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Mike,<br>
For the purposes of comparing election methods (in a rational way that tries
that at least tries to be scientific)<br>
we have a long list of technical criteria. Reasonable debate can arise
because one method will meet some<br>
crtiterion (or criteria) that the other does not, and then the question
is open as to which criterion is more <br>
important than the other. In the case of the comparison between IRV and
(Top-2) Runoff (TTR), this is <br>
definitely NOT the case (except for your "CW wins if one of the first-preference
top two" criterion, which <br>
I've never seen mentioned by anyone else in any other context). <br>
This is because the two methods are the same when there are three candidates,
and all of IRV's failings are <br>
possible with only three candidates, and yet IRV complies with criteria
that Runoff doesn't.<br>
IRV complies with the criterion that some call "Mutual Majority" and Woodall
calls "Majority", which TTR fails.<br>
IRV complies with Independence of Clones, which TTR fails. Woodall splits
this criterion into two.<br>
<br>
"Clone-Winner: Cloning a candidate who has a positive probabilty of election
should not help any other candidate.<br>
Clone-Loser: Cloning a candidate who has a zero probability of election
should not change the result of the election."<br>
<br>
TTR fails both of these. Top-two Runoff shares all of IRV's failings (except
for your one improvised exception), and<br>
its only real solid advantage over Plurality (FPP) is that it meets Condorcet
Loser. <br>
<br>
According to Woodall, both IRV (aka the Alternative Vote) and FPP have
maximal sets of properties.<br>
They both fail all the Condorcet-related criteria that he lists: <br>
Condorcet (Net), Smith-Condorcet (Net), Condorcet (Gross), Smith-Condorcet
(Gross)<br>
<br>
Plurality fails Majority and Clone-Winner; but meets Clone-Loser and all
his monotonicty criteria.<br>
IRV meets Majority, Clone-Winner and Clone-loser, but fails all his his
monotonicity criteria except Mono-add-top,<br>
Mono-add-Plump, and Mono-append. <br>
Both methods meet Later-no-help and Later-no-harm , the Plurality Criterion
and Symetric Completion.<br>
<br>
Of course when comparing any two methods that are both less than perfect,
it is always possible to contrive some example<br>
in which one seems to give a better result than the other.<br>
You wrote (Wed.Jun.2):<br>
<blockquote type="cite">
<pre>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</pre>
</blockquote>
Here we have an example where the CW is not the outright majority favourite,
and yet gets NO second-preferences.<br>
In my opinion, that is very implausible and of course it was purely
contrived for your propaganda purpose.<br>
The two real questions are:<br>
(1) Which of the two methods is more likely to elect the CW?<br>
(2) Which set of "concrete guarantees" is more important: that provided
by compliance with (mutual)Majority and <br>
Clone Independence, or the single guarantee that the CW will win if s/he
happens to be one of the top two?<br>
<br>
Regarding the first question, the answer is a simple, uncontoversial, resounding
: IRV. This can be and has been tested in<br>
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<br>
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<br>
election, in which the pundits all agree that the probable CW would have
made it to the final runoff under IRV.<br>
<br>
Regarding the second question, I thought a big part of the motivation/point
of electoral reform is to try to break the big-2<br>
"duopoly". I would have thought that CWs who happen to be one of the voted
first-preference top-2 would be winning<br>
most of the time under Plurality. I see TTR as a really insidious attempt
to cement the big-2 dominance by simply shifting<br>
the split-vote problem one step away from them.<br>
Also I find it interesting that you now distinguish "popular" CWs on the
basis of their first preference tallies. Does that mean<br>
that you now favour Smith//Plurality? Woodall lists "Condorcet-Net Top-Tier,
FPP", which picks the Smith-set member with<br>
the most initial first-preferences. If none of them have any first-preferences,
we eliminate the Reverse Smith-set and then consider<br>
the ballots as if those eliminated candidates hadn't run. In common with
FPP, it fails Clone-Winner.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
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