(2) Vote-wasting questions: Steve 2nd dialogue with Kristofer
[EM] (2) Vote-wasting questions: Steve
2nd dialogue with Kristofer
Subject: Re: APR: Vote-wasting questions from Kristofer
From: km_elmet@t-online.de
Date: Sat, 5 Dec 2015 12:59:52 +0100
On 11/19/2015 07:30 PM, steve bosworth wrote:
From: km_elmet@t-online.de
Subject: Vote-wasting questions
Date: Mon, 16 Nov 2015 22:36:08 +0100
Kristofer asked Steve:
K: > >> - What does it mean for a method to not waste any votes, as
you
define it?
S: > > I see a citizen's vote as wasted to some degree to the extent that
it does not do what APR does. APR enables each voting citizen to
guarantee that her one vote will continue to count in the legislative
assembly both quantitatively and qualitatively. Firstly, it will
count
mathematically through the weighted vote earned by the one rep who
that
citizen has helped to elect. Consequently, this rep is most likely
to be seen by this citizen also as most accurately (qualitatively)
representing her own scale of values.
[…]
S: > > In this context, each citizen's vote in plurality
systems like those in
the USA and UK can be guaranteed only of her one vote being recorded
as
cast for one of the candidates running in her electoral district. Her
vote may have been given to a losing candidate, in which case she
will
not be represented in the assembly. Even if her vote has helped the
winning candidate to win, she may not see that candidate as the one
in
the country who would represent her most accurately. Even if she does
like the elected candidate, her vote would not give this
representative
any more power in the assembly if this winning candidate received
more
than one vote more than he needed to win the plurality election.
S: This last case is an example of both a
partial qualitative and quantitative waste of her vote.
K:> True, Plurality is infamous in that regard, and APR is better than
single-member Plurality. But so are a lot of methods.
S: Yes.
K: > There would also be situations where no method, not even APR, can
ensure
full representation. E.g. two winners:
10: A
9: B
8: C > D
However you do it, at least 8 voters will end up not being represented.
Doesn't that also represent an (albeit unvoidable) waste of votes? Yet I
think it would be wrong to insist upon full ballots (as Australia does)
even if it would waste fewer votes.
S: Yes, I accept that where there are only 1 or
2 winners no system “ensures full representation”. Unlike in an APR election of many winners,
each elector would not be able to guarantee that her vote would be added to the
weighted vote of a winner she trusts to represent her hopes and fears, i.e. neither of the 2 winners in this case. Consequently, perhaps I agree with you that
if there is only 1 or 2 winners, I would favor MAM.
However,
when there are anything like 435 (USA) or 650 (UK) winners, APR still seems to
offer the best guarantee for each elector being able to add her one vote to the
weighted vote in the assembly of the one rep she enthusiastically sees as most
likely to represent her own hopes and fears.
[…]
K:>
If not wasting votes is a good thing that APR has and others do not,
then it's hard to know what makes APR good in this sense if you say
"votes are wasted to the extent that the method does not do what APR
does". …
S: I only mean that, other things being equal,
the more votes that are wasted by a method, the worse that method is. When an
alternative method like APR is available which does not waste any votes, the
wasting of any citizen’s vote is a violation of the “human right” of each such citizen to
receive equal consideration.
K:
But you do say that it matters that a voting citizen's vote
"continues to count both quantitatively and qualitatively", and
that
gives me something to go on.
It does, however, seem to be underspecified in a sense that many methods
could claim to do so. Consider the following five alternate methods for
electing 10 winners from 100 candidates:
- Count every candidate's first preference. Eliminate all but the 10
with the highest first preferences. Each of the 10 remaining gets weight
according to how many first preferences he has on the ballots where the
90 who didn't make it have been eliminated.
S:
If I understand this “alternative” of yours correctly, it would waste every
citizens’ vote who had instead listed only candidates within the losing 90 among
their preferences. The hopes a fear of
those citizens would not be proportionately (if at all) represented in the 10
member assembly.
Let
me now use your numbers to illustrate how APR, instead, would elect the 10
winners and waste no votes. Accordingly,
I will also,
assume that there are 1000 voters (i.e.
citizens c1 through c1000),
assume that your 10 candidates
(ABCDEFGHIJ) who received the most first preferences received them respectively
from each of citizens c1 through c855 as follows: 90, 89, 88, 87, 86, 85, 84,
83, 82, & 81 votes,
assume that candidates KLMNOPQRS
respectively received 45, 40, 30, 10, 8, 5, 4, 2 &1 first preference votes
from citizens c856 through c1,000, and
that the 2nd preference on citizen
c1,000’s ballot for S was candidate A.
Consequently
APR’s count would start by eliminating candidate S because he received the
fewest 1st preference votes. c1,000’s
vote would then be transferred to A,
making A now having received 91 votes.
