[EM] Re: Runoff vs. IRV

[Chris Benham]

  Mike,
For the purposes of comparing election methods (in a rational way that 
tries that at least tries to be scientific)
we have a long list of  technical criteria. Reasonable debate can arise 
because one method will  meet some
crtiterion (or criteria) that the other does not, and then the question 
is open as to which criterion is more
important than the other. In the case of the comparison between  IRV and 
 (Top-2) Runoff (TTR), this is
definitely NOT  the case (except  for your  "CW  wins if one of the 
first-preference top two" criterion, which
I've never seen mentioned by anyone else in any other context).
 This is because the two methods are the same when there are three 
candidates, and all of  IRV's failings are
possible with only three candidates, and yet  IRV complies with criteria 
that  Runoff doesn't.
IRV  complies with the criterion that some call  "Mutual Majority" and 
 Woodall calls "Majority", which TTR fails.
IRV complies with Independence of  Clones, which TTR fails. Woodall 
splits this criterion into two.

"Clone-Winner: Cloning a candidate who has a positive probabilty 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."

TTR fails both of these. Top-two Runoff shares all of  IRV's failings 
(except for your one improvised exception), and
its only  real solid advantage over  Plurality (FPP) is that it meets 
Condorcet Loser.

According to Woodall,  both  IRV (aka the Alternative Vote) and  FPP  
have  maximal sets of properties.
They both fail all the Condorcet-related criteria that he lists:
Condorcet (Net),  Smith-Condorcet (Net), Condorcet (Gross), 
 Smith-Condorcet (Gross)

Plurality fails Majority and Clone-Winner; but meets Clone-Loser and 
 all his monotonicty criteria.
IRV meets Majority, Clone-Winner and  Clone-loser, but fails all his his 
monotonicity criteria except  Mono-add-top,
Mono-add-Plump, and Mono-append.
Both methods meet Later-no-help and Later-no-harm , the Plurality 
Criterion and Symetric Completion.

Of course when comparing any two methods that are both less than 
perfect, it is always possible to contrive some example
in which one seems to give a better result than the other.
You wrote (Wed.Jun.2):

>Though it would be hoped that we'd get something better than Runoff or IRV, 
>what if it were necessary to choose between those 2?
>
>Of course they both have advantages compared to eachother, and examples in 
>which they do better than the other.
>
>But what stands out, for me, is that Runoff always elects a CW who comes in 
>1st or 2nd in the initial Plurality count, whereas IRV can fail to elect a 
>CW who is favorite to more people than anyone else is.
>
>I've posted examples of that happening. I'll post them again here. They 
>aren't contrived or implausible examples. All it takes is for favoriteness 
>to taper away from the voter median position. That's a very plausible 
>scenario.
>
>First I'll write this example in full, then I'll simplify it by leaving out 
>the preferences that IRV never looks at.
>
>Example 1, complete:
>
>67: ABCDE
>73: BACDE
>100: CDBEA
>84: DECBA
>70: EDCBA
>
Here we have an example where the CW is not the outright  majority 
favourite, and  yet gets  NO second-preferences.
In my opinion,  that is very implausible  and  of  course  it was purely 
contrived for  your propaganda purpose.
The two real questions are:
(1) Which  of the two methods is more likely  to elect  the CW?
(2) Which  set  of  "concrete guarantees"  is  more important:  that 
provided by compliance with  (mutual)Majority  and  
Clone Independence,  or  the single guarantee that the CW  will win if 
 s/he happens to be one of the top two?

Regarding the first question, the answer is a simple, uncontoversial, 
resounding : IRV. This can be and has been tested in
computer simulations. It is obvious to me that it is far more likely 
that  a CW outside of the top-2  will win in IRV than a
CW who is in the top-2 will lose in IRV. And then of course there is the 
well-known example of the 2002 French Presidential
election, in which the pundits all agree that  the probable CW would 
have made it to the final runoff  under IRV.

Regarding the second question, I  thought a big part of the 
motivation/point of electoral reform is to try to break the big-2
"duopoly". I  would have thought that CWs who happen to be one of the 
voted  first-preference top-2 would be winning
most of the time under Plurality.  I see TTR as a really insidious 
attempt  to cement the big-2 dominance by simply shifting
the split-vote problem one step away from them.
Also I find it interesting that you now distinguish "popular" CWs on the 
basis of  their first preference tallies. Does that mean
that you now favour Smith//Plurality?   Woodall lists "Condorcet-Net 
Top-Tier, FPP", which picks the Smith-set member with
the most initial first-preferences. If none of them have any 
first-preferences,  we eliminate the Reverse Smith-set and then consider
the ballots as if  those eliminated candidates hadn't run.  In common 
with FPP, it fails Clone-Winner.

Chris Benham


 
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