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

Fri Dec 21 17:34:46 PST 2007

On Fri, 21 Dec 2007 10:57:01 -0800 Ian Fellows wrote:
> 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.

See if I understand well enough to describe a trial run:
      48 B X G N
      24 N G X B
      25 G N X B

Score:
      B 144=48*3
      G 171=48*1 24*2 25*3
      N 122=24*3 25*2
      X 145=48*2 24*1 25*1
Next step:
      B 96=48*2
      G 98=24*2 25*2
      X 97=48 24 25
So B loses and G wins.
> 
> 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:

The standard method of describing IRV skips its problem of failures due to 
not looking at all that the ballot says - so implied understanding aids 
its acceptance without bothering with true understanding.
> 
>             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).

I DO NOT understand your words.  I described what the voter needs to know 
to use Condorcet - make a list of as many of the candidates as you wish to 
vote for, sort your list in priority order, and vote, indicating which you 
like the most.

What I understand of Borda indicates it has the same requirement, except 
Borda seems to exclude voting for two candidates with indicated equal liking.
> 
>             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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