In the non-mathematical world the word "equivalent" means "having
similar or identical effects" which allows for not _always_ being
_identical_ in _all_ respects. That is the context for usage in the
Democracy Chronicles article.
Even in a rigorous academic mathematical context, "equivalent" means
"having virtually identical or corresponding parts." In this context
VoteFair popularity ranking is "virtually identical" to the
Condorcet-Kemeny method because the word "virtually" allows for the
_extremely_ _rare_ cases in which there are more than six candidates in
the Smith set (which can possibly cause a difference in which candidate
is declared the winner), and allows for an election involving, say, 30
candidates that _can_ (but may not) result in different full rankings
between the two methods.
If I had instead claimed that the two methods are "mathematically the
same," then of course that would have been inappropriate.
Richard Fobes
On 4/24/2012 6:11 AM, Andy Jennings wrote:
On Mon, Apr 23, 2012 at 11:28 PM, Richard Fobes
<electionmeth...@votefair.org <mailto:electionmeth...@votefair.org>> wrote:
On 4/23/2012 12:05 PM, Kristofer Munsterhjelm wrote:
On 04/22/2012 05:07 PM, Richard Fobes wrote:
The core of the system is VoteFair popularity ranking, which is
mathematically equivalent to the Condorcet-Kemeny method,
which is
one of the methods supported by the "Declaration of
Election-Method
Reform Advocates."
You said there are ballot sets for which the Kemeny method and
VoteFair
provides different winners. How, then, can VoteFair be
/mathematically/
equivalent? You say the differences don't matter in practice,
but for
the method to be mathematically equivalent, wouldn't the mapping
have to
be completely identical?
First of all, in the context of a publication that is read by
non-mathematicians (which is what the Democracy Chronicles is) the
word "equivalent" does not refer to a rigorous "sameness."
When you qualify it as "mathematically equivalent", it definitely does
refer to a rigorous "sameness".
Perhaps you should say "essentially equivalent".
~ Andy
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