[EM] Proportional preferential voting

Craig Carey research at ijs.co.nz
Sat Sep 18 02:21:59 PDT 1999

I'll reply to 3 messages, two from Markus Schulze and one from
 Blake Cretney.

At 08:29 99/09/18 , Markus Schulze wrote:
[>Craig Carey wrote (15 Sep 1999):
>> 'permuting all preferences before a preference for a
>> particular candidate, never makes a difference to
>> that candidate's win/lose status'.
>As you ask me that directly, I have to answer that it seems
>to me that only strategy-proof preferential election methods
>meet both of your alteration rules simultaneously.
[>Markus Schulze

I don't know what is a strategy proof method is defined to be.
I am not interested in a definition that is on the voter side
 of the voting process (one that considers indications of intentions).

What about the altering of the initial preferences in more than
 one voting paper at a time. (P1) considers more than one paper
 (same as type of voting paper) and trailing preferences only,
 and my those of rules that apply to leading preferences do not
 apply to more than a pair of preference lists (papers).

An example of a rule would be permitting and prohibitting changes
 in wins between ABC and CBA.

PS. Indeed tt wasn't Mr Schulze that sent in numbers implying
 a voting method, it was a person at DEMOREP1 at aol.com.

Again: that permuting rule of mine is clearly not a desirable
 rule. That permuting rule I wrote would prohibit this
 alteration of a vote:

K wins this
0.9 ABCDEFGHIJK { LMN     (only J & K have a chance & J almost wins

K loses this:
0.9 JABCDEFGHIK { LMN     (J wins)

J can win the 2nd in all quality election methods,
 so K loses the 2nd.
If K wins the first, then the rule is not desirable in about any
 system that might be thought desirable (or ...).

At 18:36 99/09/18, Blake Cretney wrote:
>Craig Carey wrote:
>>                       Principle 1 
>>      Alterations of preferences after a preference
>>      for a winning candidate never cause that
>>      candidate to lose.
>You later revised this to a principle that seems equivalent, except
>for ties.

My first formulation of (P1) had the problem that it did not
 allow preferences to be thrown away, when the preference for the
 candidate under consideration was the first preference.

 I try to exclude ties (equality is not helpful in the derivation).

>> 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]

That's wrong since votes/preferences can be disscarded, but it is
 right for the 1st version of (P1).

Mr Cretney is wnet on to prove that that the first version of
 (P1) implies the STV feature, which Mr Cretney calls SPC.
 It seems rather obvious that the first version of (P1) is
 implied by the STV-SPC rule, so the two are the same.

It is not obvious that STV passes the 2nd formulation of (P1).
Possibly a tiny tweak could fix it if it fails (P1).
Maybe it is OK. Most people can't understand multiwinner STV
 quite likely


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

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 |

   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*")

>Then, by above, substituting X' for V and X for V'
>if c loses X', then c also loses X. 
>so, if c wins X, c must win X' (assuming no ties) [A -> B = ~B -> ~A]
>which, I think is the meaning of your original principle.
>So, the revised principle follows from the original.  I think it's

No. The first (P1) is a corollary of the 2nd, and you were
 proving that STV's similar feature (called SPC below) follows from
 the first (P1).

>obvious that you can reverse this process to show that the original
>follows from the revised.  Therefore, they are equivalent assuming no
>> I have a question for Mr Catchpole and Mr Markus Schulze, or
>>  anybody who wishes to answer:
>>  Does Condorcet (1 winner) satisfy the 'principle 1'
>>  (given above) ??.
>> Please respond with a proof or a counter example.
>I have a web site at:
>	http://www.fortunecity.com/meltingpot/harrow/124
>that lists many common methods, and which criteria they pass and
>fail.  I call "Principle 1" the Secret Preferences Criterion.
>Anyway, Condorcet doesn't exactly fail SPC, because it is undefined

Let's fail it. You failed to fail it, and is it possible?.

PS (a note): one of my rules was: except for no volume faces of the
 election simplex (i.e. ties), the method had to find the right number
 of winners. Fuzzy sets is it?.

>in some situations.  That is, Condorcet's method is only defined when
>there is a Condorcet winner (CW).  So, to violate the criterion, we

Wouldn't it be better to say it always returns a set of winners,
 but sometimes the number of winners in the results set is wrong, or
 similarly the set returned is fuzzy with a special value which could
 be complex.

>would have to be able to arrange candidates on some ballots (lower
>than the CW) and cause this candidate not to be the CW.  But changes
>between candidates other than the CW cannot give the CW a pair-wise
>loss, and therefore cannot cause the candidate to be defeated.
>On the other hand, any method that satisfies the Condorcet criterion,
>and gives a defined result in all situations, will violate SPC.

The following is unsatisfactory as one of the states is the
 paradox state.
I guess that Condorcet fails (P1).
If faulting Condorcet wrt. (P1) becomes too hard, a computer program
 using random numbers would have a good chance of getting it failed
 wrt. (P1).

>Consider a Condorcet criterion method (X) with the following ballots.
>45 A B C
>25 B C A
>30 C A B
>if the result of X is A, then alter 45 A B C to 45 A C B.  Now C is
>the CW, so must win.  SPC is violated.
>if the result of X is B, then alter 25 B C A to 25 B A C.  Now A is
>the CW, so must win.  SPC is violated.
>if the result of X is C, then alter 30 C A B to 30 C B A.  Now B is
>the CW, so must win.  SPC is violated.
>I consider SPC to in fact be a decidedly unreasonable criterion.
> If someone votes
>A B C instead of A C B, that's evidence in favour of B, whether
> or not A might have won otherwise.

So you seem to not favour Condorcet.

If you write down a list of preferences, is it safe
 to add more preferences?. SPC makes it always safe, and
 imposing SPC would tend to make a method more like STV
 That's about optimal anyway.

Who wants a voting system that fails SPC, e.g. one where
 if the vote is 'A.....' then A wins, but if the vote is
 'AB....' then A loses?. If you wish to make an exception
 so that the problem never occurs with the first preference,
 then alter every voting paper so a preference candidate
 Z (say) is inserted before the first preference. So what
 would be the theory designer's response then?.

Failure to enforce SPC is an obvious problem if each voter
 regards their first choice of candidate as nearly
 infinitely preferable to subsequent candidates. Given
 that voters are not allowed to inform about their
 preferences in these methods, what other assumption ought
 the voting system imlicitly be making about ratios of
 figures of merit of candidates?.

Suppose candidates were mathematicians, each were voting
 on their own superior theories, and each was required to
 give all preferences (optionally except the last).
 Why ould subsequent preferences be allowed to cause
 earlier preferences to flip from a win to a lose.

SPC is a good rule to enforce when the election outcome
 is very important. STV is a system that has nice feature
 for life or death elections.

(((If someone wants an exercise about IFPP, find out which
 alteration rule STV 3 candidates 1 winner fails but IFPP
 passes. I can't figure it out, but I seem to recall it
 had quantities 10, 6, & 5.)))

Mr G. A. Craig Carey
E-mail: research at ijs.co.nz
Auckland, Nth Island, New Zealand
Pages: Snooz Metasearch: http://www.ijs.co.nz/info/snooz.htm
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