[EM] (5) APR: Steve's 5th dialogue with Kristofer & Others

[Kristofer Munsterhjelm]

On 10/01/2015 11:08 PM, steve bosworth wrote:

>> > Re: (4) APR: Steve's 4th dialogue with Kristofer
>> >
>> > Date: Wed, 01 Jul 2015 22:14:11 +0200
>> > > From: Kristofer Munsterhjelm <km_elmet at t-online.de>
>> > > To: Election Methods Mailing List  <election-methods at electorama.com>
>> > > Subject: [EM] Thresholded weighted multiwinner elections
>> > > Message-ID: <55944A13.7060800 at t-online.de>
>> > > Content-Type: text/plain; charset=utf-8; format=flowed
>> >
> S: Steve's questions will follow each element of what Kristofer wrote:
>> >
>>K: I think I see why the cloning attack is possible in two-stage weighted
>> > > voting. If I'm right, then it is possible to make voting methods  that
>> > > produce results that fit weighted voting better -- at least when  the
>> > > voters are honest. However, I'm not sure if it is possible at  all if
>> > > enough voters are strategic.
>> >
>>S: Am I mistaken in believing that, in practice, APR's 'weighted
>> > multiwinner elections' would not be vulnerable to the threats either  of
>> > effective 'cloning' or of other kinds of 'strategic voting'?

Yes. I mean the very opposite.

Firstly, no method is entirely invulnerable to strategic voting; that 
was my point when mentioning Duggan-Schwarz. All you can do is find more 
resilient methods, or balance resilience against other desirable 
properties (like how good results you get under honesty).

Second, the cloning attack I mentioned specifically targets APR's 
IRV-based election mechanism. What I tried to show is that APR is 
vulnerable to cloning. Unlike STV's similar vulnerability, the IRV based 
method used in ARV has a vulnerability that favors well-organized 
participants, and so would give an advantage to parties that can organize.

>> As for the cloning attack, I specifically found it while analyzing APR's
>> voting method. So it's meant to work against APR's voting method
>> (semimajoritarian IRV). It is not quite as strong as I originally
>> thought, but would still lead to party list in an equilibrium. See below.
>
> S:Please explain what you mean by ‘party-list equilibrium’ and how it
> relates to APR.

A party list equilibrium is one where parties have an advantage over 
non-parties to a point that the results from the methods mirror that 
which would happen under party list. Parties are not explicitly made 
part of the method (unlike party list) but because of the advantage of 
belonging to a party, the method acts as if parties are formal parts of 
the system.

Again, a good comparison is the former SNTV method in Taiwan. SNTV 
itself has no mention of parties; there are just candidates and they win 
according to their Plurality counts. Yet it did in effect work as a 
party list system because everybody engaged in vote allocation.

>> > S: This practical invulnerability would seem to arise from the facts
>> > that APR's election
>> > of reps to a large national assembly would allow all citizens to rank
>> > as few or as many of all the thousands of candidates in the country.
>> > Accordingly, for example, the portion of all the perceived clones
>> > would be elected only if and when each is discover to be, for  example, one among the 435
>> > most popular candidates in the USA. Each APR elected candidate receives  a weighted vote in the assembly equal to the number of votes that each
> had received directly or indirectly from citizens.
>
> S:Yes, I must accept the THEORETICAL possibility that strategic voting
> could be used with APR.However, am I correct in understanding that all
> strategic voting requires the strategizer to have accurate knowledge
> about how all other relevant people will be voting.I do not see how any
> person or party could acquire such knowledge in the above APR election
> of a ‘large national assembly’ which allows each ‘citizens to rank as
> few or as many of all the thousands of candidates in the country’.This
> is why it seems to me that successful strategic voting would be
> impossible for PRACTICAL purposes.Your Taiwan example does explain how
> parties might try to organize strategic voting but why should we worry
> about it succeeding in the case of APR.

Suppose I'm leader of a party X and I have absolutely no idea of how 
voters not aligned with X will vote. Then I can still do the birthday 
coordination I mentioned earlier to have my supporters evenly spread 
their votes for the party's candidates.

