[EM] Proportional Representation Systems I'd Support

Abd ul-Rahman Lomax abd at lomaxdesign.com
Sat Mar 27 11:55:49 PDT 2010

At 04:43 PM 3/26/2010, Kathy Dopp wrote:
>Well that would certainly be a way of overcoming any effective
>minority representation in legislatures by always making sure that the
>representative elected by a majority made all the decisions. Not sure
>if I agree necessarily with giving more votes to one legislators than
>others, and that idea certainly is in sync with the way IRV/STV gives
>more effective votes to some voters than other voters during the
>counting process.

That is not at all "in sync" with IRV. It would give every voter the 
same "effective vote" in the decisions that count: those made by the 
legislature. It was proposed as a thought experiment. IRV is a ballot 
analysis method, and indeed wastes many or most of the votes cast. A 
proxy method would waste none. Before dropping this, because I don't 
see a snowball's chance for a non-peer legislature in the near 
future, I'll point out two thingss:

1. Proxy representation in decision process, including voting, is 
common-law standard when property rights are concerned. What if we 
thought of the government as a corporation in which each citizen has 
an equal share? What if we thought of the government as the property 
of the people? What is wrong with this concept? If you have proxy 
representation, then, at the annual meeting, say, every person there 
being a shareholder or representing one or more, can vote on motions. 
They do not have equal voting power, since, in general, they 
represent different numbers of shares. Most pernicious, with 
corporations with large and wide public holdings, is the solicitation 
of proxies by the board according to recommendations they make, at 
company expense. This has done huge damage to the accountability of 
management and warps the election of boards and thus of control of 
the corporation. So many, thinking about proxy representation, think 
of this abuse and are against it.

2. If citizens were organized outside of government, they could do 
whatever they please. They do this now, but they tend to use 
traditional forms of organization, the same ones that lead to 
problems in government. I'm trying to promote awareness that there 
are other options, that are simple and which I believe will be 
effective, and that will do no harm if they turn out to not work. It 
ought to be a no-brainer, but, hey, I also think that about Count All 
the Votes. I.e., implement approval voting by simply counting all the 
votes cast for candidates in a single-winner election. Cheap, maybe 
even cheaper than tossing overvotes!, considered by political 
scientists to be quite a respectable voting system, it's the simplest 
form of Range Voting, it avoids some of the voting paradoxes, it's 
monotonic, and it's compatible with runoff voting, making it function 
a bit more efficiently. No-brainer apparently does not mean "Let's do 
it right away!"

>I personally prefer party list systems where the voters know in
>advance what candidates will get any excess support, and where voters
>can suggest a reordering of the list itself, rather than allowing
>candidates to choose, although I suppose allowing candidates to choose
>could be done in a fair, auditable way as well.

A party list system is a variation on candidate proxy with a stated 
preference order. The candidate is the party, and the equivalent in 
candidate proxy is that one votes for a party hack or leader who is 
expected to follow a party process. The practical difference is that 
party list is inflexible, deterministic, and candidate proxy is 
deliberative and based on a kind of trust. Which could be trust in a 
political party, it's similar to trust in a candidate.

> >
> > Would you agree that, if this were done, it would be fair, that every voter
> > would be fairly represented in the Assembly? Some directly, some 
> indirectly.
>Not sure what you mean by "this" exactly, but maybe so.

This means that every voter is represented directly or indirectly, 
with "indirect" being that the seats are either approved directly by 
the voter, or indirectly by the elector chosen by the voter. The 
"election" is an extended process that does not all take place on 
election day. I think it would be fascinating to watch. And, of 
course, my question is somewhat rhetorical. I can't imagine that 
you'd think it not fair.

Every voter gets one vote in the election, and that vote is not 
wasted, and ends up being represented in the Assembly by 1/Q vote, 
where Q is the quota. The only exceptions are dregs where the 
electors can't agree on a seat, so those last elections may be 
postponed, and it's possible to handle the dregs fairly as well. As 
an example, some decisions of the Assembly might require an absolute 
majority vote, which means that some of those unrepresented as dregs 
are all considered, in effect, to have voted No on the motion. The 
level of non-representation through seats would be far, far lower 
than present practice, where sometimes a majority of those voting are 
not represented by free choice. Maybe even always a majority, if we 
realize that party candidates themselves are the result of forced compromises.

