[EM] Exhausted vs Wasted

[Blake Cretney]

" " <donald at mich.com (Donald E. Davison)>, on the subject of '[EM]
Exhausted vs Wasted', is quoted as:
>- - - - - - - - - - - - - - - - - - - - - - - - - - 11-16-00
>Dear Blake Cretney and List,
>
>     Exhausted votes and wasted votes are two different types of
votes.
>     Exhausted votes happen when there is not enough choices made by
the voters.
>     Wasted votes are caused by the design of election methods or by
some
>design feature like gerrymandering, thresholds, and/or some quotas.
>     Supporters of the Droop quota like to mix the two so that
everyone
>will blame the exhausted ballots for causing the wasted ballots, but
this
>is deception.
>     The best way to reveal the wasted votes of a system is to remove
the
>exhausted votes. This is done by assuming every voter has ranked every
>candidate. This should cause every vote to end up on one of the
winning
>candidates. Any votes not on winning candidates are wasted votes.
>     You wrote: "So, if everyone listed all the candidates in order,
there
>would be no exhausted votes, no matter what the quota."
>     You are corrrect to say that there will be no exhausted votes, but
the
>question of wasted votes depends on which quota is used. If the Hare
quota
>were used, there will be no wasted votes. All votes will end up on one
of
>the elected members. If the Droop quota were used, then one quota of
votes
>will be wasted, not ending up on any of the candidates.

I'm grateful to you for pointing out the distinction.  However, I wonder
if wasted votes as you define them are an important concept.  It seems
to me that after an election, people often complain either that they
wasted their vote, or that they voted one way to avoid wasting their
vote.  They are not really complaining that their vote didn't end up
assigned to a candidate.  I their actual meaning of a wasted vote is a
vote that was ineffective because it was sincere.

Your concept of wasted votes as votes that don't end up assigned to a
candidate may be related, or it may not.  I doubt that you would claim
that assigning every vote to a winning candidate is a goal in and of
itself.  There must be another basis for the concern, but it isn't clear
what it is.

Consider the following example (3 to be elected),

30 A B C D
30 B A C D
10 D C A B
20 C D A B

Using Hare, A and B are elected.  Then, C is elected.  No votes are
wasted.  Using Droop, A and B are elected.  Then, C is elected.  So the
same result is given, but I think you would conclude that some votes are
wasted.  However, in this case, the number of wasted votes can't
indicate a worse result, since the result is the same.  It doesn't
appear then that wasted votes is a reliable indicator of the quality of
an election result.

Here's another example (3 to be elected),  I'm imagining an AB party 54%
and a CD party 46%

54 A B C D
22 C D A B
24 D C A B

Hare gives a quota of 34.  A is elected, but the AB side loses 34 votes.

20 A B C D
22 C D A B
24 D C A B

B gets eliminated.  Then, so does A.  C and D are elected.  Note that
after being eliminated AB voters have their votes assigned to C, so that
they aren't "wasted".  On the other hand, that's probably little
comfort.  

The result seems to be that a minority faction won a majority of seats. 
This happened solely because their support was more evenly divided
between the candidates.  This kept them from winning in the first round,
which kept them from being eliminated.

Notice that when the AB group won in the first round, they paid a heavy
price, in terms of the power of their votes being scaled back.  The CD
group by neither electing candidates nor having them eliminated was able
to wait until the AB voters got assigned to them.  So, when they paid
for the later seats, it was comparatively cheap, because part of the
cost was coming out of their opponents pocket.  It seems to me that
Droop tries to offset this tendency by making early seats slightly
cheaper as well.  

It also seems to me that in an example like this, the measure of wasted
votes fails utterly, because it is not much better to have your vote
assigned to your opponents than to have it thrown out.

---
Blake Cretney