[EM] What is a wasted vote in a STV election??

[pct0039 at wiz.connected.net.nz]

At 21:46 23.10.99 , Donald E Davison wrote:
>Greetings,
>
>     There is some misunderstanding as to what exactly is a wasted vote in
>a STV election.



A definition of a 'wasted vote' would be useful.



>                So, the questions I will answer are: What is a wasted vote
>and what is not a wasted vote.
>
>     A wasted vote is a vote that does not end up on one or another of the
>winning candidates.
>     There are three different ways in which wasted votes are created:
>     1) When a voter does not make enough choices and his ballot becomes
>exhausted of choices for the next transfer.
>     2) When groups lower the number of votes on their candidates. This
>will result in ballots being left over after all candidates have been
>elected.
>     3) When the rules of the method include the Droop quota. This will
>also result in ballots being left over after all candidates have been
>elected.


(Paragraph "3" doesn't seem to be that significant to me. Item "1" is hardly
 significant. Regarding "2", that would require simulation on a computer
 would it not?. ...


Strategic voting done voting papers
-----------------------------------

Let V be a vector of papers: V[i] = paper p. Let the weight of each paper
 be g[i] (i.e. the number of votes).

Function W(V) returns the set if winners.

Voters that voted with preferences p (p=V[j]) would be dissatisfied if
 there existed a group of papers, z, such that
      Satisfaction(W(V+z)) > Satisfaction(W(V)), and
 subject to 0 <= weight(z)/weight(p) <= 1.

'Satisfaction' is defined to be [using REDUCE code]:
    forall W,p let Satisfaction(W,p) =
       for k:=1:length(p) sum if member(part(p,k),W) then 2**(-k) else 0;

One problem with this is that the (Q1) satisfaction value doesn't emphasize
 the badness of an event when the last potential winner is a loser. Here's
 an example:                                      (Hare vs Droop Example 1)

(1) 'Hare' : (A B C D E F G H I J K L M), Winner = {E,G,L,M}, Satisf.=323/8192
(2) 'Droop': (A B C D E F G H I J K L M), Winner = {C,D,E,L}, Satisf.=897/4096

In this example, (2) is better.

A paper can be checked against (Q1) in as many ways as there are types of
 papers.
Papers would be allowed to group together and combine their weight.

For example, in an election with candidates {A,B,C,D,E}, the papers
 AB, ABC, ABCD, ABCE, ABD, ABDC, ABDE, ABE, ABEC, ABED,
 can sum their votes and cause a (Q1) violation if the 'satisfaction' number
 can be increased by altering any or all of those papers, to any other papers.


When all the paper counts are given, then a method may fail rule (Q1) for some
 truncated preference lists and not others. The whole method could be said to
 fail (Q1) for that particular count of the papers, if any of the groups of
 papers could do better with strategic voting (i.e. don't satisfy (Q1)).

Finding the relative volume in the simplex (representing paper count ratios),
 of (Q1) failures, would quite possibly lead to a problem which is that the
 relative content would approach unity as candidates or winners were added.
 A hypothetical example:
      99.2% of the interior of the Droop-STV simplex fails (Q1), and
      99.9% of the interior of the Hare-STV  simplex fails (Q1).

This message gives a practical way to compare the two STV methods using a
 computer. I doubt I will be writing such a program. ((It would be just as
 easy to derive an IFPP competitor (for less than or equal to 3 candidates),
 or prove that such a method is not nice.))

Mr Davison has used the idea "wasted votes".
But the meaning allowed to that phrase, was something like this:

   "after a vote has been transferred from winners (with typical wastage,
    sometimes with more wastage than the statistically expected wastage),
    and/or transferred from losers, the vote is said to be 'a wasted vote',
    if it had no power in the last stage to affect the outcome of
    [only] one winner".


----------------------------------------------------------------------------
...
>level, with mathematical precison. And, it follows that the Droop quota
>will leave more wasted ballots at the end of the count.
>
>     So, there you have it:
>           Exhausted ballots are wasted votes.
>           Ballots left over after the count are wasted votes.
>
>     Votes between the Hare Quota and the Droop Quota are not wasted votes.
...
>
>Regards,
>Donald
...
>                        http://www.mich.com/~donald
>          - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

(I'd pick the Droop quota as being a better choice [opinion]).

G. A. Craig Carey