The loss of representation is even more fully addressed if electors 
can vote directly, say over the internet. They are public voters, so 
there is no security problem, other than ordinary identity 
verification. Because the vast bulk of votes, I'd predict, would be 
cast by seats in actual attendance at sessions, the common worry 
about the loss of deliberation, the bedrock of democracy, would not 
be a problem. Why would you bother to read all the transcripts, or 
just to vote knee-jerk without that study, if you have someone you 
chose, you trust, who is there and is paid to do this?

Basically, these are the kinds of systems we'd be considering if, 
today, we started to carefully design governmental systems, from the 
ground up, instead of only looking at how to tweak them. And I'm 
proposing that we do just this: design and build the systems, but 
outside of government. Show that they work, if they do, and *then* 
maybe change the formal governmental systems and if these ideas 
worked outside of government, the power would exist to make the 
change happen. Bootstrapping, sidestepping what might seem like 
formidable obstacles. If it's tried, I predict it will work. Failure 
will be from not trying, not from any other enemy. Not even the 
special interests, they could not stop this and very likely won't try.

> > The electors, I call the candidates holding the votes, vote publicly, so
> > every voter knows where his or her vote went, and exactly whomo it elected.
> >
> > This is very, very different from a contested election, in which 
> some voters
> > lose. In this, all voters win. (Except for what can be called the "dregs,"
> > which reduces to a very small problem with Asset Voting like this, and what
>Well the benefit of Asset voting over party list voting might be that
>the ballot is simpler and perhaps, I don't know, it'd be an easier
>sell. Although there are lots of party list systems internationally
>that seem to work well, and I haven't heard of existing asset systems.

Aside from share corporations, of course! The analogy is this: Shares 
are voters. The voter chooses a proxy. The proxy is at the annual 
meeting with amalgamated proxies from many voters. (There are 
companies which do just this for instituional shareholders.) If 
proxies can get together and vote in a coordinated way (and this is 
always done, in effect, where a single proxy holds enough votes to 
elect more than one member of the board), the board election ends up 
representing, each one, Q voters, where Q is equal to the number of 
voters (shares) divided by the number of seats.

However, because some voters may not vote efficiently, some votes are 
wasted. Cumulative voting is used, and cumulative voting is efficient 
and fair if voters are coordinated. I.e., if there is a faction with 
2 * Q members ("shares"), and each voter gets N votes to cast, they 
cast Q*N for one candidate and Q*N for the other, presumably by each 
voting for both, and for no others. Have I done the math right? They 
get two seats, which is exactly their fair share.

It works the same if each gets only one vote to cast, and the voters, 
then, divide their votes according to coordination, so that half are 
cast for one candidate and half for the other.

Note that with this voting, you can't just count overvotes as with 
approval, you have to divide them to make it fair. So if you have one 
vote, and you vote for two candidates, they get a half vote each.

The basic concept of cumulative voting in share corporations is 
effectively the asset idea, and the absence of this from public 
elections simply shows how governments are not the property of the 
people, in existing systems. If we owned the government, don't you 
think our attitude toward it would be different?

> > you would do is, if you want N seats, you'd allow the election of "as many
> > as N + X seats." Where X is a variable determined from experience to
> > represent the level of non-negotiable differences among the electors. If by
> > some miracle they all agree, you actually get N + X seats, a small problem,
> > maybe even not a problem at all.
>Huh?  Wouldn't funding, office space, facilities in the legislaturs be
>a problem if no one knows in advance how big the legislature will be?
>Never heard of variable-sized legislatures before. Doesn't sound very

No, you missed the point. The size would be fixed. X is a small 
number, like one or two. Existing legislatures are variable, because 
seats go vacant for various reasons. In large elections like a state 
legislature, my guess is that X wouldn't be larger than 2, it would 
be a small fraction of seats. One of the advantages of Asset is that 
it would be quick and easy to fill vacancies that appear, no need for 
a special election or an appointment. The electors just recast the 
votes freed up. The missing seat (perhaps he or she died) would have 
named a proxy to act in his or her absence, so the votes that the 
seat held directly would not be lost. If any votes are actually lost, 
the quota would be recalculated to a smaller number, and those 
already in the legislature would have a few votes to toss in the pot.

