Fwd: [EM] Re: Participation criterion: a thought

[Kislanko at aol.com]

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 
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From: Chris Benham <chrisbenham at bigpond.com>
Subject: [EM]  Re: Participation  criterion:  a thought
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