[EM] Voting systems theory and proportional representation vs simple representation.

Abd ul-Rahman Lomax abd at lomaxdesign.com
Sat Mar 13 11:53:52 PST 2010

Voting systems theory should properly be a subtopic within social 
choice theory, which is -- or should not be -- based on instantaneous 
process, as from a single ballot, but from the whole set of 
procedures whereby a community of interest discovers and makes choices.

In small-group process, choices by secret ballot are quite unusual, 
outside of elections, and, again, in such process, even with secret 
ballot (which is by no means universal), voting is traditionally 
vote-for-one, with a majority required for a result to be declared, 
otherwise the election is null as to legal effect and "must be 
repeated," in the language of Robert's Rules of Order. Which means, 
among other things, no eliminations are automatic, they are voluntary 
or up to whatever renomination process is used. However, the repeated 
ballots are based on information from prior ballots as to likely 
results, thus the results shift as voters compromise their positions, 
with communication outside the ballot process being quite likely. In 
the end, the proof of adequate compromise is in a result approved by 
a majority, and, in some organizations, even a supermajority is required.

Generally, standard democratic choice is through votes which are Yes 
or No on stated propositions, which are themselves amendable through 
Yes or No votes on proposed amendments. The amendment process 
typically procedes until there is a supermajority in favor of closing 
debate and process on each amendment and then on the main motion. 
Thus a single final Yes or No decision may have been preceded by many 
polls, compromises, etc.

Elections with multiple candidates might be seen as an exception; 
however, if the majority requirement remains, it represents a 
collapse of a longer process that would be the more rarely used 
election by orginary motion. Election by motion is, intrinsically, 
with adequate participation, Condorcet-compliant, and probably tends 
to be more social-utility optimizing than we might expect, in healthy 

However, with public elections, and particularly with secret ballot 
and the lack of an ability to conduct repeated ballots in short 
order, the focus came to be on methods of determining some kind of 
ideal winner from a single ballot, and this has suffered from lack of 
precision in the definition of "ideal winner," there are competing 
criteria that can sound optimal at first blush that may not be so. 
Returning to basic social choice process, it is easy to demonstrate 
that, under some conditions, the winners required by the Majority 
Criterion or the Condorcet Criterion may not be ideal, with ideal 
being defined as a result that would be approved by *all* voters 
given full information. (I have used the "pizza election" to show 
this, with an "ideal result" that would be approved unanimously by 
voters, even though the first preference of a supermajority of voters 
was different.)

It is possible to roughly predict such results using social utility 
analysis, in situations where true absolute voter utilities are 
known. Those situations are rare; however, their value was not 
recognized by Arrow et al. Individual voter preferences are not fixed 
things, they are an interplay between the voter's ab initio 
preferences, which may be initially uninformed, and the preferences 
of the rest of the society. It is possible for voter preferences to 
actually reverse based on knowledge of the preferences of other voters.

But when it comes to representation in public process, where scale 
does not allow direct participation by all voters, it has sometimes 
been assumed that representatives would be chosen based on overall 
utility for each choice, and this is diametrically opposite to the 
principle of representation by choice, as distinct from 
representation by appointment. I.e., the King might appoint a 
representative for a colony, that's by appointment, obviously. A 
choice of a single representative for a community by majority vote 
(or worse, plurality) is representation by election for the community 
as a whole. But it is not representation of the individual voters by 
choice, and those who did not explicitly accept the winner cannot be 
said to be personally represented in whatever decisions the elected 
representative makes.

Proportional representation was intended to address this, bringing, 
at least and in theory, various factions to the legislative table so 
that they may negotiate more broadly acceptable solutions, which then 
become, to the extent that they are, in fact, more broadly accepted, 
unifying factors for the society, which increase efficiency and 
voluntary compliance and support and a sense of connection with government.

However, the concept of representation remained collective rather 
than personal, severely limiting this approach. Generally, with PR, 
it is a party that is represented. If one is in a minority in the 
party, one can easily end up inaccurately represented. A totally 
different possibility has been suggested from time to time, but it 
has never, to my knowledge, been used in political elections. It's 
standard practice with corporations, in theory, though it is in 
practice corrupted by certain power-centralizing practices which were 
allowed to disrupte the democratic character of corporate elections, 
and shareholders were not sufficiently organized, independently of 
the corporations -- centralized power -- to resist this.

Corporations generally allow proxy voting, so that those who actually 
vote in corporate elections or other decisions made at regular 
meetings of the shareholders are casting votes not only for their own 
shares (if they have any, there are professional proxies who do this 
representation), but for those who have voluntarily chosen them as 

Attempts have been made to apply this to public elections. I forget 
the city, but there was a proposal in the early 20th century to hold 
an election for a City Council where, in the council, representatives 
would exercise the votes they recieved in the general election. This 
would have been, for the first time, true and accurate representation 
before the Council. Because some council members would have many more 
votes than others, others would have less; this would produce a more 
representative result than a scheme in which votes are allocated to 
seats equally, because smaller groups could still obtain seats. 
(Assume a fixed number of seats. Suppose the top N vote-getters are 
elected in a vote-for-one election. Look at the minimum number of 
votes obtained by a candidate who nevertheless obtained a seat. In a 
system which redistributes votes somehow so that a faction with 2Q 
votes gets two seats, and Q votes are required to win a seat, and 
there are N seats, compared to one where the top N candidates get 
seats, with variable voting power, it's obvious that since for some 
seats in the latter case, more than Q votes were obtained, some must 
have less, and thus smaller factions get representation.)

