Id said:
What an elaborate counterfactual story. Its amazing what lengths to which
some people will go, to make Plurality fail Condorcets Criterion without
mentioning preference.
I've already answered about that. It's based on a privileged balloting
system. My criteria make no mention of any balloting system.
Though you go to great lengths to avoid mentioning preferences, you don't
mind saying that the voter intends to vote a ranking, when s/he votes in
Plurality. I've talked to voters, and many of them are adamantly opposed to
any voting system other than Plurality. They don't intend to vote a ranking
when they vote Plurality. And that's only part of the counterfactual nature
of your fictitious-rankings system of criteria.
Chris now replies:
Mike, notice that I specified that the voters' intended ranking is "maybe
truncated". It doesn't matter if the voters subjectively
don't have "rank" in their vocabulary: those that plan to cast a valid
Plurality vote intend to rank a single candidate above all others.
I reply:
No, that isnt good enough. For FARCS to work, it must be that sometimes the
intended ranking of the Plurality voter is _not_ truncated below first
choice. So then youre saying that the voter, coming to a Plurality
election, intends to vote a ranking. And you cant use your story of voters
who thought they were coming to a Condorcet election, because your Plurality
voter has, in first place, in his intended ranking, the candidate hes
voting for in the actual Plurality balloting. It doesnt make any sense. As
I said, the intended rankings cant be intended, even in principle, and
they have no real-world interpretation.
Chris continues:
Whatever balloting system is used all votes (that make any distinction among
the candidates) contain some (logically implicit)
ranking data and there is no other type of data that they all contain, so I
can't see that your reference to a "privileged balloting
system" is a meaningful criticism.
I reply:
Ranking is present in all balloting systems if you substitute, for votes X
over Y, ranks X over Y. Youre ignoring that if.
Ok, but its true that all balloting systems receive some candidate
ordering.
But my criteria dont need to mention any balloting system.
And FARCS, too, needs the definition of voting X over Y.
Kevin continues:
Mike apparently didn't think that I or Kevin had properly defined Kevin's
way of applying criteria
I reply:
I hadnt seen such a definition. So I wrote one. I later realized that it
was necessary to use my sincere voting definition, as described above. When
I posted about that, Kevin had already posted about the same fact, though I
hadnt yet read that posting.
Here is my attempt at a definition of the Venzke approach to applying
criteria with Mike-satisfying precision:
I reply:
That definition, below, does not have precision that satisfies me.
My word-processor is having trouble with the format of this posting. There
may be almost a full blank page below, before Chriss definitions starts.
Chris wrote:
Venzke rules for demonstrating a voting method's failure of criterion X:
Criteria are written in the form of "if A, then B" where A refers to some
stipulation about the votes and B refers to
something about the election result that must happen.
It is assumed that the voters have an 'intended ranking' of the candidates
that may be truncated and/or include some
above-bottom equal ranking. By definition, if the balloting rules allow the
voters to fully express this ranking then
that is what the voters will do.
I reply:
Not good. Youre explicitly stating one rule for rank methods and a
different rule for nonrank methods. It was to avoid that that I and Kevin
both independently suggested using my sincere voting definition as the way
to say what ballots are permissible, given a certain ranking.
When it is done that way, there is one rule for all methods, regardless of
their balloting.
Here is the separate rule that Chris would apply to nonrank methods:
If the balloting rules don't allow the voters to fully express their
intended ranking, then we assume that the voters
vote to express as much of it as the balloting rules allow, giving priority
to expressing as many of their intended
strict pairwise preferences as possible followed by expressing as many of
their intended pairwise equal-preferenes
(indifferences) as possible.
I reply:
That is completely vague. For a definite rule, say it as I did:
The failure-example writer can, for any particular voter, write that voters
actual ballot in any way that complies with these two rules:
1. The actual ballot may not vote X over Y if that voters intended
ranking ranks Y over X.
2. If the voters actual ballot votes X over Y, and his ranking ranks X over
Y, then that ballot is voting an ordering in the intended ranking.
The actual ballot must not fail to vote any ordering in the intended ranking
that the balloting system in use would have allowed it to vote in addition
to those orderings in the intended ranking that it actually does vote.
[end of rules for deriving an actual ballot from an intended ranking]
Chris continues:
If the voters can only express some or all of their intended ranking by
giving preference data that isn't on their
intended ranking, then we assume that they do so in a way that contradicts
their intended ranking as little as
possible.
I reply:
Vague.
Mike Ossipoff
If in testing for a method's compliance with criterion X, we can follow the
above rules/assumptions and show
an example of "A and not B", then we have proved that the method fails
criterion X.
----
election-methods mailing list - see http://electorama.com/em for list info
