[EM] Democracy Chronicles, introductions
ElectionMethods at VoteFair.org
Tue Apr 24 11:37:17 PDT 2012
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.
On 4/24/2012 6:11 AM, Andy Jennings wrote:
> On Mon, Apr 23, 2012 at 11:28 PM, Richard Fobes
> <ElectionMethods at votefair.org <mailto:ElectionMethods at 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
> Reform Advocates."
> You said there are ballot sets for which the Kemeny method and
> provides different winners. How, then, can VoteFair be
> 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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