[EM] Condorcet complicated?

[Dave Ketchum]

Could it be that this is made more difficult by asking the wrong question? 
  I will try a bit:

Condorcet is in the business of finding the best liked candidate, just as 
Plurality is.

Often one candidate is truly much the best liked, Plurality will have no 
problem, and Condorcet will agree since most voters will rank that 
candidate as their first choice.

Toward the other extreme, three candidates can be about equally best 
liked, Plurality may declare any of them the winner (near a tie) and the 
voters can make life hard for the vote counters by not ranking a single 
best liked candidate:
      A preferred over each other candidate except B
      B preferred over each other candidate except C
      C preferred over each other candidate except A

Here we say the top candidates in such an election form a cycle - each is 
liked better than the others by many voters and each candidate outside the 
cycle is liked less than any cycle member.  Now if A is liked much better 
than B and C liked much better than A, while B is only liked a bit more 
than C, we ignore B>C and declare C the winner.

MAJOR point is that all the members of the cycle got there by nearly equal 
backing by voters and, while we must pick a winner, it is most important 
that we have a rule that picks from the cycle members, while different 
counters might write different rules.

There could be more than three candidates in a cycle - IF - voters choose 
such ranking.  This does not change the concept.

Likewise, IRV can suffer spoilers, a problem Condorcet avoids by reading 
all the ranking in each ballot.
==========================

For example:
    3 ABC
    4 BCA
    5 CAB

counts as:
    8 A>B, 4 B>A
    7 B>C, 5 C>B
    9 C>A, 3 A>C

Here we gave a cycle of A/B/C with 9 of 12 voters agreeing C is better 
than A, and C winning under Condorcet.

Also, with permitted truncation for IRV or Condorcet:
   6 A
   5 CB
   4 B

Condorcet will see that C is not liked enough to win, and 9 B wins over 6 
A.  IRV would discard the 4 B, and the 6 A would win, for IRV would not 
notice the 9 B represents stronger liking by a majority (even though 5 of 
them liked C better).

On Wed, 13 Oct 2004 14:42:14 +0000 MIKE OSSIPOFF wrote:

> 
> Someone wrote:
> 
>> However, the lack of any real world implementations to point
>> to, and the difficulty of explaining the tie-breaker make it very
>> difficult to explain to voters.
> 
> 
> I reply:
> 
> How difficult is it to explain this:
> 
> If no one is initially unbeaten, drop the weakest defeat. Repeat till 
> someone is unbeaten.
> 
> [end of PC definition]
> 
> Or:
> 
> If no one is unbeaten, drop the weakest defeat that's in a cycle. Repeat 
> till someone is unbeaten.
> 
> [end of SD definition]
> 
> Mike Ossipoff

-- 
  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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                  If you want peace, work for justice.