[EM] Pattanaik and Peleg's 'Regularity' is not better

[Craig Carey]

This message has little of interest to most.
This regularity definition is taking a few more arguments than I had
 expected. It is opposed to proportionality and instead favours unfair
 outcomes.


At 15:29 15.12.99 , David Catchpole wrote:
>On Tue, 14 Dec 1999, Craig Carey wrote:
...
>>  a connection and none exists. It is a weak form of rebuttal: to connect
>>  one failing idea to another when they are in truth separate.
>
>You're using that awful circular logic again. Please stop. ...

There is no circular reasoning. To say there is when there isn't is to
 make a misleading statement. I had written that 'regularity' prohibited
 the closing of a B-wins region in a simple example and that that 
 problem rejected the method instead. How could that be circular? (it is
 not).


>Maybe you're getting the drift now? I'm going to go through the slog of
>sending the introduction of "Distribution of Power Under Stochastic 
>Social Choice Rules" by Pattanaik and Peleg, Econometrica Vol. 54 No. 4
> to you.
>Hopefully then you'll understand-

That paper by Pattanaik and Peleg describes a dud idea named 'regularity'.

It is very similar to Mr Catchpole's regularity and it fails under the
 same considerations, as indicated below

...

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At 16:49 15.12.99 , David Catchpole wrote:
>Distribution of power under stochastic social choice rules
>Prasanta K. Pattanaik and Bezalel Peleg
>Econometrica Vol 54 No 4
...
>  (iii) "regularity" (a "rationality" property postulating that given
>      the individual preference orderings, if the feasible set of
>      alternatives is expanded, then the social choice probability for 
>      an initially feasible alternative cannot increase);
...
>      ...                             Regularity implies that given the
>profile of individual preferences, if one enlarges the feasible set of
>alternatives by adding more alternatives, then the probability of the
>society's choosing any of the alternatives figuring in the original
>feasible set cannot increase after the feasible set is enlarged. This
>seems to be the natural probabilistic counterpart of Sen's ...

> ... We show that these three assumptions, together with the
>assumption that the universal set of alternatives has at least four
>elements and that individual preference orderings are strict, imply that
>for every proper subset of the universal set of alternatives, the
>probabilistic social decision procedure must take the form of random ...
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Consider election examples [it seems that Mr Catchpole did read my
 message that wrote off his regularity idea, so a bit of repetition
 is perhaps appropriate]

What follows is a repetition by me...

--------- (1): ---------

Note that in the 1st of the 2 following examples, A could have won but
 C won instead. Candidate B was then added and then candidate A won.
 A was a 'feasible alternative' presumably, in the smaller election.

At 20:48 09.12.99 , Craig Carey wrote: ...

>>:   A. 2
>>:   C. 3
>--- ------ A loses after B is removed

>>>> A. 2
>>>> BC 2
>>>> CA 1
>--- ------ A wins ... (The IFPP quota = 1.666, so STV=IFPP here)


--------- (2): ---------

Note that if B is added to the first example of the next two, then the
 feasible alternative A, becomes the winner.

4 A
5 C        Now candidate A loses.   The IFPP/STV winner = C

4 A
2 BA
5 C        IFPP/STV winner = A      (the IFPP 1/3 quota = 3.666)


At 20:48 09.12.99 , Craig Carey wrote: ...
>>At 17:51 09.12.99 , DEMOREP1 at aol.com wrote:
>>>s349436 at student.uq.edu.au wrote in part-- ...

>>>The addition (removal) of a candidate does not, for any other candidate, 
>>>increase (decrease) the probability of that other candidate winning.

The idea of regularity has not got any plausibility to is.
Suppose there are 100 papers with an average of 10 preferences.
Suppose candidate Z is added to the system and Z's preferences
 are near the 1st in each paper.
STV-like transfer values  can be imagined for any system, and the
 transfer values can't always be zero even in a perfect method.
Even strict enforcing of (P1) can lead to wastage associated with
 imagined transfer values. The example I recently wrote to M. Schulze
 was this:
   (DCB {A+)--(DC {B+) : failed.
   (DCB {A+)--(D {B+)  : allowed.
 (P1) requires that votes passing over C be wasted.

So it is odd to suggest (via a 'regularity' definition) that putting 
 preferences for Z at the front are not ever able to make an old loser
 become a new winner. In any case regularity rejects 100% of all 
 plausible 3 candidate methods and I don't know how David found that
 to be acceptable. He may not be a method designer but instead a
 trainee method inspector.


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At 18:56 15.12.99 , DEMOREP1 at aol.com wrote:

>I repeat my observation about clones-
>
>34 A>B>C
>33 B>C>A
>32 C>A>B
>
>99
>
>Circular tie
>A>B>C>A
>
>Adding D-- a 100 percent clone of B
>
>34 A>B>D>C
>33 B>D>C>A
>32 C>A>B>D
>
>A>B>D>C>A

The winners of the 1st are {A} or {A,B}.
C should lose the 2nd since the 2nd is a (P1) alteration of the 1st
 w.r.t. C, and C loses the 1st.
B should have the same in lose state in the 2nd as it has in the 1st,
 by SPC.
It might be that D rather than A, is a winner of the 2nd.

>Many criteria floating around are totally irrelevant to real elections
>for real candidates by real voters. 
Does that include (P1)?. I suspected you were trying to make an argument
 noting small deviations from symmetry, but the 2nd election is not
 even nearly symmetrical: it could be if there was a 4th paper with about
 33 votes).

Craig Carey