Arguments against systems like this, on the face, seem to be based on 
the idea that it would assign too much power to individuals, though 
the power of an indivicual councilmember would probably be less than 
that of, say, a single elected mayor; I would more precisely claim 
that opposition is based, in the end, on distrust of democracy.

Fortunately, a relatively simple system, rooted in early study of 
Single Transferable Vote by Charles Dodgson (Lewis Carroll), 
published in 1884 or so, allows the creation of a peer assembly, 
where all seats represent exactly the same number of voters. Dodgson 
recognized a basis fact of electoral democracy, one which actually 
underlies the power of Plurality Voting and explains why, in spite of 
its obvious deficiencies, it has remained: most voters have 
sufficient information to be clear about their Favorite, but may have 
much less information about lower preferences. Thus preferential 
ballot, so easily seen as obviously superior, may be collecting 
noise, unless special importance is given to the first preference. 
And where that preference is not strong, this, too, may be quite 
noisy. Dodgson harness the power of first preference, to create 
accurate proportional representation that did not effectively 
disenfranchise those who only voted for one candidate (when that 
candidate did not win). He hit upon the idea of what Warren Smith 
later called Asset Voting; it was earlier known as Candidate Proxy 
when proposed by Mike Ossipoff and Forest Simmons in the late 1990s. 
In an STV election, let the candidate in first position on any 
otherwise exhausted ballot recast the vote.

Dodgson's proposal was lost in the noise for a long time, even though 
he's been considered one of the foremost experts on voting systems of 
the nineteenth century. The implications and possibilities are 
enormous, from such a simple tweak.

A long time ago, the United States was founded on rhetoric about "No 
Taxation without Representation." But I have personally never been 
represented by anyone I chose, nor, even, by the somewhat lesser 
standard of being represented by someone who was chosen by someone I 
chose. In direct democracy (i.e., New England Town Meeting 
government), I can vote directly on many issues. But as the scale has 
increased, this ability is almost always lost, for reasons that are 
obvious and that are not addressed merely by devices such as internat 
voting. Deliberation by representation is essential when the scale 
becomes large.

And no voting system that massively anonymizes the process can 
actually create this, no matter how idea the system seems on pater as 
to "social utility" or various measures of representational quality. 
What Asset Voting would do is to create a set of "electors" who then 
*publicly* elect an assembly to actually conduct legislative 
business, which could include the election of public officers, which 
can then use the highly effective deliberative processes, not 
depending only on limited single-ballot procedures or even restricted 
ballot (i.e., top-two runoff, as an example).

I would know where my vote went, exactly, I would know if it was used 
a part of the election quota, or perhaps was wasted, and if it was 
wasted, in general, I'd know that the candidate I trusted might be 
responsible. I've recommended the Hare quota, i.e., a fixed quota 
designed to set a maximum number of seats, not to necessarily elect a 
fixed number. I.e., if candidates holding the dregs cannot find 
compromises, they and those they represent lose representation, until 
and unless they do compromise. If Assembly rules require, at least 
for some purposes, an absolute majority of the theoretical maximum, 
there is no gain in power by refusing to compromise, there is, 
instead, a small loss.

Under these conditions an absolute majority of the Assembly would, 
with absolute free choice in representation, represent a majority of 
the electorate. I know of no other proposed system of proportional 
representation (other than variations such as the early 20th century 
variable voting scheme described above) that can accomplish this.

Because the electors are public voters, who have assigned their votes 
in a public process, it also becomes possible to separate 
deliberation and aggregation. I do not know how much difference this 
would actually make, given how freely seats would be elected, but if 
electors are allowed to vote directly on any issue before the 
assembly (other than Questions of Privilege, another matter), the 
seats can be seen, then, as representatives in deliberation and only, 
in aggregation, as "default voters." The process would work fine if 
no electors vote directly, but it means that the dregs, the votes not 
used to elect a seat, would not be wasted, they could still be 
exercised, if the electors took the trouble. It means that an elector 
might more readily make a compromise based on general usefulness in 
deliberation, even if the elector fears that he or she will disagree 
with the choice on some issue. An elector holding a lot of votes 
might have some significant impact, if the vote was close in the Assembly.

Asset Voting could create a penumbra of electors who serve as 
intermediaries between anonymous voters and elected seats. Electors 
are directly chosen, presumably with little or no restriction. I 
could choose someone with whom I can actually sit down and talk. My 
elector will generally be known as someone with influence over the 
seat, because the votes are explicitly known. Asset Voting would 
connect me with the Assembly. To get something to the floor of the 
Assembly, I'd only need to convince my elector that it's worthwhile, 
and then the elector must convince the holder of the seat. Yet 
general noise, bad ideas, etc., would tend to be filtered out, but 
not with simple rejection and igorance, as happens at present. My Bad 
Idea would be rejected, hopefully, by a specific person, either my 
elector, or, at the next step, my elected seat. Who can explain it, 
through the elector. Someone I trust, in general. If it actually goes 
before the Assembly, then I know that it has a shot at being 
considered by a wider group. If for some reason, my elector and seat 
aren't willing to consider it, I can find anyone else with a 
different elector, and the idea has a shot.

