Fwd: [EM] Re: Participation criterion: a thought
Kislanko at aol.com
Kislanko at aol.com
Sun Sep 21 10:28:02 PDT 2003
In a message dated 9/21/03 11:45:19 AM Central Daylight Time,
chrisbenham at bigpond.com writes:
>>Do you mean "not possible in any known ranked-ballot method",or do you mean
"not (mathematically,logically or in principle)possible in any possible
ranked-ballot method"?
Presumably you are using some definition of "ranked-ballot method" that
doesn't include the
Borda or Plurality methods.What is it?<<
Clearly I should have qualified "ranked ballot methods" with "that depend
upon pairwise comparisons only". Any "rating-based" ranked-ballot system,
including Borda and some based upon "utilities" are easily provable to conform to
consistency. But in any case, I meant mathematically/logically provable. My
sloppy use of language was inexcusable, so apologies are in order.
Further said:
>>Can you refute Marcus Schulze's claim that Participation is met by
Woodall's
"Descending Acquiescing Coalitions" method?
Woodall gives this definition of Participation:
"The addition of a further ballot should not, for any positive whole number
K, reduce the
probability that at least one candidate is elected out of the first K
candidates listed on that ballot."<<
I wouldn't even try, but I would agree that by that definition of
"participation", it is clear that it is fundamentally different from "consistency."
"Consistency" says that if A wins in every partition of n ballots, then A must win
when all ballots are considered as a group. By this definition of
"participation", the question is not of partitioning existing ballots, but of adding
ballots that all have A>(anybody A was ranked ahead of in the smaller set of
ballots).
I have seen examples on this list where someone tries to prove consistency
with the phrase "now add these ballots", and based upon the definition of
consistency you can't use that to make a claim. To prove anything about consistency,
you can't begin with
5: A>B>C
4: B>A>C
and add
2: C>B>A
you have to begin with all 11 ballots individually and count them in sets
like:
{2: A>B>C +
4: B>A>C}
{3: A>B>C +
2: C>B>A}
In this particular partitioning, consistency doesn't appy, because there are
different winners for the partitions I chose, but you get the picture.
As to why consistency may be important, consider the US Presidential
election. It is demonstrably possible for a candidate to win even though he receives
500,000 fewer votes than another candidate.This is because of the way votes are
assigned to the particular partitioning used by that method.
Further, Chris said:
>>If it is true that Participation is incompatible with some essential
standards,(and we should
therefore just "get over it"), then I think that we should also become more
relaxed about
Monotonicity,because in my mind they are almost exactly the same thing.<<
It seems to me that Monotonicity is closer to Consistency than Participation.
I have a hard time using Participation to charactize a "method", because by
definition when you "add ballots to" a counted election, you're analyzing more
how the method works in a DIFFERENT election than how the method works in
general.
I have no pre-disposition to any particular method, but I find
"participation" less useful as an analytical tool.
Paul Kislanko
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20030921/00e76fc2/attachment.htm>
-------------- next part --------------
An embedded message was scrubbed...
From: Chris Benham <chrisbenham at bigpond.com>
Subject: [EM] Re: Participation criterion: a thought
Date: Mon, 22 Sep 2003 02:15:28 +0930
Size: 4574
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20030921/00e76fc2/attachment.eml>
More information about the Election-Methods
mailing list