[EM] Two Condorcet Winners?

[Elisabeth Varin/Stephane Rouillon]

Adam,

it seems right using your definitions. I will use now on a Condorcet
Winner CW
when he/she exists and winners using differents criterias: winner (m),
winner (rm)
and winner (wv) respectively for margins, relative margins and
winning-votes.

>When Mike says "with wv, truncation won't steal the election from a
>majority-supported CW", he's saying that truncation on some ballots
>introduced a cyclic ambiguity into an election that otherwise had a
>Condorcet winner (the one and only kind of Condorcet winner), but the
>truncation does not change the outcome.

Could you answer these questions please, I put my answers too:

1) Why is it that important that "truncation won't steal the election
from a
    majority-supported CW"?

For me if you change a set of ballots S1 into a new set S2 by truncating

some ballots, it is quite possible and normal to obtain a different
winner:
we have different ballots! Why would I preserve a CW of S1 as a winner
if he is no more a CW of S2?

2) Is it an incentive to tell people "go ahead you can truncate, it will
not change the winner"?

 I do not think it is your goal since this is not guaranteed to preserve
the winner if there is no
 CW. Why not ask voters to put their real full sincere preferences
instead?

3) Is it an incentive to the people to give their real sincere
preferences?

    I imagine you could say to the people "vote for what you really
like! Others have no
   strategical mean to truncate their real preferences in order to steal
a CW from you"?
    But still, you cannot assure voters that strategy is removed when
there is no CW, and
    in addition you cannot ensure voters that an opponent could not
steal your CW.
    He/she could add artificial preferences (ABDEF) instead of voting
sincerely (AB)
    in order to artificially sink the CW (C) and put it into a cycle
where C could loose.

4) Thus, isn't the expression of sincere preferences aimed to by using
winning-votes
    dependent on having a CW and voters having no sincerely truncated
ranking
    preferences from the start?

    Since both conditions have no guarantee, I think winning votes only
offer a partial
    incentive toward sincere votes, and thus another criteria
representing optimal fairness
   (relative margins) should be considered.

5) What do you prefer, a "good enough" winner obtained from a set of
votes containing an
     additional incentive toward sincerity or the fairest winner
obtained from a "sincere enough"
     set of votes?

   I think it is a matter of proportions. Thus I need some kind of
measure to compare both.
  When I try to evaluate both I find that very few people would decide
to truncate their
  own preferences and expect to steal a CW with relative margins.  I
find a lot more of cases
   where tight elections could still the election from the fairest
winner (rm) to a good winner (wv)
   without changing the ballots set. Do you agree it is a matter of
comparing probabilities?

Steph.

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