Random Ballot Tiebreaker

[Markus Schulze]

Dear participants,

Blake wrote (25 Aug 1998):
> This method might work, maybe it's what Tideman intended:
> 1.  Pick a random ballot and use its rankings, consider
>     ties as unsorted with regard to each other.
> 2.  Continue picking ballots.  When you find one that
>     orders previously unsorted candidates, use the ballot
>     to sort them.  Do not change the order of the already
>     sorted.
> 3.  If you go through all ballots, and some candidates
>     are still not sorted, order them randomly.

To my opinion, your method is _unnecessarily_ random.
I would propose the following random tiebreaker:

   If an algorithm doesn't lead to a unique winner
   but to a set of potential winners, then pick a random
   ballot. That potential winner, who got the best
   preference of this random ballot, is elected. If more
   than one potential winner got the best preference of this
   random ballot, then the whole algorithm is restarted
   with the top ranked potential winners of this random
   ballot.

To my opinion, randomness should be used _only_ in those
cases in which no other justifiable reduction of the set
of potential winners can be made. The reason: I doubt,
whether a randomly chosen winner will have the authority
that he needs to do his work.

*****

Quoting Tideman, Norman wrote (25 Aug 1998):
> "A proper subset of two or more candidates, S, is a set
> of clones if no voter ranks any candidate outside of S
> as either tied with any element of S or between any two
> elements of S."

To my opinion, Tideman's definition is too weak. I prefer
the following definitions (3 Oct 1997):

Definition ("clones"):

   A[1],...,A[m] are a set of m clones if & only if

   for each pair (A[i],A[j]) of two candidates
   of the set of m clones,

   for each voter V, and

   for each candidate C outside the set of m clones

   the following statements are valid:

   V prefers A[i] to C, if & only if V prefers A[j] to C.
   V prefers C to A[i], if & only if V prefers C to A[j].

Definition ("Generalized Independence of Clones Criterion"):

   A voting method meets the "Generalized Independence
   of Clones Criterion" if & only if additional
   clones cannot change the result of the elections.
   [If one clone is elected instead of another clone of the
   same set of clones, then this is not regarded as a change
   of the result.]

The aim of clone criteria is to verify, whether a method can
be manipulated by presenting additional candidates with
absolutely identical opinions. Tideman's definition of clones
is too strong (because he supposes that clones must no be
ranked identically to non-clones by any voter), so that
his definition of clones is -to my opinion- not meaningfull
enough.

Markus Schulze