[EM] Trying to out-do... a result! pt 2

[Kevin Venzke]

A note or two, a multicandidate generalization, and naming idea...

--- En date de : Dim 20.2.11, Kevin Venzke <stepjak at yahoo.fr> a écrit :
> 1. If there is a Condorcet winner, elect him.
> 2. (optional) eliminate Smith or Schwartz losers. Transfer
> or don't 
> transfer preferences due to this. If ballots are exhausted,
> redetermine
> or don't redetermine the meaning of majority/50%.
> 3. Label remaining candidates A,B,C in descending order of
> first-
> preferences.
> 4. If B has a majority pairwise win over A, elect B.
> (Alternative: Don't
> require a majority win.)
> 5. If A has a >50% pairwise win over B, elect A. (The
> 50% is required
> here.)
> 6. If A does not have a >50% loss to C, elect A.
> (Alternative: Don't
> require a majority loss, just say any loss. You could even
> delete this
> rule completely.)
> 7. Otherwise elect C.

After digesting this a little, I believe that the majority requirements
of rules 4 and 6 are necessary. Half the point of investigating this
method was to satisfy minimal defense. But if you don't have the majority
wins of B over A or C over A, and you elect B or C respectively, you
don't know whether those candidates are actually permissible under MD.

In the three-candidate case this should be unnecessary, but I'm trying to
enable general use.

On that note here is how I suggest to generalize the rules for any
number of candidates. Rules 1-3 are the same.

4. For every (remaining) candidate B through Z, check whether A has a
majority pairwise win over that candidate, or vice versa, or neither.
In the first case elect A. In the second case elect the other candidate.
In the third case continue to the next candidate.
5. If there is no next candidate, A wins.

Another way of saying it:
4. Find the (remaining) candidate with the most first preferences who is
involved in a majority-strength contest with A. If there is no such
candidate, or if A is the winner of the contest, elect A. Otherwise elect
this candidate.

Thus the only pairwise contests considered are those involving A, and
decisive contests tend to end the method, making them difficult to
manipulate.

Minimal defense is guaranteed: If there is a majority over X but no
majority for X over anyone, then X can't take the win from A (if X is
not A), and if X is A, he will lose the win to whoever has the majority
win against him.

Now, if only we could use something more clone-friendly than first
preferences... The tricky thing is that most other metrics (such as
worst pairwise loss) are already vulnerable to burial.

I'm inclined to name this mechanic "king of the hill." I am picturing
candidate A as controlling the hill, and the first time someone gets 
knocked down, the parents end the game.

Kevin Venzke