[EM] Hybrid/generalized ranked/approval ballots

[Peter Zbornik]

Hi Kristoffer,

answers in the text of your email below.

For the Czech Green party, we might get some STV elections (probably
IRV-STV, maybe Meek-STV) for some of the party councils encoded in our
statutes by the end of this year.

For now, proportional party list elections, ranked proportional council
elections and condorcet based elections seem to be out of the picture for
now, as the interest is too low.

 For information: ranked proportional party lists are used by at least
the Scottish greens, the English greens and the UK Liberals in at least some
elections.
I can send some references to their statutes, in case anybody is interested.

STV in green political parties seems to be exclusively used only in
anglo-saxon countries, where it is used rather often.

Best regards
Peter Zborník


On Thu, May 26, 2011 at 8:00 PM, Kristofer Munsterhjelm <
km_elmet at lavabit.com> wrote:


> Peter Zbornik wrote:
>
>
>> Dear all,
>>  Please let me return to an older discussion (see emails below).
>> The issue of the hybrid ballot A>B=C>D.
>> Just an idea on this topic, which might be worth mentioning.
>> It could be a way to handle the problem of bullet voting.
>> Ant it could be a way to disband the dichotomy between different criterias
>> of winning in condorcet elections (margins, winning votes, quotas losing
>> votes).
>>  1] IRV-based elections:
>> Basically in IRV-based STV, when arriving at an equal sign in the ballot,
>> the ballot could simply be split into the number of candidates with equal
>> preferences and re-weighted accordingly (i.e. for instance A=B=C would give
>> three ballots, A>B=C, B>A=C, C>A=B, each with weight 1/3 of the original
>> weight).
>>
>>
>
> This sounds a lot like Woodall's concept of "symmetric completion". A
> method passes symmetric completion if truncated ballots are split into
> ballots with the latter (truncated) preferences filled out, for all possible
> ways those can be filled out, and with the same cumulative power. E.g. with
> candidates A,B,C,D and a method satisfying symmetric completion,
>
> 1: A>B
>
> is the same as
>
> 0.5: A>B>C>D
> 0.5: A>B>D>C.
>
> Unless I'm mistaken, you're generalizing symmetric completion to
> equal-rank.
>
>

Yes, I am generalizing symmetric completion to equal rank.
Unlike Woodal my proposal is computable for a large number of candidates in
IRV based STV elections.

 If we wanted to perform symmetric completion according to Woodall and if we
would have, say seventeen candidates, who were equal-ranked, then for each
ballot, we would need to generate 17!=355.687.428.096.000 strictly-ranked
ballots in order to exhaust all permutations, which is not computationally
feasible.

Example an IRV-STV election: A=B=C would according to Woodall be broken down
into 3!=6 ballots: ABC, ACB, BAC, BCA, CAB, CBC.

I propose that the ballot to be broken down into 3 ballots: A>B=C, B>A=C,
C>A=B, which is nicely computable and the result is the same as Woodalls
proposal for IRV-STV elections.

Maybe the reason why equally ranked ballots aren't used in STV elections
might be that a computable solution hasn't  explicitly been given.

The issue of a truncated ballot (incomplete ballot or partially blank
ballot) is different from the treatment of equally ranked candidates.


> Woodall writes about symmetric completion here:
> http://www.votingmatters.org.uk/ISSUE3/P5.HTM , where he also shows that
> STV does not obey that criterion, but that IRV does. In another Voting
> Matters article (http://www.votingmatters.org.uk/ISSUE14/P1.HTM ), he
> shows how STV can be made to obey symmetric completion, but says that doing
> so isn't a good idea.
>

It seems that this is a matter of taste.
The authors argue for their criterion based on one example.
I do not find the example convincing, since when adding a candidate with a
large number of additional votes in an STV election, then we have a
different electorate which should be differently proportionally represented.

After reading the articles above, I've come to think that the issue boils
down to how to handle blank votes.
The issue is not as clear-cut as I thought :o)

 Weather one accepts the plurality criterion really depends on the preferred
treatment of incomplete ballots, or partially blank ballots as I would
rather call them.

In order to guarantee to get all seats elected in an STV elections, it seems
that four different treatments of partially blank votes are possible:
1] the symmetrical completion, which is equivalent to requiring all voters
to rank all candidates as Kevin pointed out.
2] dynamic (or shrinking) quotas based on the number of active votes.
3] the candidate X: "none of the above" and new election if "none of the
above" is elected (http://en.wikipedia.org/wiki/None_of_the_above)
4] some seats simply are not elected (using static quotas). A new election
is held for the remaining seats.