This can never harm me (or my party), but it can help by displacing 
other candidates. What candidates will be displaced? There are two 
types: minor candidates who have less than a Droop quota, and members of 
other parties that didn't coordinate and so *appear* to have less than a 
Droop quota, yet would have had more if surpluses had been distributed 
as in STV.

Here's a simple proof sketch for why it can never harm to spread the 
votes evenly:

- Suppose that party X gets one candidate elected when it doesn't 
strategize.
- Now suppose that X tries to clone this candidate to win more. By 
cloning, every voter ranks all the clones next to each other (but not 
necessarily in the same order).
- Then the worst that can happen is that all the clones but one are 
eliminated, after which the election is just like if the party hadn't 
done any cloning at all.

So it works when the party gets one candidate without strategy. For more 
candidates, the only danger is that say, k of n candidates won without 
strategy, but spreading out the support means IRV eliminates more than 
n-k in one go.

Let's say the party evenly distributes votes among the k candidates who 
won (but not among the other n). It's clear that doing so won't push any 
of the k candidates off the council because if the votes for the k 
candidates were unequally distributed, one of them must have had less 
votes before the even distribution than after. However, he still got 
elected. So he'll still be elected when he gets more votes.

That leaves the other n-k. Suppose the votes are distributed evenly. But 
at the point where n-k have been eliminated, all we're left with is a 
group of k candidates. Since the votes are evenly distributed among the 
n, they'll be evenly distributed among the k once n-k have been 
eliminated, and by the argument above, these k will always be elected 
anyway.

So the worst that can happen to party X is that they don't gain any new 
seats by evenly distributing the votes. Hence it can never harm to clone 
as long as the party ensures even distribution. W5.

More precisely: the party never loses by cloning if they can make the 
distribution among their candidates more equal than it was without 
cloning. The more information the party has about how others vote, the 
better it can cancel out unevenness in their votes, but even if the 
party knows absolutely nothing, cloning can't harm it.

Why does that matter? Since cloning can push off candidates that are not 
as well-organized, the method favors groups that can pull off an 
organized coordination campaign, i.e. parties.

(I also note that furthermore, the presence of organized cloning would 
subvert the asset voting fix that you refer to. A party could spread the 
support for its candidates so that nobody gets above the threshold.)

>>
>>K: As I may have mentioned, we can abstract the two-stage voting method [….]
>
> S: Yes, you did mention this but I do not yet understand why you are
> discussing it.

I discuss it because the "run IRV until k candidates remain and they're 
the winners" method is equivalent to it, and splitting it into two 
stages makes it more clear what the problem is.

Once only k candidates remain in IRV, they have a weight according to 
the number of first place preferences they have on the ballots where 
every other candidate (not in the set of the k) has been eliminated. But 
that is precisely the weight that the second stage of a two-stage method 
would assign them.

In an IRV-until-k method, the remaining k winners' weights matter, 
that's true. But just as important is *who* those k are, because if 
you're not one of the k, you don't get any weight at all. That's how the 
cloning benefits party X: by pushing off people that aren't members in 
favor of those who are.

Or as I said in the cloning example of my last post: "the first stage 
weakens the second - the Z-voters' first preferences are no longer 
counted, instead only their third preferences are".

> APR’s counting of all the ranking in the general election
> is a one-stage method with 4 counts:These are explained in the following
> Endnotes (4 and 9) to my article:
>
> 4. APR's use of Asset Voting (also see Endnotes 2 & 12) provides two
> ways in which a representative may also receive some votes from citizens
> indirectly:Firstly, when none of the candidates ranked by a citizen have
> received enough votes to be elected, she can require her first choice
> but eliminated candidate to pass her 'default' vote on to the candidate
> he most trusts, e.g. the candidate highest on his pre-declared list.He
> must sequentially do this until one of his favored candidates is
> elected.All these available 'default' votes must be sequentially
> transferred, one by one, beginning with those held by the eliminated
> candidate who currently has the fewest number of votes.If more than one
> eliminated candidate share this position of currently being the least
> popular, the order in which they will transfer the 'default' votes each
> holds will be determined by lot.
>
> If and when any of these default votes fail to help elect any
> representative after all the holders of these default votes has made
> these provisional transfers, each must then be given to the
> representative who has now been elected and is most favored by the
> eliminated candidate who holds it.

