[EM] (6) APR: Steve's 6th dialogue with Kristofer & Others

[steve bosworth]

(6) APR: Steve's 6th dialogue with
Kristofer & Others



 


>
From: election-methods-request at lists.electorama.com

> Subject: Election-Methods Digest, Vol 136, Issue 19

> To: election-methods at lists.electorama.com

> Date: Mon, 19 Oct 2015 12:02:10 -0700

> 

> 1. Re: (5) APR: Steve's 5th dialogue with Kristofer & Others

> (Kristofer Munsterhjelm)

> 

> ----------------------------------------------------------------------

> 

> Date: Mon, 19 Oct 2015 00:22:46 +0200

> From: Kristofer Munsterhjelm <km_elmet at t-online.de>

> To: steve bosworth <stevebosworth at hotmail.com>,

> "election-methods at lists.electorama.com"

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

> Others

> Message-ID: <56241BB6.6070603 at t-online.de>

> Content-Type: text/plain; charset=windows-1254; format=flowed

> 

> 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'?

> 

K: Yes. I mean the very opposite.

> 

K:> 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 [i.e. APR] has a vulnerability that favors well-organized


> participants, and so would give an advantage to parties that can organize.


 


S:
Given these and your later words, it seems that either you are not understand
exactly how my APR is counted or I am not understanding the terms you are using.  Thus, in order for me fruitfully to address
your argument, please explicitly define, explain or comment on the following words,
phrases, and dialogues copied from all that is repeated after the +++++++++++
line:  


1)     
the exact differences you have in mind
between IRV, STV, and APR; 


2)     
vote allocation (is this simply
ranking?);


3)     
Droop quota (Strictly speaking, APR has
no use for the Droop quota.  APR may
elect some candidates who have received fewer votes than this quota.  This will occur as a result of some candidates
being elected with more votes than this quota and therefore receiving more
‘weighted votes’ in the assembly.);


4)     
spread the votes evenly (Does this mean
giving all the party voters’ 1st preferences to the most favored
candidate while they give the same number to 2nd or lower preference
clones?  In any case, I do not yet see
how this strategy would give this party more ‘weighted votes’ in the assembly,
or could ‘push off’ any opposing candidates.);


5)     
k of n candidates (k is the total
number the party’s most favored candidates while n is the total number of
candidates the party is running.  However,
I see that k seems to have a different meaning nearer the end of your post.);


6)     
n-k candidates (means the total number
of candidates less favored by the party. 
If so, I do not understand how ‘IRV eliminates more than n-k in one go);


7)     
What ‘threshold’?  I do not see APR as having any ‘threshhold’.  APR simply continues to eliminate the
candidate that currently has the fewest votes until only the pre-established
number of candidates remain to be elected to each electoral association.


8)     
‘the first stage weakens the second’ (I
think you are referring more simply to APR’s 4-stage count explained in Endnote
4.)


 


Also,
please clarify the following questions. 
These question have also been copied from also remains below the
++++++++++ line:


 


S:
I do not yet understand why you think an analysis of Single Non-Transferable
Voting (SNTV) is relevant to STV or APR. 



[….]

> > S:  Does this make it any
clearer that strategic voting would be

> > practically impossible using APR?

> 

>K: It doesn't seem to invalidate the proof sketch.


 


S:  Again, I appreciate that your ‘proof sketch’
(especially if I fully understood it) may have shown how a strategizing party
will lose nothing in trying (except time, the money for some of the deposits
for some of its eliminated candidates, perhaps confusing its voters, etc.).  What I do not yet understand is how, in
practice, they will acquire the for knowledge needed to get any more benefits
than this.

> 

K: > 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.


 


S:  No. ‘Default votes’ are passed onto winning
candidates by the 1st choice candidate of the voter who has not
ranked any winning candidates.

> 

K: > 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:  By saying this, you seem to have forgotten
that APR does not use thresholds.  Instead,
APR requires very popular elected candidate to retain only up to 10% of all the
‘weighted votes’ in the assembly.  Any
votes received above this 10% limit must be non-returnably passed on by the
relevant MP to other MPs she trusts.


[….]


 


K:
> I think my cloning example in that email 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?


