[EM] Democracy Chronicles, introductions

[Richard Fobes]

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
> <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
>             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