[EM] [RangeVoting] IRV vs Condorcet vs Range/Score

[Dave Ketchum]

I started this thread to compare IRV vs Condorcet, believing that IRV is 
provably less capable and deserves discarding.

To make room to concentrate on this I call for a truce between Condorcet 
and Range, though ready to claim that Condorcet meets voter needs better 
than Range.

Approval is a side issue, though anything expressible there is also 
expressible, easily, in Condorcet.

DWK

On Thu, 9 Oct 2008 16:37:05 -0400 (EDT) Stephen Unger wrote:
> 
> Steve
> ............
> 
> Stephen H. Unger
> Professor (retired)
> Computer Science Department
> Columbia University
> ............
> 
> On Wed, 8 Oct 2008, Dave Ketchum wrote:
> 
> 
>>I suggest a two-step resolution:
>>     Agree to a truce between Condorcet and Range, while they dispose of
>>IRV as being less capable than Condorcet.
>>     Then go back to the war between Condorcet and Range.
>>
>>Condorcet uses essentially the same ballot as IRV, with essentially the
>>same meaning:
>>     Any IRV ballot would be acceptable to Condorcet.
>>     Condorcet also accepts such as A=B.
>>     IRV often demands that voters vote for more than one candidate;
>>Condorcet accepts as few or many as the voter offers.
>>
>>IRV gives extra credit for ranking a candidate first, while Condorcet cares
>>only which is most liked.  The following example shows this:
>>     IRV starts by discarding B for least first-place votes, and then
>>solves A vs C.
>>     Condorcet sees that B is liked better than A and B better than C, so
>>B wins.
>>
>>Condorcet is better for validation:
>>     All that is said by a collection of Condorcet voters, such as a
>>precinct, can be recorded in an NxN array.  These arrays can be summed for
>>whole counties, states, etc.
>>     When the first name on an IRV ballot loses, such as B in the example,
>>the next name on that ballot must be known and substituted.
>>
>>An example:
>>
>>42: C>B
>>39: A>B
>>10: B>A
>>4: B
>>5: B>C
>>
>>B is the Condorcet winner, and also the first loser discarded by IRV.
>>
>>Actually, IRV and Condorcet usually agree as to winner:
>>     If most ballots agree as to top rank, that candidate wins.
>>     Ditto agreement on most other ballots.
>>     If there is a near tie among three or more, they often disagree but
>>usually get one of the leaders - matters little since the leaders were
>>about equally deserving.
>>     IRV discarding the truly best liked, as in the example, is a strong
>>argument for discarding IRV.
> 
> 
> *****
> Good arguments for Condorcet over IRV.
> *******
> 
> 
>>My 2-cents as to Condorcet vs Range:
>>
>>Consider A good, B soso, and C bad:
>>     In Condorcet I rank A>B>C, expressing my basic opinion.
>>     In Range I rate A high and C low.  Then I have a headache as to B -
>>the higher I rate B, the more danger of B beating A; the lower I rate B,
>>the more danger of C beating B.
> 
> ********
> Good point, but I think we need to look closer.
> 
> The basic weakness of Condorcet (or any other ranking scheme) compared
> with range is that the vote A>B>C could mean "I think A is fine, B is
> almost as good, and C is terrible" OR it could mean "I think A is
> fine, B is very bad, and C is even worse". OR it could mean anything
> in between. There is NO way for a voter to cast different votes that
> distinguish among these cases.

In one sense a Condorcet weakness.  In another sense Range has a weakness 
of demanding that voters successfully understand and productively use Range 
ratings.
> 
> This has the interesting consequence that the Condorcet voter is never
> in a quandary in such a situation. The vote A>B>C is the best that can
> be done to support A against all other candidates, and, at the same
> time it does the best job of supporting B over C.
> 
> But the Range voter DOES have a problem when the polls indicate that
> A, B, and C each have a chance to win. After giving A the maximum
> score and C the minimum score, the problem for the voter who ranks
> the candidates A>B>C is that giving B anything but the minimum score
> might help B beat A, while giving B anything but the maximum score
> might help C beat B, which would be bad if A's score is lower than
> both the B- and C-scores. If most of the voters consider B to be
> roughly midway between A and C in acceptability, then it is tough to
> decide how to score B. But this might be considered as a real problem
> having to do with the relative merits (in the eyes of voters) of the
> candidates. It is not a problem for Condorcet voters simply because
> their options are more restricted.
> 
> On the other hand, an RV election can produce a winner that is more
> satisfying overall. Consider the following example, where X>>Y
> indicates a very strong preference of X over Y.
> 
> 4 A>>B>C
> 3 C>>B>A
> 2 B>A>C
> 1 B>C>A
> 
> In a Condorcet election, B would win (beats A 6-4 and C 7-3).
> 
> But, in an RV election (range 0-5), a plausible vote expressing the
> same views would be:
> 
>      A  B   C
> 4   5  1   0
> 3   0  1   5
> 2   3  5   0
> 1   0  5   3
> 
> The winner here is A (26-22-18).  And this makes more sense, since 70%
> of the voters think B is very bad.
> 
> For the same voter views, an Approval Voting election would almost
> certainly also lead to A winning.
> **********
> Steve
> .......>
-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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