[EM] Hybrid/generalized ranked/approval ballots

[Kristofer Munsterhjelm]

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.

> 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.

> 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.

> 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.

>     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.

> 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.

> 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.

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.