Re: [EM] (3) Vote-wasting questions: Steve 3rd dialogue with Kristofer

From: km_elmet@t-online.de

Kristofer

To
Kristofer and everyone:

S:    Sorry, given your most recent response to our
2nd dialogue, I must have failed to make my definition of “wasting
votes” clear.  Mistakenly, you still
believe that APR must waste some votes.
Please let me try again.

In
our 2nd dialogue, you had asked me to respond to your suggestions
that APR would waste some votes regardless of which of the follow 2 candidate
might be elected in the following example:

K:

[…]

S:  Now I want to more fully explain that In this
case, APR would elect A with a “weighted vote” of 22 votes in the legislative
assembly and C with a weighted vote of 11 votes in the assembly, i.e. no votes
wasted.  A would get 22 “weighted votes” because 11
citizens had ranked A over all the other candidates and 12 had ranked A over
each of the other candidates as specified, i.e. as a result of the 1st
count of all the first preferences, it would be discovered that A had received
a total of 22 and C a total of 11.  In
this way, no votes are “wasted” because each of the 33 citizens has both helped
to elect and added their one vote to the elected candidate’s “weighted vote”
each most prefers.

In
my article, I only claim that ‘each citizen could guarantee
that her one vote will fully continue into the legislative assembly by
giving a ‘weighted vote’ to each elected representative exactly equal to the
number of citizens who had helped to elect him or her’ (Abstract).  If any vote is ‘wasted’ this would ‘result from the
citizen's choice, ignorance, or disability’ (page 4).

I hope this more detailed explanation will
also help you make sense of the following exchanges between us in our 2nd
dialogue:

K:>> then if the winners are A and B, 11 votes are wasted.

11 votes are wasted when the winners are A and B because the C>D ballots

S:

qualitatively partly be wasted because these 12 citizens preferred their votes
to go to A.

K:>> if the winners are A and C, no votes are wasted;

S:

K: >> if the winners are A and D, no votes are wasted;

S:

preferred C over D would not be quantitatively wasted but would be
qualitatively partly wasted;

K:>>
and 10 votes are wasted when the winners are B and C because the 10 A-only

S:>
Yes, in this suggestion, the 10 from the citizens who preferred A over all the
other candidates would be entirely wasted (i.e. quantitatively and
qualitatively).  However, also the 12 who
preferred A over B>C>D would not be quantitatively wasted but would be
qualitatively partly wasted.

K:>>
Is that correct?

S:  >Yes, partly correct and incorrect as
explained above.

K:

S:
No, but perhaps that is my fault.

K: >> From this point on, all my vote-wasting discussion will be of the
quantitative

S:
No.  In this case, APR would elect C with
a “weighted vote” of 11 and D with a weighted vote of 12.  The 10 votes given to A would be wasted only
by ordinary IRV using “weighted votes”.
APR would not waste these 10 because it gives each citizen who fails to
rank any candidate that is elected the option of requiring her 1st
choice but eliminated candidate to transfer her one vote to the elected
candidate who that eliminated candidate trusts most (e.g. see the Sample Secret
Ballot at the end of the article).  However, perhaps I have never sent you a copy
of my article that systematically explains APR:
“Equal Voting Sustained”.
Separately I will send it to you now and to anyone else who might
request it.  Perhaps together with the
above additional explanation, my APR proposal will be clearer?

Of
course, I will gladly respond to these or any of the other elements of your
last post to me that you may still believe are not solved by the above.

I
look forward to your next reply.

Steve

On 01/22/2016 11:28 PM, steve bosworth wrote:

Thanks for doing so. So your definition is, if I've understood it right:

A voter's vote is not wasted if either

1. one of the candidates he ranked above last is a winner, or
2. none are, and the voter lets his first preference choice give his
   vote to someone who is a winner.

(end definition)

Suppose for simplicity that every voter lets his first preference choice
delegate his vote in that manner (otherwise, it's impossible to not
waste votes), and that every voter's first preference has a winner that
he can tolerate (again, otherwise it's impossible).

In the past posts, I first said asked about examples since it seemed to
me that the condition of not wasting votes was weak enough to let many
methods could pass it. Then you showed what you meant in a more detailed
way, to which I replied that the resulting property was both impossible
to satisfy completely, and in some cases undesirable even if relaxed.

Now you've further specified the criterion, and I hope the definition
above is accurate. That further specification does solve the issue of
impossibility and undesirability, but it simply moves the problem back
into the old situation where "not wasting votes" is underspecified (i.e.
the property is weak).

Consider the Plurality alternative where you mass-eliminate the n-k
candidates with fewest Plurality votes. That is, if there are 20
candidates and 10 seats: the method eliminates the 10 candidates with
the fewest first preference votes in one blow at the first round, then
elects the 10 remaining as winners.

You correctly said that such a method can waste votes (as I understood
it in the original definition) because there may be voters who voted
only for the 10 that got eliminated. However, given the fix above, that
"each citizen who fails to rank any candidate that is elected [is given]
the option of requiring her 1^st choice but eliminated candidate to
transfer her one vote to the elected candidate who that eliminated
candidate trusts most", it's pretty easy to patch the Plurality method
too. You end up with something like:

1. Eliminate the 10 candidates with fewest first preferences.
2. Assign each voter who ranked any of the 10 remaining winners to the
   winner he ranked first.
3. Ask each voter who failed to rank any of the 10 remaining winners the
   option of requiring the first ranked on his ballot to transfer his votes
   to one of the 10 remaining candidates.
4. Once done, no votes are wasted.