It is possible that in a large election, there would always be one 
seat left vacant. That's why I mentioned X. It would probably be one 
or two. It's even possible that the last seats would be filled with 
an ordinary election, and possibly with special voting rights just 
for them, if one wants to be rigorously fair. Those seats would have 
been elected with less than a quota, so, to avoid giving them extra 
power, they might have a fractional vote to cast. I'm not terribly 
interested in working out all the miserable details, because we need 
to gain experience with asset elections before they become practical 
for governmental usage. Asset is a crackerjack idea for any peer 
organization. Simple and, I expect, effective at creating boards or 
committees that really do represent all the voters. In small 
organizations, literally all of them. No losers. On each motion, 
sure, the minority loses. That's democracy. But the minority is not 
some fixed faction, ordinarily, it moves around. Win some, lose some. 
What goes around comes around. Give some slack to a different faction 
with high preference strength on an issue you don't care about so 
much, they turn around and do the same for you when your turn comes. 
That's why deliberative process in collegial environments resembles 
range voting.

> > But look what happens to the votes: This is an STV election! The only
> > difference is that the vote transfers are in the hands of chosen electors,
>If the STV method is used within asset voting, then I oppose it
>strongly because STV has all the same counting flaws as IRV including
>nonmonotonicity, unequal treatment of voters' votes, and not being
>precinct summable.

No. You have not understood STV comprehensively. You are aware only 
of its problems when used for single-winner. It's much better for 
multiwinner elections because, in the end, we want only one vote from 
each voter to count, if we want fair representation. STV, you should 
remember, was invented for proportional representation, not for 
single-winner elections. Used with Asset, it is monotonic in substance.

As to precinct summability, that's a technical detail that, were it 
the only problem with STV, would not militate against its use. STV is 
still flawed when used as a deterministic multiwinner method, though 
the flaws vary with the exact method. In Asset, there is no unequal 
treatment of voters' votes, especially if the vote for one only. 
Voters who vote for two, by choice, lose power, not gain it, though 
this would, with Asset, vary with the exact method.

Suggested Asset/STV method. Ranked ballot. (Given the Asset 
provision, three ranks might be just fine.)

1. Q = V / N. (This can be done with the Droop quota to make it more 
deterministic. I oppose it for reasons I won't detail here.)
2. Any candidate with Q votes gains a seat. Those ballots are then 
deweighted, if there were M votes for the candidate, to now represent 
collectively M-Q votes. Think of each ballot as now being marked with 
the fraction (M-Q)/M.
3. On each ballot where the first position candidate gains a seat, 
the candidate in first position is marked as inactive (because 
elected) and the second rank vote, if any, becomes active, being 
added to the existing totals, according to the fractional value for 
other candidates. If multiple candidates are elected from a ballot, 
the fractions are multiplied appropriately, so that a voter, if the 
ballot is fully used up, has contributed no more than one full vote 
to all elections summed.
4. This iterates until all ballots have been read. No eliminations 
have taken place.
5. Because there have been no eliminations, all elections so far can 
be seen as rigorously correct and fair. And, so far, this is 
monotonic. You never hurt a candidate by ranking the candidate higher.
6. In an election where voters vote with rigorous coordination, this 
will elect the entire Assembly, with every voter being represented.
7. That won't happen, though. So when this process is complete, Asset 
process begins.
8. Any exhausted ballots, ballots read to the bottom of the list, are 
assigned to the candidate in first position, as their "property."
9. At this point, a choice must be made. What if a voter has voted 
A>B, and neither A nor B are elected directly? STV will start 
eliminating candidates, lowest vote first. There are other options. 
At this point, the election can collapse to pure Asset, so only the 
first rank on each ballot with any vote value remaining is still 
active. Lower-ranked votes for these ballots become moot. So it 
remains monotonic, by raising the rank of a candidate you either help 
elect the candidate, or you give the candidate more voting power in 
the choice of winners, or your raising is moot. It never hurts. At 
this point it is pure Asset, with some seats already assigned, 
following the wishes of the voters and no Asset decisions have been 
made. But an alternative.
10. The ballots are treated as Bucklin ballots. The second rank is 
counted. ("Second rank" means "second active rank.") Seats are 
assigned whenever a candidate, in a round of counting, gains a quota 
of votes, and those ballots are devalued accordingly. In this case, 
an elected candidate might be in a lower position on the ballot. The 
candidate is marked as elected, but the higher position candidate 
remains active.
11. When all ballots have been counted to the last rank, the election 
then collapses to Asset for any ballots remaining with unused voting power.
12. The Asset electors complete the election by negotiation of 
amalgamation of votes to the quota.

