[EM] Condorcet How?

[Abd ul-Rahman Lomax]

At 03:55 AM 4/9/2010, Kristofer Munsterhjelm wrote:

>I'll note here that Bucklin is not cloneproof, and in some cases it 
>can reward cloning. See 
>http://www.mail-archive.com/election-methods-electorama.com@electorama.com/msg02705.html 
>. Thus it might pay for voters of some opinion to add lots of 
>write-ins of the same opinion (leftist, right-winger) as clones.
>
>Your limit to the number of write-ins would help fix that issue, but 
>it does exist.

Write-ins are usually limited to one....

The method examined in that old post was not Bucklin-ER, which I 
highly recommend over "pure Bucklin," i.e., no equal ranking allowed, 
and I didn't find the example clear, so I'll look at it here.

>[EM] Bucklin not clone-independent
>
>Rob LeGrand
>Thu, 08 Apr 2004 16:26:32 -0700
>
>Mike Ossipoff wrote:
> > By the way, if anyone knows of an example in which Buckling fails
> > Independence from Clones, would they post it?
>
>20:A>B>C
>17:B>C>A
>13:C>A>B
>
>B wins under (usual) Bucklin.
>
>20:D>A>B>C
>17:B>C>A>D
>13:C>A>D>B
>
>Now A wins, so adding a clone of A (D, which doesn't win) caused B to lose.

What's "usual" Bucklin? The example I've usually seen was Duluth 
Bucklin, which allowed equal ranking in third rank.

I've learned that preference analysis without some explanation of 
underlying preference strength can be quite misleading. First of all, 
with real Bucklin, large numbers of voters would truncate.

There are three candidates. It makes no sense that all voters 
approved all candidates, so the third rank must be not actually as-voted.

Notice, however, that there is no Condorcet winner, there is a cycle. 
That means that there is no spectrum that works, there is no "middle."
The behavior that all voters fully rank is unseen in the real world. 
The expectation I have of Bucklin is that voters will only vote for a 
candidate, if the candidate is a frontrunner or is preferred to the 
preferred frontrunner. Bucklin strategy is Approval strategy, only 
with the ability to express first preference, thus it is easier, the 
compromise is postponed.

Given the very unusual condition that all voters rank all candidates, 
we have, for the second round, an Approval election with these results:

A: 33/50
B: 37/50
C: 30/50

Notice, however, that there is no Condorcet winner, there is a cycle. 
That means that there is no spectrum that works, there is no "middle."

With 50 voters total, all candidates have a majority in the second 
round! B wins. Note that the most common complaint about Bucklin has 
been that voters bullet voted. As Bucklin settles in, multiple 
majorities are unusual. Three would be astounding. Something very 
unusual is going on here.

Okay, Clone dependence. First of all, the votes only make sense if 
equal ranking in the first rank is not allowed. Forced ranking can 
cause odd effects to appear. Now, the term "clone" is used with 
special meaning among estudents of election methods, meaning that all 
voters rank the clone together with another candidate. This alone is 
preposterous as to real elections! Some voters just won't like his 
name, reminds them of their stinky uncle, and another voter is his mother.

This clone trick only works because the B votes are shoved down, so 
the second rank votes for B (from the A voters) disappear.

Now, remember, Bucklin is an Approval method. The (first rank) 
frontrunners are A and B in the original election. D, however, is 
preferred by all of the A voters! This alone is odd in itself.

I think the votes in the first election are unrealistic. The voters 
know that A and B are the frontrunners. This would be more realistic:

20:A
17:B or B>C
13:C>A

A wins. The clone would give us

20:D>A
17:B or B>C
13:C>A or C>A>D

Second round, majority for A only, unless B voters add the C 
preference, in which case it's an additional majority for C, but A 
still has a plurality.

The problem election was poor voting strategy on the part of the A 
voters which allowed B to win. If the preference between A and B was 
weak, this could make sense. It's highly likely that A and B and C 
all have roughly the same overall social utility. Examples like this 
can be really misleading.

This is the general problem with "election criteria." They are 
presumed to be desirable characteristics of elections. It seems 
strange, indeed, that the presence of a clone would affect an 
election outcome, but the defect here is caused by a change in the 
behavior of the voters upon the appearance of the clone; it's 
behavior that didn't particularly make sense in the first place, but 
it is also a change forced by a senseless prohibition against equal 
ranking. The change is caused by the demotion of B to third rank for 
the A voters. But we can assume that the *absolute* approval of the A 
voters for B did not change!

To know if the outcome represents a loss of utility or a gain 
requires information that we do not have.

Bucklin is an approval-class method, but when it is used with forced 
ranking, it takes on other characteristics.

The proper use of Bucklin is as a simulation of a series of Approval 
elections with loosening approval cutoff to allow the election to 
find a majority. So Bucklin will, I expect, perform as if the ballot 
were a Range 4 ballot, with rating 1 missing. Rating 2 or higher has 
the meaning of "approval."

The A voters would not vote A>B, if they vote for B at all, they 
would vote A>.>B, so B would not win! And D would not change the outcome.

(Bucklin specifically allowed voters to leave a rank blank and then 
vote in the next lower rank. This facility shows even more how the 
ballot is really a range ballot. Allowing equal ranking in all ranks 
makes this much stronger, and adding a "disapproved rating" of 1 
would make it more complete, but a vote of 1 would not be considered 
approval; if those votes were needed for a majority, there would be 
majority failure, which, properly, should mean that the election 
fails and must be repeated. The vote of "1", though, could possibly 
indicate directions for future compromise, and campaign and voting strategy.