

the conclusion is that C is preferred over A who is preferred (but  
just barely, hence some controversy that we are hearing about) over B  
by the aggregate of these 100 people.  the symbols might be changed  
from "A,B,C" to "K,W,M" respectively and you'll know whom  
specifically we are talking about (there's a slight rounding  
difference).

now, Terry, why should this contrived example you just created serve  
as a better object lesson than what we already know has really  
happened?  just like i find the likelihood of a Condorcet cycle to be  
small (until we get some data that says otherwise), i also find the  
likelihood of the "warm bucket of spit" winning over the two  
polarized candidates to be small.  until we get some data that says  
otherwise.

or maybe, in your polarized situation, the warm bucket of spit *is*  
the best for society.  (what if your A is Stalin and your B is  
Hitler?  or Mao vs. Saddam?  the difference is that if A wins, the B  
supporters get lined up on the wall and, if B wins, it's the A  
supporters get shot.)  it might be a useful Solomonic resolution that  
the baby gets sliced into two and neither mommy A nor mommy B get it  
whole and intact.  that's the problem with winner-take-all.

whether C is the warm bucket of spit or just the sensible centrist  
with ostensibly wide appeal (but not as deep as A or B) is not a good  
reason to elect C to office.  the reason to elect C over A is that C  
is preferred by the electorate over A when they're asked to choose  
between the two.  the same can be said for C and B.  not considering  
unofficial polling, but only the official voice of the electorate  
(their ballots), *that* is what the electorate says.

if C is "better" than A and C is "better" than B, then who is  
"better" than C?  whom would you give it to, the minority?

that is the only reason that C taking office is more legit than A or  
B (even in your hypothetical, pathologically polarized scenario).   
and that is good enough.

> This is where the Range voting utility advocates enter the fray.

but why should anyone dilute their vote by splitting it right on  
their ballot?  for example, why should a C voter (we know who they  
are in Burlington) water down his/her vote for C by tossing some  
points onto A or B?  (perhaps your fav is going up against A or B and  
you would be forsaking your fav.)  there *is* an answer to that  
question, but that answer involves voter strategy and that is what we  
are trying to avoid, no?  it involves worrying about who might really  
win (other than your candidate) and then worrying further about  
covering one's butt.  we should be able to cover our butt without  
forsaking our favorite candidate.  and we know, first hand, that both  
Plurality and IRV have failed that.

> My point is merely that the Condorcet-winner criterion is desirable  
> in most cases, but not the only legitimate, nor ultimate criterion.


i'm still unconvinced.

but IRV does better in either your contrived example or in our real- 
world "example" than does Plurality. the old rules (40%+ plurality or  
delayed runoff) *might* have done okay in Burlington in 2009 (but  
only as good as IRV did, no better), but if not enough air-head  
liberals bothered to come back to the polls on Runoff Day (and we  
just don't know what those numbers would be, but we can expect about  
50% reduced turnout and we know that conservatives like to wield  
power and they *do* show up in bigger numbers), the old rules might  
have failed even more miserably than IRV did and that is the fact  
that Kathy just does not want to come to terms with.

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."