I believe this is monotonic. It is also an STV method, but does not 
use eliminations except of elected candidates. Asset in general 
doesn't actually eliminate any ballots or candidates. I do not know 
how Carroll would have specifically applied his asset concept to STV 
counting methods. I just made up the above. I actually prefer Asset 
with a non-ranked ballot. It is also STV, in fact, but with flexible 
vote transfer as determined by the effective proxy for the voter.

>The nonmonotonicity and non-precinct-summability of both IRV and STV
>arises due to its unequal treatment of voters' votes. I strongly
>oppose any method that treats voters' votes unequally in the counting

Sure. But that's a description of a consequence, not the actual 
problem. The problem is candidate elimination. Don't eliminate 
candidates, the problem isn't seen. There are STV methods, I think, 
that don't rigorously eliminate candidates, but handle the 
"single-vote" problem differently, but I don't know much about it.

> >
> > You should realize that those who are elected before eliminations, with STV
> > (and this includes IRV!) are obviously appropriate winners.
>Yes. I agree with that.

Thus the problem arises in or in connection with the eliminations. 
What would we call STV without eliminations? Bucklin! But it is not 
thought of that way, because of confusion over the meaning of "single 
vote." Approval is a single-vote method, in fact, because only one 
vote can elect, it never happens that a voter casts two votes that 
result in election. The votes are really, with more careful analysis, 
"alternative votes." Considered equally. With Bucklin, they are not 
considered equally, but all votes on all ballots that are at a 
certain rank are treated equally. That is, with Bucklin, your higher 
ranked vote is considered first, so it's not equal to your second rank vote.

In the method above, as seats are elected, the ballots are all 
treated equally, and, in the end all votes cast have been counted, 
and, to the extent not used to actually elect a seat, are transferred 
to the elector who will complete the election, presumably.

It's possible to use the Droop quota, as I mention, which is simply a 
lowering of the quota from V/Q to V/(Q+1). But that, then, will 
distort the true voting power of each seat to a (generally small) 
variation from it. It was intended to force, with fully ranked 
ballots, the completion of the election of all seats, and it really 
breaks down when true eliminations start, unless the quota remains 
the same, which will then result in failure to elect some seats, 
unless there are no exhausted ballots. If all ballots are fully 
ranked, using the Droop quota will mathematically guarantee 
completion, that's why it's done. But the cost is voter coercion.

> > The flaws arise
> > in elimination rounds. Get rid of eliminations, but sequentially pick
> > winners, that problem disappears, and you are left with only the problem
> > that if you use a single ballot, there will likely be seats where nobody
> > gets the quota. So what do you do?
>Not sure about that. Depends on if the reallocations if treatment of
>votes is equal for all voters or not I suppose.

The problem is the one Carroll considered. He got rid of true 
eliminations. I don't know how deeply he got into the details.

