Condorcet(x( ))

[Steve Eppley]

Lucien Saumur wrote:
>Steve Eppley writes:
>>You may or may not have implemented Condorcet(.5), depending on how
>>you resolve circular ties.  How do you calculate the size of each
>>candidate's worst defeat?  By "margin of difference" (not Condorcet)
>>or by "votes for the pairwinner" (Condorcet)?
>
>          As I have said before, I am not sure what to make
>of circular ties.
[snip]

You haven't answered the question I asked: what did you implement
in your web page?  
  Size of pairdefeat = Margin of difference?  
  Size of pairdefeat = Votes for pairwinner?
  Something else?

>>Would you consider implementing Condorcet(0), where nothing is
>>tallied against the tied pairs, in your webpage? 
>
>          My system could be changed in this way but I do
>not see why this would be necessary.

The reason would be if it's a better method than the one you've
implemented.  We can address this question more clearly if you 
explain what you've currently implemented.

Are you planning to change it so it implements drawing lots?

I think I put the address of your webpage in the ER welcome message 
text.  Now I'm not sure it belongs there.  My guess is that you've 
implemented "margin of defeat" and are calling it Condorcet's method.
Perhaps this does more harm than good.

>          I do not understand why we have so much problem with
>truncated ballots. I think that a truncated ballot may not be
>interpreted otherwise than to mean that the voter has no preference
>between the unranked candidates and that no preference logically
>means equal preference. 

No such interpretation is valid if the voting method rewards voters
for truncating.  For example, if truncating could change an election
from one where a candidate beats all others pairwise to one where
there's a circular tie, and the tie-breaker may be won by someone
other than that would-have-beaten-all candidate, then some voters 
have a strong incentive to truncate.  They don't have to express 
their sincere preferences; it's more rational for us to expect the 
voters will try to optimize the results for themselves.

[snip]
>my system also lets the voters indicate whether some or all of the
>candidates are unacceptable independently of the ranking
[snip]

A nice feature, but not always desirable.  There may be some
circumstances where it's better for the group to have a disapproved
winner than no winner.  For example, suppose your softball game is 
about to start, and your team captain unexpectedly failed to show up.
You must have a temporary captain, or you forfeit.  So in this case 
you'd want to use a method which must elect somebody.  A similar 
argument might be made about the undesirability of having no 
President when the world is in crisis.

How does your system tally disapprovals?  Does it disqualify each
candidate disapproved by 50%+1 of the voters?  (There are other ways 
to tally disapproval...)

Is it a problem for your implementation if the rankings and 
disapprovals are inconsistent?  Like if someone votes A>B, yet
disapproves A but not B?

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)