For simplicity, now I will also assume that all the other voters from
c857 through c999 gave K as their 2nd preference candidate. This would mean that eventually K would be
elected with a total of 144 APR votes in the assembly (i.e. 45+2+4+5+8+10+30+40
= 144).
Thus
K, not J would be one of the 10 winners, as J only has a total of 81 votes. This means that each of the 2nd
preference candidates for the 81 citizens who had given their 1st
preference to J would now also receive more votes within their respective final
weighted votes. For simplicity, again I will
assume that all of the 2nd preference votes were given to B. This gives B a total weighted vote of 170 (i.e.
89+81).
As
a result, each of the 10 winners would finally have earned the follow weighted
votes: A(91), B(170), C(88), D(87),
E(86, F(85), G(84), H(83, I(82) & K(144).
Thus, in this example, APR would provide each of the 1,000 citizens with
the rep among the 10 who she judged most likely to speak and act on her behave
and to whose weighted vote she had added he own vote.
For
simplicity in the above example, I have ignored APR’s suggested rule that no
member of the assembly should be allowed to keep a weighted vote larger than
10% of all the weighted votes in the assembly.
Any rep who receives more than 10% must give the extra votes to his
trusted elected colleagues. This rule is to prevent any member from being in a
position to dictate to the assembly.
K:> 2. Count the Borda scores for each candidate. As long as there are more
than 10 candidates in the running, eliminate the candidate with worst
Borda count. Once only 10 are left, they get 10.
S: Again, some citizens’ votes would be both
qualitatively and quantitatively wasted in this Borda count, i.e. the votes
given by all citizens who had given their smallest number of points to each one
of the 10 elected candidate and had given their largest number of points to
candidates not elected.
K:> 3. As APR, but repeatedly eliminate the MAM loser rather than
the Plurality loser until only 10 candidates remain[1].
S:
I currently see MAM as the best way to
elect one winner because it elects the winner only after considering all the
voters’ preferences. Its winner is shown
to be preferred more than any one of the other candidates. Unavoidably, however, some voters will not be
happy with this winner and so their votes will be wasted in the sense that they
do not see this winner as representing their own scales of values. MAM seems successfully to minimize these
disappointments in contrast to the other available systems, e.g. Kemeny-Young,
plurality, IRV, approval, score, etc.
Still,
perhaps I have not understood you because I do not see how you could use MAM
“as APR”. I can see how MAM could be
used to elect multi-winners and how it could be used to give its winners
weighted votes but, unlike APR, it would still waste some votes both
quantitatively and qualitatively.
K:> 4. Each voter ranks the candidates and gives each candidate either a
thumbs up or down. Eliminate candidates with fewest thumbs up until only
10 remain. The remaining candidates get weight according to how many
voters ranked them first among the 10.
S: Again, all the votes from citizens who had
given a “thumbs down” for each of these 10 winners would be wasted in the sense
defined.
- Each voter rates the candidates. Start the first round with no
winners. In each round, each voter gives his vote to the winner [i.e.
candidate???] he rates highest, and a winner's
[i.e. candidate’s???] weight so far are [is] the number of people who
give a vote to him.
Repeatedly find the candidate that would get the greatest weight
("steal" the most votes) if he were to be added to the group of
winners.
Add him to the group of winners and go to the next round. Break ties by
total rating. After the tenth round, you have 10 winners and their
weights.
S:
My additions represents my attempt to understand this last “alternative”. I have failed in this regard. Please explain it more fully if you still
think that what you have in your mind would not waste votes in the sense I have
defined.
K:
If "a citizen's vote [is] wasted to some degree to the extent that
[the
method] does not do what APR does", then these should waste votes
where
APR does not. But how do they waste votes? How are they less
proportional than the method you're using for APR?
I'm not saying these methods are good or bad - those are just ones that
came to mind - but in every method there, each voter contributes to the
weight of the candidate he prefers.
S:
Yes, but, unlike APR, each of these methods leaves some citizens without any
elected member in the assembly who they see as likely to speak, work, and vote
on their behalf, i.e. no member they like and whose weighted vote in the
assembly has been increased by these citizens’ votes.
K:
The objection to Plurality and
unweighted vote methods thus doesn't apply.
S: Yes, many methods are much better than
Plurality, but I still see APR as the best for large multi-winner elections.
K: > If you have more candidates than winners, you have to narrow down the
field somehow. No matter how you do so, you can later weight those who
remain according to how many voters ranked or rated them first among the
- So what makes one method of narrowing down the field better than
another in a vote-wasting sense? It would seem that the idea of
"guarantee[ing] that her one vote will continue to count in the
legislative assembly both quantitatively and qualitatively" is
independent of the exact way you do the mathematical count….
S:
I hope my above responses have shown that, unlike APR, these other methods do
not “guarantee” these desirable features.
K:
….. so long as the method is at least somewhat reasonable.
S:
I still see APR as entirely “reasonable” assuming that we start with the belief
that each citizen should be represented to the full extent that may be
possible.
[…]