This is IRV-until-k, right? I suppose that the "pre-declared list" is 
that voter's ballot. Or do you mean something else? If it is something 
else, how does the voter signal that he wants his vote to go down a 
separate list instead of following the list given by his ballot?

> Secondly, in response to the possibility that a very popular
> representative may initially receive more than 10% of the country’s
> weighted vote, she must publish exactly how these 'extra' votes will be
> non-returnably added to the weighted vote of her trusted fellow
> representative(s).This is to avoid any question of a representative
> being in a position to ‘dictate’ to the assembly.The transferring of
> these extra votes would proceed sequentially, starting with the
> representative who had received the most votes above the 10% limit.

An organized party can circumvent that restriction, as mentioned before. 
It doesn't really matter because the party's intention will be very 
clear when it engages in vote allocation, but the restriction can't 
protect against a party who wishes to render it irrelevant.

> Consequently, the list of all the elected candidates and their different
> weighted votes is finalized only after two earlier ‘provisional’ counts
> have been completed.The first produces a provisional list of the
> pre-established number of elected candidates by counting all citizens'
> votes, except those which had been given only to eliminated
> candidates.The second provisional count would produce a somewhat
> modified list by also counting the 'default' votes as described above.
>
> The third count would include all the transferred 'extra' votes from the
> above very popular representatives who had received more than 10% of all
> the votes. Consequently, this third and final list would contain all the
> pre-established number of representatives, each with his or her
> finalized weighted vote in the assembly, none with more than 10% of all
> the citizens’ votes.Each citizen would know to which representative's
> weighted vote her vote had been added.Also see Endnote 9.
>
> 9. The FEC both ensures that each association’s APR general election
> ballot paper will be given to each of its registered voters at his or
> her local voting station on election day, andcoordinates the countrywide
> counting of all citizens' rankings. This count determines both which
> candidates are elected and exactly how many weighted votes each
> representative will have in the House of Representatives.Each will have
> a weighted vote exactly equal to the number of citizens whose votes
> helped to elect them.
>
> All 435 elected candidates (congresspersons) would be discovered by
> counting the rankings from all voting citizens in the country.They would
> be found by sequentially eliminating the least popular candidate from
> the race, one by one, until only the pre-established number of reps for
> each association remain.Again, each of these representatives would have
> a weighted vote in the House of Representatives exactly equal to the
> number of rankings (votes) each had received by the time the last
> candidate had been eliminated, and all the 'default' and 'extra' votes
> had been transferred (see Endnote 4).
>
> S:Does this make it any clearer that strategic voting would be
> practically impossible using APR?

It doesn't seem to invalidate the proof sketch.

For default votes: either they are the ballots themselves, in which case 
there's no problem, or they're optional different lists, in which case 
voters for X could just not use them.

For extra Asset reallocations: they don't come into play when cloning is 
used because no single member amasses enough weight to go past the 
threshold.

> S:What do you think?
>
> S:If you still think that the remaining parts of your reply to our 4^th
> APR dialogue are relevant, let me know and I will respond to them as
> best I can.

I think my cloning example in that mail is relevant. I showed an 
instance where APR would first choose {X, Y, Z} as the winners to 
distribute weight among. Then X clones and the outcome switches to {X1, 
X2, Y}: Z is pushed off. Since the method moved from thinking Z should 
be included into thinking Z should not, it was mistaken in at least one 
of these cases. Which is it? Should candidates with less than a Droop 
quota (Z in this case) always be retained, or should they be excluded 
beforehand so that cloning has no effect?

More generally, I'd like to know how you define proportionality. Do you 
have a method-independent criterion as to what it means for an outcome 
to be proportional, and if so, what is it? Such a definition could help 
answer the question above, and it would also explain how you would 
conclude that my method sketches of an even earlier post were 
necessarily less proportional than APR's IRV.