[EM] Did Mr May bungle 2 candidate SNTV election maths to hide the fact of 5 papers?

[Craig Carey]

I was browsing around for webpages describing Mr May's theorem of 1952.

It seemed that Mr Kenneth May excluded all 0 winner (2 candidate) elections.

Mr Schulze did not get the wording copied right, and introduced all 0 winner
2 candidate elections, for the theorem to fail on.

Here is a brief description of the 1952 May 'theorem' I got from the Internet:

| May's theorem: When choosing among only two options, there is only one
| social decision rule that satisfies the requirements of anonymity,
| neutrality , decisiveness and positive responsiveness, and it is the
| majority rule.

http://216.239.63.104/search?q=cache:gaZP6TtDgy0J:www.dc.eclipse.co.uk/PDF_files/Voting.pdf+%22May%27s+theorem%22+1952+voting&hl=en


At a first glimpse the theorem seems to be completely wrong/untrue, since
this parameterized method passes but is not the "majority rule":

  (a0 + t*ab < b0 + t*ba) implies (B wins).
  (a0 + t*ab > b0 + t*ba) implies (A wins).

  t is a real number greater than 0.

Perhaps Mr Schulze can help out with research into the meaning of those
two words:
  (1) "decisiveness" and
  (2) "responsiveness",
  (3) "majority rule" [not ignoring the 2nd preference for some values of "t"]

Their plain English meaning and the other words would torpedo and sink the
 theorem of Mr K. May.



At 2005-01-02 21:37 +1300 Sunday, Craig Carey wrote:
...
>| Chris Benham wrote (1 Jan 2005):
>| > To me, it is axiomatic that a single-winner voting method
>| > should, with sincere voting, reduce to FPP when there are
>| > only two candidates.
>|

It is axiomatic until the time when some alternative seems better.

>| Mike Ossipoff replied (1 Jan 2005):
>| > Axiomatic? You're giving to us a fundamental standard that
>| > you have. That's your axiom. You mustn't expect everyone
>| > to have the same axioms that you have.
>|
>| That's not Benham's criterion. That's May's criterion:
>| If there are only two candidates A and B and the number
>| of voters who strictly prefer candidate A to candidate B
>| is strictly larger than the number of voters who strictly
>| prefer candidate B to candidate A, then candidate A must
>| be elected with certainty.
>|
>


An interesting thing about this mailing list is that the oldies can't learn
to stop making thinking mistakes that get exposed in these scenarios:

 (1) negative vote counts;

 (2) zero winner elections;

 (3) Asimov robots instead of voters. (They are not sincere, etc., and they
   can fill in papers without coughing up info naming the OSSIPOFF "favorite").




--C.