Random Ballot Tiebreaker

[Blake Cretney]

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On Wed, 26 Aug 1998 14:33:56   Markus Schulze wrote:
>Dear Blake,
>
>you 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.
>
>If you go through all ballots, and some candidates are
>still not sorted, means, that every voter ranks those
>candidates identically. That means, that the voters are
>not decisive about these candidates.
>
>I have to add to my last mail, that I always suppose,
>that the voters are decisive. That means, that for every
>pair of two candidates A and B there is at least one
>voter, who either ranks candidate A ahead of candidate B
>or candidate B ahead of candidate A.
>
>Those versions of "Complete Independence of Clones," that
>I use, always suppose that the voters are decisive. Otherwise
>my versions of "Complete Independence of Clones" don't make
>any sense.
>
>Example 1:
>
>   There are 2 candidates (A and B) and every voter ranks
>   both candidates identically. Then the only way to choose
>   the winner is to choose him randomly. Every other
>   method would violate Neutrality.
>
>   Thus, candidate A is chosen with a probability of 50%.
>
>Example 2:
>
>   Suppose, that candidate A is cloned and that A1, A2, and A3
>   are his clones. Suppose, that every voter ranks candidate A1,
>   candidate A2, candidate A3, and candidate B identically.
>   Then, the only way to choose the winner without violating
>   Neutrality is to choose him randomly.
>
>   But this would mean, that a clone of candidate A is chosen
>   with a probability of 75%. Thus "Complete Independence of
>   Clones" is violated.
>
>Summary:
>
>   You cannot ask an election method to meet "Complete
>   Independence of Clones" in every possible situation.
>   To get "Complete Independence of Clones," you have to
>   suppose decisiveness of the voters in at least some very
>   weak meaning.
>
>Markus Schulze
>
My intention with that step 3 was to make sure my method was always decisive, not to meet the impossible "Complete Independence of Clones" criterion.


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