In our SODA development we came to something of an impasse for determining the
"order of play" for
the candidates casting their approval cutoffs.
Here's a suggestion:
Let the DSC winner go first, because the DSC winner is easily calculated,
satisfies Later-No-Harm (so
does not unduly encourage truncation), and can be thought of as the minimal
acceptable modification of
plurality, namely de-cloning it without destroying its montonicity. In a way,
DSC elegantly
accomplishes what IRV attempts but botches.
[In the context of SODA where there is only one faction for each of the n
candidates, the DSC method
has to score at most n*(n-1) subsets, and it takes no more than the order of
n^2 steps to determine the
DSC score of each of these subsets. So the whole thing can be done in the
order of n^4 steps at worst.]
>From then on the next player in the sequence is the candidate that ranked the
>previous player X the
highest. If there is a tie, say Y1, Y2, and Y3 each ranks X equally high (and
higher than anybody else
does) then the member of {Y1, Y2, Y3} ranked highest by X is the next player.
This order is clone consistent, i.e. if Y is replaced by a clone set, then the
entire clone set will be
intercalated into the order in place of Y.
This order discourages burial, because if X is first in the order, and Y buries
X, then Y will not follow X,
unless all of the other candidates bury X, too, in which case X could not have
been first.
Note that we could reverse the roles of X and Y in determining the order and
breaking ties: The
remaining candidate Y that X ranks the highest is next, and if X ranks no
remaining candidate, then the
candidate that ranks X the highest is next. My intuition is that this order
might not be quite as burial
resistant, but it would be better at discouraging what we could call "fawning,"
namely ranking the
presumed DSC winner artificially high for the sole purpose of getting into the
order earlier.
Another option would be to use the DSC winner's rankings for all of the rest of
the players, and passing
to the second player's rankings to resolve any equal rankings made by the DSC
winner, etc.
We need to experiment to see if any of these is adequate, and if so, which is
best.
What are some good scenarios to test?
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