[EM] Nanson Criteria was Re: Fw: A further elucidation of my arguments

[Blake Cretney]

Paul Dumais wrote:
> Criterions:
> 
> Consistancy: Can someone give me an example of how Nanson fails this?

Let me first say that I don't care about the Consistency Criterion. 
My Path Voting web site gives a detailed explanation for why not in
the Average Ratings comparison.

40 ACB, 35 BAC, 25 CBA 
   A   B   C
A  X   40  75
B  60  X   35
C  25  65  X

C eliminated -> B wins 

51 B C A
49 C B A

  A   B   C
A X   0   0
B 100 X   51
C 100 49   X
A eliminated -> B wins

Put them together

   A   B   C    Borda
A  X   40  75   115
B  160 X   86   246
C  125 114 X    239

A eliminated -> C wins

> GITC: I'm not sure how Nanson fails this iether.

GITC relates to the idea of twins.  The concept of a twin is useful
for determining how parties running multiple candidates will affect
the outcome.  Basically, candidates are twins if they are always
ranked the same with respect to other candidates.

For example
5 D1 D2 D3 R
4 R D1 D2 D3

D1, D2, D3 makes a twin/clone set because there is never another
candidate ranked between them.  D1, R is not a clone set because 5
voters rank D2 and D3 between them.

Anyway, even though in real elections, true twins won't exist, if the
method discourages them, we can be certain it suffers from the
vote-splitting problem to some extent.

40 A B C
34 B C A
26 C A B

A 106
B 108
C 86

C eliminated.  A wins.  Now, replacing A with A1 A2
   3  2  1  0
40 A2 A1 B  C
34 B  C  A1 A2
26 C  A1 A2 B

A1 166
A2 146
B  142
C  146
B eliminated.  C will go on to win.

> Monotonicity: This criterion is not required to produce a fair result.
> Since by changing some ballots such that X goes into lower positions you
> put other candidates into higher positions. I'm not sure if Nanson can
> fail without changing the relative postion of other candidates (which
> would make the criterion inapplicable).

> Reverse consistancy: I can't imagine an example where Nanson fails here.
I think my corrected example on my previous email provides one.

> SPC: This criterion doesn't seem to be necessary for a "fair" result.

Not to me either.  It's more of an IRV-fan's criterion.

> LIIAC: Doesn't seem necessary for a "fair" result.

I don't think I'd go so far as necessary.  I tend to think it is
useful though. It ensures that as much as possible, the introduction
of new non-winning candidates won't affect the result.  So, we don't
have to worry about voters burying a candidate below fringe candidates
or the relative placement of fringe candidates affecting the result. 
However, I think its fair to say that a method can be very secure
against these things without meeting LIIAC.  I don't see this as a
serious problem for Nanson.

---
Blake Cretney