[EM] Don't ignore the margins.
Roy
royone at yahoo.com
Thu Aug 16 14:51:32 PDT 2001
Blake Cretney wrote:
> Methods that sum margins or number of defeats tend to violate
> independence of clones. If you have a victory A>B, and you add a
> clone of A, then B is worse off if you are summing.
What I mentioned was akin to Dodgson, except instead of finding the
row that can be made the Condorcet winner with smallest impact, I was
eliminating the row that could be made the Condorcet loser. Perhaps
the weakness is not looking at both possibilities:
Given a winning-margins matrix, consider all row totals and all column
totals. Pick the lowest total; if it is a row, push it onto the stack
of losers; if it is a column, put it in a queue of winners. If
multiple rows tie for lowest total, construct a margins matrix of only
those candidates to determine which of them is the real loser; handle
tied columns similarly. If a row and a column tie, score a loser and a
winner. Winners and losers are, of course, removed from the matrix.
Obviously, Condorcet winners and losers will be low totals at any time
they appear. An interesting feature is that the first winner
encountered is the overall winner, which is very Dodgson-like, with
the difference being that there may be losers to eliminate first,
which can make a difference.
I'm not able to see a problem with clones at this point. As for
monotonicity, if a candidate is reduced in rank, that increases his
column total or decreases his row total, so it seems unlikely to be a
problem.
Roy
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