[EM] Hybrid/generalized ranked/approval ballots

[Peter Zbornik]

On Tue, May 31, 2011 at 3:24 PM, Kristofer Munsterhjelm <
km_elmet at lavabit.com> wrote:

> My net access was down for a while, so if you wrote something later that
> invalidates what I'm replying to here, oops.
>
>
> Peter Zbornik 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.
>>
>
> If complexity doesn't deter the party, why not go directly to Schulze STV
> instead of using Meek STV? It could be a good precedent for other parties,
> as they'd then know the method is actually used for political elections.


Maybe I wasn't clear in my response.
Complexity can deter the party.

Well, I like Schulze-STV, but it is nor very vell documented, nor tried nor
tested and it is a Condorcet-STV method, where Condorcet as an election
method has little support in our party and I personally have some question
marks about the method.

I was only able to get the grip of the Schulze-STV method after reading the
wikipedia entry, Schulze's paper and further some key posts by Markus
Schulze to this list and that was not easy.

I am not even close to be able to describe the method in our elections rule
book in a way that everyone understands.

I am neither able to certify that the vote-counting program is a correct
implementation of the method described in the rule book.

The method is not used in any organization, except for a showcase website
and I am hesitant to let my party become the test case of a brand new
method.

Meek is at least used on New Zealand and it is possible to explain in the
rule book (I hope), and there is some example of it being coded in
legislation.
OpenSTV has been around for a while, so I guess it can be trusted enough,
but even OpenSTV dont issue certifications for Meek STV (
http://www.openstv.org/certified-reports), so that is a problem too.

The most realistic expectation is that our party will settle for the STV
implementation for the Green Party of California (static
quotas) disregarding my own personal opinion on the appropriate election
system..


>
>
> 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.
>>
>
> But symmetric completion doesn't have to be done in such a brute-force
> manner. Wouldn't Fractional-Plurality IRV do the same, but "behind the
> scenes"? I.e. you use IRV but you just turn A=B=C into 1/3 vote for A, B,
> and C. Elimination works as usual: if you have A=B=C and C disappears, the
> ballot is now A=B.


Yes, that system is simpler than the system I propose below and the result
the same.

>
>
> 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.
>>
>
> Which is more or less the same as a fractional positional system, yes.


I think it is exactly the same, in the sense that the results are the same.


>
>
> 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)
>>
>
> There's a difference here, I think, between intentionally blank ballots and
> ones where the voter doesn't know/doesn't feel it important enough to fill
> in the rest. Say you had an STV election for 5 seats and each party fields 5
> candidates just to be sure they'll get them all if some improbable swing
> goes in their favor. You likely wouldn't bother ranking all 5 candidates of
> the minor parties, but that doesn't mean you'd prefer the seats to be
> vacant. You just have no opinion. In that case, I have no problem with a
> dynamically shrinking quota.


> On the other hand, if you have an election of 3 democrats and 10 dictators
> to a 5-winner district, you might want an explicit X, but that's different.
> That involves the question of whether to add an approval threshold to a
> ranked ballot. If one doesn't, the method will have to pick one
> interpretation or the other, and that depends on the circumstances of the
> system. If the 5-district is fixed, then you're going to have at least 2
> dictators anyway and it better be ones that will give you some time you can
> use to run away; but if it's not fixed (i.e. could handle being smaller or
> larger), then being able to say "nobody else" ("none of the below"?) would
> be useful indeed, as it could block the 2 dictators outright.


Yes, your examples illustrate the limited expressive ability of the
truncated ballot compared to the generalized ballot or the ballot with an
approval threshold.


>
>
>    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.
>>
>
> The Plurality criterion has nothing to do with Plurality, the voting
> system. Instead, the criterion says that if some candidate gets more first
> place votes than another gets *any* place votes, then the latter shouldn't
> win. This seems very reasonable to me, because you'd figure that even if you
> consider the worst case and say any position is equal (that is, that
> first-place votes are equal to second-place votes), the former candidate has
> more of what you want (votes) than does the latter.
>
> For multiwinner systems, it might be a little more murky since the
> distribution of the first-place votes could force disproportionality if it
> were adhered to. I'm not sure that is possible, but I'm not sure it is
> impossible, either. Still, for a single-winner method, Plurality just seems
> to be common sense.


I agree.


>
>
> 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.
>>
>
> If I could find a consistent way of implementing the truncation and
> equal-rank logic, it could. I have been focusing on the single-winner part
> of my simulator recently, though; I want to get that done before I add the
> multiwinner aspects back in.


See the following emails (especially the last one to Juho). There are two
possible rules (usung a generalized ballot allowing for blank voting):
Rule 1: A vs B is a win only if A beats B+X, i.e. A is preferred both to B
and to noone elected, requiring A to have >50% of all votes in the election
between A and B+X..
Rule 2: A will win a Condorcet election only if (s)he beats X.


>
>
> 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.
>>
>
> There are many proportionality measures for parties, but not so many for
> ranked ballots in general. The way I do it in my simulator, I create a
> hidden opinion space and then measure proportionality of that opinion space.
> Concretely, there are n yes/no issues. For these, the simulator determines
> how many voters feel "yes" about each, and, where the voters rank candidates
> that agree with them on more issues closer to top, how many of the elected
> candidates feel "yes" about each. The disproportionality between the issue
> space given by the voters and that given by the candidates can then be
> determined using any of the party-based proportionality measures.
>
> You can find many of the possible measures here:
> http://www.mcdougall.org.uk/VM/ISSUE20/I20P4.PDF . I tend to use the
> Sainte-Lague index with an appropriate constant to avoid division by zero;
> since the performance is normalized in any event (just like with Bayesian
> regret), it doesn't matter that the proportionality measure is
> near-unbounded. If that is a problem, you can use the Loosemore-Hanby index
> or the GhI least squares index, both of which correlate well with the
> Sainte-Lague index - although optimizing correlated variables may produce
> quite different results than optimizing the original variable.
>

OK, thanks.


>
> Warren suggests another way of measuring multiwinner method desirability,
> by having the method elect candidates (who disclose their behavior in some
> way), then the winners vote on bills (according to some other logic), and
> the method that produces results the people like is valued highly. That
> doesn't directly measure proportionality, however.
>
>
> 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.
>>
>
> I can't fit opinion spaces to arbitrary ballots, I can only generate
> (space, ballot) pairs. Thus I can't determine the proportionality of
> election 12's results given the ballots alone since the hidden data isn't
> there.
>
> It might be possible to find a consistent hidden data set, but I think that
> would be hard. There could be more than one such set, and the process might
> be prone to overfitting as well.
>
>
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