Option three is used in the UK green party and possibly in other green
parties.
Personally I think that the blank vote should be respected, as a protest
vote (this is in a way a very Green political issue, I think) and always be
included in the quota.

Personally I would probably prefer option 4. The seats, which were not
filled due to the partially blank ballots (i.e. incomplete ballots) would be
filled in a new election.
In the Czech green party, the blank vote is counted as a legitimate vote and
counted into the quora needed to get elected (i.e. if one candidate gets 45%
of the votes the second gets 10% and the rest of the votes are blank, then
new elections are held)
The green party of California is using static quotas.

The voters, who did not complete their ballots are simply over-run in the
second election, but have the option "to protest".

 I guess I prefer the options in the following order 4>1>2>3

What is your preference ordering and why, if different from above :o)


> In a more general sense, there are two possible ways to handle equal rank
> in a weighted positional system. I think the first has been called "whole"
> and the second "fractional" on the list - that is at least the names I use
> in Quadelect.
> If the method is "whole" (or ER-, e.g. ER-Plurality), equal ranks give the
> same point value to every candidate that is equal ranked. With ER-Plurality
> you can simulate approval, for instance, by simply voting all approved
> candidates equal first, ahead of all not-approved candidates.
> If the method is "fractional", equal ranks distribute the point score over
> all the candidates equally ranked. Equally ranking k candidates first in
> Plurality would give each 1/k of the ballot's weight, and if I'm not
> mistaken, this is equivalent to generalized symmetric completion. You can
> simulate cumulative voting with fractional Plurality.
>

>
>
>> Condorcet-based elections:
>> In Condorcet elections (including STV) then A=B would simply mean 0.5 wins
>> for A>B and 0.5 wins for B>A.
>>
>>
>
> That's what Margins does. As a consequence, methods based on Margins can
> meet symmetric completion, but methods based on WV can't. However, Margins
> methods can't meet the Plurality criterion whereas WV can.


To paraphrase Woodall, I think that Plurality is "a rather arbitary property
that surely mustn't hold in any real election".
Indeed plurality voting has very little to do with proportional
representation and is in some sense contrary to the idea of proportional
representation.

To state it differently: my hunch is that for incomplete ballots, dynamic
IRV-STV quotas give a less proportional representation than IRV-STV with
symmetrical completion.

Could this be tested in your simulator?
Say IRV-STV elections with three or four candidates and incomplete ballots
(say some bullet-voting voters).
Method 1: static quotas and symmetrical completion
Method 2: dynamic quotas and no symmetrical completion
Method 3: static quotas and a new election if the option "none of the above"
is elected
Method 4: IRV-STV with static quotas and no symmetrical complketion and new
elections if all seats are not elected.
Method 5: IRV-STV with static quotas and no symmetrical complketion
and no new elections if all seats are not elected.
The result could be maybe shed some light on this problem.
My hunch is that method 5 gives the most proportional representation.

I guess the scenario above could be repeated for any STV method (like
Schulze-STV etc).

I am not at this point able to specify the scenario closer.
Basically it depends on how "proportional representation" is measured.
I have not been following the discussion on this forum and don't remember if
there was ever a continuous "proportionality measure" proposed, but I
remember you worked extensively with the issue.
My appologies for my bad memory.
What measure do you recommend.

Maybe election 12 in http://www.votingmatters.org.uk/ISSUE3/P5.HTM could be
used as a starting point, as this example is what Woodall seems to base his
argument for the plurality criterion on.


>
>
>
>> Kevin Venzke wrote in his mail below (May 9th 2010):
>>
>>
>>> 35 A>B
>>> 25 B
>>> 40 C
>>> A will win. This is only acceptable when you assume that the B and C
>>> voters meant to say that A is just as good as the other candidate that
>>> they didn't rank. I don't think this is likely to be what voters expect.
>>> It seems misleading to even allow truncation as an option if it's treated
>>> like this.
>>>
>>>
>> End of quote
>>  Well I think think that as a voter I would indeed be pleased if A would
>> win and not C.
>>
>>
>
> The example above shows how Margins can fail to meet Plurality. The
> Plurality criterion says that if some voter X has more first place votes
> than Y has *any* place votes, then Y shouldn't win. Yet that's what happens
> above:
> C has 40 first place votes. A has 35 any place votes, yet A wins. Margins
> elects A. Any other method that does, also fails Plurality.
>
>
>
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