His solution not only treated all voters the same, it provided rights 
to the ordinary voter, not a specialist on politics, that were a dead 
letter previously, and that remain a dead letter today. 
Theoretically, you can vote for anyone, in the U.S., in most 
elections. But that's a right to waste your vote. With Asset, your 
unpopular vote is not wasted, it serves a purpose and is an actual 
exercise of voting power. One person, one vote. Period.

> > You can't hold a "runoff election," and here is why: Some voters 
> already got
> > their candidate. A runoff under these conditions has no way of knowing who
> > "won" and who didn't. You only want those who didn't "win" to be able to
> > vote. Asset Voting avoids this problem. Every ballot is available to be
> > voted. (I would recommend that every candidate be required to designate a
> > proxy, to vote for the candidate if the candidate becomes unavailable.
> > Consider how much easier this would be than holding a special election! And
> > that choice would be public record, I presume. No surprises.)
>If asset voting is *not* like STV and is monotonic, precinct-summable,
>fair and equitable etc. I would probably not oppose it, but personally
>I prefer the party list system with voter ability to alter the list
>order based on Condorcet counts better.

You could, with Asset, assign your vote to a party, which begs the 
question. How does the party determine the list?

The basic problem with your thinking, Kathy, is that voters simply 
don't have the information. Sure, they might trust a party more than 
a particular candidate. I don't oppose party list, but it moves the 
power base to political parties, which are sometimes closer to the 
people (good) and sometimes not (they can be influenced by the same 
media manipulation as the general voting process). And once we 
realize the potential of asset, we will realize that Asset can 
amalgamate representation through proxies that represent "factions" 
much smaller than political parties, that require no financing at 
all, just people talking to each other. That is the power of "no wasted votes."

> >
> > Asset will work with STV, and my prediction is that not too many will use
> > additional ranking on the ballot. It probably becomes unnecessary. Asset
> > would also work with IRV! It would make IRV into an excellent 
> voting method.
> > No majority, no election, runoff of some kind. If holding a runoff is a
> > problem, it would be obvious who could be blamed for it! 
> Candidates who were
> > unwilling to compromise. If that's a majority, I'd say this 
> electorate has a
> > problem! Normally it won't be.
>If IRV/STV counting methods are used, I oppose it due to its
>inequities and the vagaries the inequities cause.

Those inequities, however, generally bite only with the last election 
or last few elections. With five seats being elected in a district, 
as with some places, they are not major. They are still short of full 
representation. Why not go for full representation?

You do know the answer to that question, historically, don't you?

Because full representation will elect some Socialists, Communists, 
and, er, Negroes. New York, what, 1940s?

> > STV for proportional representation, even with eliminations, is much better
> > than multiseat methods in use. But I'm hoping that we can look at 
> ways to do
> > it even better, and what Asset would do is to create a penumbra of electors
> > that stand between the voters and those who are actually elected to the
> > Assembly. They generally represent the voters to those whom they 
> elect. This
> > "Electoral College" is *fully representative,* along the lines of that old
> > proposal for a city council where the winners exercise the number of votes
> > they got in the election. They are public voters.
> >
> > And there goes the need for campaign financing. Spending a lot of money to
> > get elected would become a suspicious action! Rather, 
> increasingly, electors
> > would not be candidates with a chance of winning, except in small
> > jurisdictions. They would be people, your neighbors for the most part,
> > interested in helping see that the people are represented in the Assembly.
> > You would know them personally, almost always. You could talk to them. And,
> > because it's known who they voted for in the actual seat elections, they
> > could talk to the seat holders directly, as people with real political
> > power, the power to elect, known and identified.
>Don't know about that. It sounds nice. Gotta get back to more coursework.

Real life? Come on, Kathy, I thought you were serious!

Good luck with it.

To an extent, this is pie in the sky bye and bye. But what I'm trying 
to promote, here, is a concept that would be rigorously fair, so we 
have something to compare existing systems with, as well as proposed 
reforms, so we can then judge whether they are moving in the right 
direction or not. First reform, please keep in mind, is Count All the Votes. 

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