[EM] Hybrid/generalized ranked/approval ballots

Fri May 27 04:10:09 PDT 2011

Kristoffer,

just a small P.S. to my email below.

Maybe the problems with the incomplete ballots and dynamic quotas below have
something to do with electing a fixed number of seats.
That's just a hunch.

I think you mentioned that a variable number of seats might give better
proportional representation than a fixed number.

However electing a variable number of seats will probably have little
political support in my party, so this question is more a question out of
curiousity.

Peter

On Fri, May 27, 2011 at 12:28 PM, Peter Zbornik <pzbornik at gmail.com> wrote:

> 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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