[Election-Methods] Borda-elimination, a Condorcet method for public elections?

[Ian Fellows]

Dave
"I see Borda as more complex, without offering benefits to justify the cost.
I do not see counting Borda as a flavor of Condorcet."

The Borda count is not a flavor of Condorcet, but when it is done by runoff
(i.e. iterative deletion of the lowest borda count) then it is a condorcet
method.

The basic thrust of my thought was that people seem willing to accept IRV as
a method of single winner determination. But it has serious weaknesses
compared to other rank ballot measure. On the other hand, it is very simple,
and easy for people to understand:

            Electing a candidate using IRV proceeds as follows:
Step 1: All 1st place votes for each candidate are counted
Step 2: The candidate with the lowest count is eliminated, and the 1st place
votes are recalculated using only the non-eliminated candidates
Step 3: If only one candidate is left, she is declared the winner; otherwise
step 2 is repeated

Most condorcet methods are much more conceptually difficult, requiring the
voter to think about all pair wise relationships in order to figure out how
their ballot effects the outcome. Baldwin's method, is just as simple as
IRV. note: I prefer a descriptive name for the method Total Points Runoff
(TPR).

            Electing a candidate using TPR proceeds as follows:
Step 1: The total points for each candidate is found
Step 2: The candidate with the lowest number of points is eliminated, and
the points are recalculated using only the non-eliminated candidates
Step 3: If only one candidate is left, she is declared the winner; otherwise
step 2 is repeated

"Cycles are a Condorcet complication.  Not expectable too often, for they
result from 3 or more candidates approaching a conflicting tie for winning -
such as A>B>G>A."

Also, if you don't expect cycles to occur too often, then Condorcet methods
have very nice properties:
TPR satisfies the following Criteria:
1.	Condorcet winner
2.	Condorcet loser
3.	Smith set
4.	Majority
5.	Mutual majority
6.	Reversal Symmetry
7.	Pareto
8.	Universality
9.	Non-imposition
10.	Non-dictatorship
11.	Resolvability

It can also be shown that if there is a condorcet winner:
1.	TPR is monotonic
2.	TPR is independent of clones.
3.	TPR is independent of irrelevant alternatives
4.	TPR is invulnerable to compromise
5.    TPR is invulnerable to favorite betrayal

TPR is also resistant to burying, in that if there is a condorcet winner, a
voter insincerely burying (giving a low ranking) a candidate will lead to
three possible outcomes:
1.	The condorcet winner will still be the winner
2.	A candidate less favorable to the voter will be the winner
3.	the smith set will contain the condorcet winner, and candidates both
less, and more favorable to the voter than the condorcet winner.

Thus either the burying makes no difference, or it is against the voters
interest, or it is very risky because the smith set contains both more
favorable, and less favorable candidates. Thus, because small changes in
voter preferences can change which candidate is chosen within the smith set,
the voter would be taking a big risk that his more favorable candidate would
be chosen from the smith set, verses the less favorable candidate that he
buried the condorcet winner behind.


cheers,
Ian



-----Original Message-----
From: Dave Ketchum [mailto:davek at clarityconnect.com]
Sent: Thursday, December 20, 2007 7:47 PM
To: Ian Fellows
Cc: Election Methods Mailing List
Subject: Re: [Election-Methods] Borda-elimination, a Condorcet method
for public elections?


"Condorcet" caught my eye - I think it deserves more attention but do not
know how to get there.

I see Borda as more complex, without offering benefits to justify the
cost.  I do not see counting Borda as a flavor of Condorcet.

Answering your questions:
      1- Condorcet is understandable if properly presented to voters and
public.
      2- Still Condorcet.
      3- What is really that much better than Condorcet (based on what a
voter normally knows on election day - all kinds of nonsense can be based
on knowing what all others are doing, with your own plotting kept secret).
           Remember that Range allows stating numeric ratings - for which
it must demand that the voter ASSIGN numeric ratings.
           I see Range as competitive, deserving careful analysis of
differences - perhaps mixed with true comparison by voters.

Voting:
      Rank one or more candidates, thus indicating liking them better than
the sea of unranked candidates.
      Use higher ranks for better liking (see voter instructions as to
whether 3 is higher or lower than 4, as a rank).
      Equal ranks are permissible for equal liking.
      If, for example, you only wish to rank a couple, 4&5 would have the
same meaning as 1&7 - it is relative values that matter, not magnitude of
rank difference.
      If, for example, you like neither of the most likely winners, smart
to rank at least one such, unless you see them deserving to tie.

Analyzing results:
     Results are publishable for whatever parts of a district are counted,
looking much as a tournament score, giving results for each pair of
candidates.

Cycles are a Condorcet complication.  Not expectable too often, for they
result from 3 or more candidates approaching a conflicting tie for winning
- such as A>B>G>A.

On Thu, 20 Dec 2007 11:37:15 -0800 Ian Fellows wrote:
> Hi all,
>
>     I've been thinking a bit lately about the lack of Condorcet methods in
> public elections. I have written a rough outline of why Borda-elimination
> (Baldwin) is an attractive option for implementation in the public sphere.
>
> If you are interested, check out:
> http://thefell.googlepages.com/statisticalsnipstprelections
>
> Does anyone have thoughts on why Condorcet methods have not been used more
> often? Are there proponents here of different winner criteria (i.e.
Borda),
> or is there a relatively strong consensus that if a Condorcet winner
exists
> he should be elected? If so, what methodology do you think is 1.
> understandable by the public, 2. Theoretically justifiable, 3. Resistant
to
> tactical voting
>
> Cheers,
>
> Ian Fellows
> Statistician
> University of California, San Diego
> http://thefell.googlepages.com/
--
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  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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