Random Ballot Tiebreaker
Blake Cretney
bcretney at my-dejanews.com
Wed Aug 26 11:42:13 PDT 1998
--
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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