For very popular electors, the scale would be too large, and I'd 
expect the system to adjust toward smaller and smaller vote counts 
for electors, with, possibly, intermediate aggregations, more or less 
along the lines of delegable proxy. But delegable proxy could be 
totally informal, advisory, which is pretty much how I've proposed it 
everywhere. It's just a way of communicating in large-scale 
organizations, that can also help with very small-scale organizations.

So I'm not terribly interested in methods of aggregating 
representation through theoretical optimization from a single ballot. 
They seems like utterly impoverished approaches to me, that would not 
result in true, clear representation. The social intelligence of a 
single ballot is very, very limited, given that alternatives not only 
exist, they are routine in small-scale direct democracy and in 
certain large-scale applications. Proxy voting is considered 
inappropriate in membership organizations, by Robert's Rules of 
Order, for reasons that I won't go into here, but RRONR was 
contemplating only direct democracy, as practiced and implemented for 
centuries, and, I'd suggest, the arguments against proxy voting were 
shallow, mostly based on the idea that property rights are not 
represented; they are quite in favor of proxy voting with respect to 
property rights.

But ... what if the members of an organization are encouraged to 
think of the organization as "theirs" in some way? What if the 
property right analogy is more applicable than was thought, what if 
this would encourage a deeper sense of participation and "ownership"? 
If I invest a thousand hours of volunteer time in an organization, 
how is this different from investing thousands of dollars in some 
piece of property. The difference I see is that in the organization, 
generally a nonprofit, I don't gain "personal ownership." But there 
are other kinds of ownership, including collective pride and a sense 
of responsibility.

However, Asset Voting only represents narrow representation by what 
resembles proxy voting, in the process of electing an assembly. I 
raise the ownership issue because, indeed, I believe that our 
societies will function better if citizens feel "ownership." I've 
seen it in small New England Town Meeting towns. Citizens have the 
sense that it is "their town" and "their town government." They take 
responsibility for the town and for each other. What if we could 
foster this on a large scale? Wouldn't that be interesting?

The biggest opposition to Asset Voting, once the power of it is 
realized, would be from political parties and those who benefit from 
the divisions that political parties represent. Parties must 
amalgamate issues to be efficient, so minority representation gets 
lost; if you are, as an example, a Pro-Life Progressive (they 
exist!), you are out of luck. Even though, in theory, if you are 
truly pro-life you would also be against war and the corporate rape 
of the planet (from this point of view). Asset makes political 
parties much less important, I'd expect, because it's people being 
elected, not parties or issues, even though these people may have 
their own political affiliations and issues they consider important. 
They would not need to affiliate with a party to gain voting power as 
electors, and because the electors are a reduced set of voters, they 
might be readily elected based on personal communication within the 
elector body with no need at all for public campaigning, which 
requires major expense.

Address campaign finance reform by making it unnecessary! Tell me, 
what would you think of someone who tried to persuade you to vote for 
them instead of a person you already trust, by spending a lot of 
money? Would you be inclinded to trust this person? I wouldn't! The 
very fact of campaign spending, in an Asset environment, would mean 
that the person has some axe to grind, some cause to advocate, a 
cause that can collect money, and the most obvious candidates would 
also be major sources of corruption, who, instead of relying upon 
cogent argument and relationships of personal trust, want to 
influence large numbers through media manipulation.

I don't think this is a difficult argument to fathom! The fact is 
that most voters do *not* trust politicians, it's a profession that 
is down somewhere below "user car salesman." They don't trust them 
because they know that the system requires politicians to lie in 
order to gain enough votes to win election, and that politicians must 
also gain campaign funding, which is most easily gathered through 
large donations from special interests of various kinds. Voters 
nevertheless vote for these politicians, whom they do not trust, 
because they don't have any other better choice that wouldn't waste 
their vote. And many don't vote at all, because they have no 
confidence that their vote would make any difference at all.

Asset Voting causes every vote to count, to make a difference. In the 
systems I'd propose, if you don't trust *anyone* (a bad condition to 
be in!), you can register as a candidate for a nominal fee and vote 
for yourself, and then participate directly in subsequent process. 
But most people would not bother with that, too much work for too 
little benefit, if one only gets one vote. (It might be necessary to 
get two or three or more, and registered candidates might be required 
to cast a separate identified preferential ballot when they register; 
the "two or three" might be necessary for security reasons. Details. 
If they get less than the minimum number, then, in the actual secret 
ballot process their vote would be reassigned to a candidate from 
their preferential ballot and the official results would only show 
that the candidate got less than the minumum, it would otherwise be 
anonymized. Under this scheme, candidates would not vote in the 
general election directly, they would vote by identified ballot.)

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