 


S:  I do not yet understand these claims.  In APR, only the very popular elected
candidate (i.e. any with more than 10% of the weighted votes in the assembly)
would be allowed to ‘distribute weight’ to their less popular colleagues.  Also, it would help me if you could express
the same argument without relying on abstract mathematical symbols like X, X1,
X2.  In any case, do these 3 symbols
represent 3 different parties; 3 different candidates; or one most preferred
candidate, a 1st choice clone candidate, and a 2nd choice clone candidate?


 

K: > 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.




S:  For me, complete proportional representation
would be mathematically achieved when every citizen vote counts for one in the
assembly (no votes wasted), the percentage of each different MP’s vote in the
assembly is equal to the percentage of voting citizens who had voted for that
MP.  Qualitatively, representation would
be as complete as possible if the electoral system allows each citizen to rank
any of all the candidates which she sees as being able to represent a scale of
value similar to her own.  I see the
associational element of APR as structurally maximizing the chances that each
citizen will be able to see the largest number of such candidates that are
available in her society, i.e. APR seems to maximize the chances that each
citizen’s vote will be added to the weighted vote of the person in the society
who has become an MP and who most accurately and reliably will represent her
hopes and fears in the assembly.


 




I look forward to your clarifications so I can usefully address your whole
argument.


 


Steve
Bosworth


 


++++++++++++++++++++++++++++++++++++++++





K: > >> 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.

> 

K: > 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.




S:  I do not understand this paragraph. 




> 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.


 


S:  Given my incomplete understanding, I still
can imagine that the above strategy might fail to elect any candidate other
than the ones it would have elected without strategizing.  However, I still do not understand how anyone
could acquire sufficient for knowledge to be confident enough to go to the
bother (time, expense, danger of confusing your voters, etc.) of try to
strategize.

> 

K: > 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, 


 


S:  I do not yet see how the relevant non-party
candidates might be ‘pushed-off’ in this way.


 


K:>
…. 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.)


 


S:  What ‘threshold’?  I do not see APR as having any
‘threshhold’.  It simply continues to
eliminate the candidate that currently has the fewest votes until only the
pre-established number of candidates remain to be elected to each electoral
association.


>


> >>

> >>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.


 


S:
Here, k has a different meaning than given to it above.

> 

K: > 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…..


 


S:
I do not know if this is important for your explanation but some of the
candidates would also have some lower than ‘first place preferences’ before
they are eliminated.  Also, some winning
candidates would have been elected with the help of some lower than 1st
preference votes.


 


K:
 >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.


 


S:  Either you are not understanding APR’s method
of counting or at least I am not understanding you at this point. 

> 

> 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".

> 

> >S: 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, and coordinates 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
directly or indirectly

> > 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?

> 

>K: It doesn't seem to invalidate the proof sketch.


 


S:  Again, I appreciate that your ‘proof sketch’
may have shown how a strategizing party will at least lose nothing in trying
(except time, the money for some of the deposits for some of its eliminated
candidates, etc.).

> 

K: > 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.


 


S:  No, ‘default votes’ are passed onto winning
candidates by the 1st choice candidate of the voter who has not
ranked any winning candidates.

> 

K: > 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:  By saying this, you seem to have forgotten
that APR does not use thresholds.  It
requires very popular elected candidates to retain up to 10% of all the
‘weighted votes’ in the assembly.  Any
votes received above this 10% limit must be non-returnably passed on to other
trusted MPs.




> 

> > 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?

> 

K: > 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.




S:  For me, complete proportional representation
would be mathematically achieved when every citizen vote counts for one in the
assembly (no votes wasted), the percentage of each different MP’s vote in the
assembly is equal to the percentage of voting citizens who had voted for that
MP.  Qualitatively, representation would
be as complete as possible if the electoral system allows each citizen to rank
any of all the candidates which she sees as being able to represent a scale of
value similar to her own.  I see the
associational element of APR as structurally maximizing the chances that each
citizen will be able to see the largest number of such candidates that are
available in her society, i.e. APR seems to maximize the chances that each
citizen’s vote will be added to the weighted vote of the person in the society
who has become an MP and who most accurately and reliably will represent her
hopes and fears in the assembly.


 


 		 	   		  
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