[EM] (P1) defined

[Craig Carey]

At 22:21 18.09.99 , Craig Carey wrote:
>I'll reply to 3 messages, two from Markus Schulze and one from
....


-------------------------------------------------------------
>From an 18 Sept 1999 message I sent:

This is SPC which STV and FPTP satisfy:

>>                       Principle 1 
>> 
>>      Alterations of preferences after a preference
>>      for a winning candidate never cause that
>>      candidate to lose.
>

(P1) is very similar, but it modified slightly so that it implies
 monotonicity. First a single candidate is considered, then one,
 some, or all papers naming that candidate with a preference
 may have preferences after that candidates preference  altered
 in any way at all.

A difference  from SPC is that the preference for the candidate
 itself can be altered, and where SPC says that where there is
 no change in the candidate's win-lose status, (P1) says only
 that the candidate can't change from a loser into a winner.

The definition of SPC just above says "never cause .. to lose"
 but it in fact it means the stronger condition, "never causes
 the candidate's win-lose status to flip".


A definition of (P1)L:

>> For all c (c is a candidate), all V, all V' (where 
>> V and V' are election systems), then if 
>>  V' in AltAtAfter(V,c) and c loses V, then c 
>>  also loses V'. 
>
>Assuming X' in AltAtAfter(X,c)
>
>it follows that X is in AltAtAfter(X',c) [I think this is obvious]

=========================================================================

For example, consider (P1) applied to candidate B in this:

V:
  10 ABC
  11 B
  S

One system in AltAtAfter(V,'B') is this:
  6 A
  5 AB
  3 ACB
  2 AD
  1 B
  1 C
  S

No deletion of the A in the ABC papers was possible by B, so
 all the 10 ABC papers must have been transformed into the
 10 papers, AB, ACB, AD.

Candidate B can change the 11 B papers into anything and even
 discard them, and those 11 B papers were changed into the 8
 papers, A, B, C.

That is a valid 'AltAtAft(V,B)' (P1) transformation, and (P1)
 says that if B loses V then it loses the 2nd election also.

(That is noit an old example)

=========================================================================


An 'AltAtAfter Deletion/Disarding' does not allow voting
 papers to be discarded unless the 1st preference is for the
 losing candidate under consideration.

The following is quoted from an earlier message:

I'll clarify the 'AltAtAfter(..,..)' definition...

Preference Discarding: Let the candidate (c) be B:

V1 =  | 10 B |
      |   S  |

V1' = |  9 B |
      |   S  |

The following are true:
   V1' is in AltaAtAfter (V1, B) { discarded a voting paper
V1 is not in AltaAtAfter (V1',B) {  .. and can't get it back

Omit S (= the rest of the voting papers).

V2 =  | 10 ACBD |

V2' = |  7 ACBD |
      |  2 ACDB |
      |  1 AC   |

R =   |  9 ACBD |

True:
   V2' is in AltaAtAfter (V2, B) 
V2 is not in AltaAtAfter (V2',B) { Can't get D out of ACDB
 R is not in AltaAtAfter (V2, B) { can't discard papers (the "AC*")

_____________________________________________________________ 


For all methods, (P1) holds implies (monotonicity holds and
 SPC holds).


(P1) can be seen to fail STV because of what STV does with this
 alteration of two papers:

------------------------------------------------
       Sample Election example (E1)

V1:
  5 AB
  6 B
 10 C

STV: B wins, IFPP: C, FPTP: C, Cond: B

V2:
  7 AB
  6 B
  8 C

STV: C wins, IFPP: C, FPTP: C, Cond: {}

The STV alteration is: (C {B+)--(AB {C+), and the very serious
 problem of a 1st preference loser becoming a winner has occurred.

------------------------------------------------

(P1) does nothing to make a method proportional; FPTP satisfies
 (P1) and it the major rule that shapes my IFPP theory solutions.






+++++++++++++++++++++++++++++++++++++++++++++++

At 01:52 16.12.99 , Markus Schulze wrote:
>Dear Craig,
>
>you wrote (14 Dec 1999):
>> I now consider the participation axiom to be uninteresting.
>
>But many other people consider the participation criterion
>to be interesting. Even you said a few days ago that election
>methods that violate this criterion were "too defective to be
>used in practice." It is surprising ...

I didn't say that Schulze: My too defective comment was in my mind
 about a method deliberately damaged to make it so that voters were
 punished, but at the time I wrote, you had not defined "punished".
 That term later got associated with the "participation axiom" later.
I still consider it to be not particularly interesting ((P1) is so
 much more effective).

>
>******
>
>Craig Carey wrote (14 Dec 1999):
>> At 06:33 15.12.99 , Markus Schulze wrote:
...
>
>You wrote (15 Dec 1999):
>> That is is a contradiction and so the steps are a proof by contradiction
>> that Demorep1's clone rule is just a corollary of (P1). (I've assumed
>> I've understood the clone rule).
>

You are quite right: clone theory seems to be very different.
 I could be a dud.

Mr Cretney's website mentions "clone" and does not state a rule,
 and maybe there is doubt about what to do with the "clone" idea.

Perhaps you could tell me why it might be an important idea, although
 no one has suggested that so far.

>It is true that Alternative Voting meets SPC and clone criteria.
>But that doesn't mean that SPC and clone criteria are the same.
>For example: FPTP meets SPC and violates clone criteria; Tideman
>violates SPC and meets clone criteria.

What has to be sacrified to get the 2x2 (?) clone criteria?.

>
>You should really browse through Blake Cretney's home page at
>http://www.fortunecity.com/meltingpot/harrow/124

I can't imagine proponents of STV finding a lot of merit in the
 "clones" ideas  that paird of two preferences have the same order
 or both are reversed but it is not that case that one is permuted
 and the other isn't. 


Craig Carey, Auckland, 16 Dec 1999