Even a most unsatisfying "upside-down" method could be made to waste
no votes:

1. Eliminate the 10 candidates with the most first preferences.
2. Assign each voter who ranked any of the 10 remaining winners to the
   winner he ranked first.
3. Ask each voter who failed to rank any of the 10 remaining winners the
   option of requiring the first ranked on his ballot to transfer his votes
   to one of the 10 remaining candidates.
4. Once done, no votes are wasted.

Thus, clearly this fixed criterion can not distinguish good methods from
bad ones by itself. It is weak (or ambiguous) in the sense that it
admits both good and bad methods. It's not a bad thing for a property to
be weak in itself - for instance, the monotonicity criterion is quite
weak - but that does mean that it cannot alone be used to determine
whether a method is good or not.

You could try to firm up the property by counting direct non-wasted
votes more strongly than indirect ones, and then say that directly
non-wasted votes are better. That would automatically render upside-down
methods like the on above inferior, because the good methods would have
much fewer voters ask their favorites whom to delegate to. However, then
we're back to the previous case again: that APR is not optimal and that
being optimal leads to very strange destinations.

In short, not wasting votes becomes either impossible or not always
desirable (if using the previous definition); or very weak (if using the
current definition). To show just how general it is, consider that it
technically lets single-winner elections be free of vote-wasting:

1. Elect a single winner by your method of choice.
2. Ask the voters who failed to rank this winner to let their first
   preference choice say "I choose the winner" and thus transfer the
   voter's vote to the winner.
3. No votes are wasted.

Re: [EM] (4) Vote-wasting questions:
Steve 4th dialogue with Kristofer

Kristofer

From Steve to Kristofer and everyone:

Kristofer

with Kristofer

election-methods@lists.electorama.com

K: > >> For something like

exact),

and

not waste these

is

candidate

eliminated

of

my

K: > Thanks for doing so. So your definition is, if I've understood it
right:

S:
Yes.

K: > Suppose for simplicity that
every voter lets his first preference choice

S: Yes.

K: > In the past posts, I first
asked about examples since it seemed to

underspecified (i.e.

given]

method

S:
Yes.

K: > Even a most unsatisfying "upside-down" method could be made
to waste

S:  Yes, but we agree that this method’s starting
by eliminating the 10 with the most 1st preferences would be
especially crazy, i.e. “upside-down”.

K: > Thus, clearly this fixed criterion cannot distinguish good methods from

both good and bad methods. It's not a bad thing for a property to

S:  Correct.

[….]

K:

the

S:  Correct.  Still, APR seems to be the best method to
which such “default” asset voting should be added for the reasons presented
below.  However, before I do that, I want
to claim that in comparison to all other electoral system not using the above
asset voting, APR (also without this asset addition) still does all it could do
to allow each citizen to guarantee that her one vote will be added to the
weighted vote of the one elected candidate of all the pre-established number of
the assembly’s members whom she most trusts to speak, work, and vote faithfully
on her behalf.  Do you agree?  Also in this case, this simplified APR might
waste some votes.

In our previous dialogue you said you would only deal with
“quantitative” wasting of votes and all your examples illustrate perhaps how
any electoral system could be design not to waste any vote mathematically if
“default” asset voting were to be added to it.
Thank you for making this point clear.

At the same time, I would still appreciate your assessment
of my claim that APR (now including the above “default asset voting” feature
will not be “qualitatively” wasting any votes either, i.e. APR enables each
citizen to guarantee that her one vote will be given to the one member’s
“weighted vote” of all the members of the assembly whom she is likely to see as
the most likely to represent her faithfully.

In fact, APR’s inclusion of the “default” asset feature seems
to use this feature more efficiently than any other system could as far as I
can see.  This is because APR allows each
citizen to choose the one candidate from all the many candidates in country
whom she most trust (and whom may be eliminated) to transfer her one vote, if
necessary, to the elected candidate he believes is most likely to represent him
and her faithfully in the assembly, e.g. to the elected candidate highest on
his own pre-published list during the general election campaign.

In addition to these 2 aides to increasing the average
quality of representation using full APR, a 3rd aid starts with APR’s
primary election.  It enables each citizen
to help to select one geographically or non-geographically defined voluntary organization
to become the official electoral “association” through which she will vote
during the later general election.  While
making this selection during the primary, she is both helping to give extra
political influence to the organization which she sees as embodying many of her
own scale of values, and encourages more attractive fellow citizens to run to
represent her and her “association” in the assembly.  This makes it more likely that she will have
a longer list of very attractive candidates from her point of view to rank
during the general election.  In turn, this
makes it more likely that the “weighted vote” of the member in the assembly to
which her one vote will be added will be the one member in the assembly seen by
her to be the most attractive elected candidate, i.e. the one most likely to
represent her faithfully.

Do you agree?  What do
you think?

Steve