[EM] Hare-STV not proven better than Droop-STV

[Craig Carey]

Abstract: Droop STV is not being argued against, yet it could be
 if its properties and that of Hare STV were found using a computer.


At 22:37 19.11.99 , Donald E Davison wrote:
>Greatings,                              11/19/99


I am finding Mr Davison's arguments have a missing link.
I wouldn't say that they are evolving or even able to be regarded
 as weighty or plausible or logical. They are not convincing.

They make an argument about the last stage in STV, after most winners
 have been found, and the arguments have not indicated how to get from
 that minor conclusion, to the big conclusion, which is that Droop-STV
 is worse than Hare-STV (and the latter is better).
So long as that missing link in a crucial area exists, Mr Davison might
 as well take a low profile over religion bashing, at least to this list.

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

I'll make this plainer: Here's an example that can be regarded as an
 analogy.

Definitions:
   There is a function good(x). When it is small, then that is bad.
   The variable x ranges from 0 to 10.

   1.   For the Hare0-Triangle-method, good(x) = 10
   2.   For the Droop1-Triangle-method, good(x) = 10 + 0.3*(x-3)

Nobody could quite reasonably say that Droop1-Triangle-method is
 significantly more bad all throughout 0..10 on examining the behaviour
 of its good(x) function for x such that 0.7<=x<1.3.

Similarly for Mr Davison's arguments: If Droop is worse than Hare in a
 small region, then the method could quite reasonably be better in the
 95%, say, exterior.

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

Let's integrate (Q1) failures. If (Q1) is not acceptable to you, then
 what fully defined function would you prefer to have integrated?.
Perhaps the matter should be put aside for a long time, and a note
 prepared saying that Droop-STV is best judged by using local data.

I request some computer source code that implements STV.

Then what could be done is to precalculate solutions over a fine lattice
 in the simplex of ratios of paper counts, and for each grouping of
 papers (= each paper), integrate the (Q1) failures, i.e. the regions
 where redistributing papers could lead to a better outcome, as indicated
 by the (Q1) binary satisfaction value;
   [this: e.g. satis({B,C,E},(ABCDE))=(1/4)+(1/8)+1/32].

 (A lattice rather than random numbers just for speed. I have done some
 tests and REDLOG symbolic quantifier elimination is going to be too
 slow (e.g. for 4 candidates). There is a lot of symmetry with the number
 of corners rising in approximate proportion to the factorial of the
 number of candidates, so precomputing solutions seems an option.)
 
As an aide to understanding, here are some (Q1) failure regions.
There are 3 types of papers, (AB), (B), and (C).
Some (Q1) failure regions are (1 winner case):
     (a<c)(c<a+b)(b<a)         for STV : C wins rather than B
     (a<c)(c<a+b)(b<(a+b+c)/3) for IFPP: C wins not B

In those regions, C wins, whereas compliance with (Q1) [no strategic
 voting, or proportionality (or no vote wasting?)] would have candidate
 B win.

Mr Davison might say, let the 'measure of badness' function be 0
 everywhere except for just those types of examples he had written about.
 In those examples where an argument was able to be made, the function
 would return 1. Then integration would then estimate nothing but the
 hypervolume of the regions which Mr Davison did argue about.



At 20:06 17.11.99 , Donald E Davison wrote:
>Greetings,                              11/17/99
...
>     The real reason for the Droop Quota is to take some representation
>from the smallest groups and give that representation to the largest
>group.
... 

>
>     During any `Droop War' I have always tried to present my side of the
>issue based on logic, fairness, honesty, and that which is mathematically
>correct.

People can be opposed to you without being opposed to Hare-STV.


>     We need to thank David, he has placed Droop into its proper context
>for us. It will be much easier now for us to understand the arguments of
>the Droop People.


Mr D Catchpole is advocate of rules that apply to methods irrespective of
 the discovered ratios of paper counts.



If methods should favour disintegrated parties that get votes in leading
 preferences, then let's have that bias clearly stated.  Maybe "corrupt"
 is a code phrase for people that cause Greenies to lose at elections, or
 perhaps it is a word for incumbents. Incumbent mayors may need
 proportionality and methods that collect all their votes that became
 shifted quite some distance from the first preference (e.g. in the
 election after a bad term in office).

[The needs of mayors are also what is needed if a method is to be good
 for very large elections.]

Greenies, will, I guess, have preferences nearer the first, and need more
 FPTP-like methods that waste more of the votes of the big parties during
 transfers. I guess that particular group might prefer Hare-STV or any
 variant that has even bigger quotas for winners, to keep the transfer
 values smaller (?). Whether greenies call others corrupt "Droop People"
 is hardly relevant.

If Mr Davison can't quantify what is bad about a preferential voting
 method (no matter what the count of papers), then how can Mr Davison say
 that Hare-STV is better than Droop-STV, using only "that which is
 mathematically correct"?. 

I have argued here that (Q1) ought decide the issue, and that Mr Davison
 may be opposed to (Q1) if it aims for proportionality instead of simply
 wasting votes that are held with large parties in some stage of the count.



>     Their chanting is necessary, it affirms their belief in Droop. We are
>big enough to endure that noise.
>
>     But, ... Droop is still corruption.

 



Mr G. A. Craig Carey, research at ijs.co.nz
Auckland, New Zealand.
Snooz Metasearch: <http://www.ijs.co.nz/info/snooz.htm>