[Election-Methods] Measuring power in a multi winner election

[Abd ul-Rahman Lomax]

At 11:22 AM 9/21/2007, Howard Swerdfeger wrote:
>The drive behind thes moves it usually that the old system fails to
>translate votes into seats "fairly". (Votes != Seats)

If we want to understand fair proportional representation, we must 
look back to the principle of representation itself, and to pure 
representation, which does not involve elections, except in the most 
basic technical sense.

If we have an assembly at which all members of a society may attend 
and vote, and if every eligible voter actually attends and 
participates, we have a pure and complete democracy. Unfortunately, 
as scale increases, and even on a small scale in common situations, 
this goal is impossible to attain, because there are differing 
abilities of members to actually attend a meeting and devote the 
necessary time to the issues. So even Town Meeting government, as we 
have in New England in many small towns, fails in certain respects. 
Town Meeting in the small town where I lived for some years often had 
trouble finding a quorum for meetings, and the quorum was five 
percent of town members.

However, it still worked reasonably well, because town government 
tended to operate seeking consensus. These were neighbors and 
friends, and the people who actually attended Town Meeting were, 
informally, representing many of those who could not. But not all, 
and not proportionally, which we could see clearly in some situations.

Massachusetts law requires secret ballot votes, at the regular polls, 
for tax overrides. It is fairly common for a tax override to be 
approved by Town Meeting and to fail at the polls. Obviously, Town 
Meeting is not accurately representing (or shaping, same thing) Town 
opinion. We can presume that most people active in Town Meeting also 
vote at the polls, but then there are many more who vote in the polls 
but who don't attend Town Meeting (perhaps larger by a factor of ten or so).

So, in order for everyone to be represented in an assembly, we need 
some kind of representation. There are two basic forms, and the 
difference between them is so drastic that it is a wonder to me that 
we have the one, in political practice, supposedly in democracies, 
when, in situations where people have free choice, they would never 
pick it! But, to my knowledge, for governmental applications, we have 
never been offered that choice, and, where we might have been able to 
implement it -- as with Town government in New England -- the idea 
seems to have never even occurred.

The two systems are, of course, elected representatives by some 
scheme, for better or worse, or chosen representatives. A "choice" is 
an "election" which is why I will acknowledge that proxies are 
"elected," but it is not a contested election. That is, the "voter" 
has the absolute right to choose anyone as representative, or to 
participate personally. This is the *norm* in business! But it is 
*never* done in politics!

Part of my task is to ask the obvious question, as with the emperor 
wearing no clothes: "Why?"

I do have pieces of the answer, but it is an open question. Much of 
it is simply history. Our present governmental systems, in 
"democracies," evolved from undemocratic forms, with a gradual 
extension of freedom coming down from the top. That is, a collection 
of feudal lords were able to demand rights from the sovereign whom 
they chose to govern the overall society. But they were a small 
group, and they had no need for proxy representation. (But note that 
in some assemblies, even governmental ones, such as in New York, 
members can vote by proxy in some situations, I think committee votes 
can be by proxy. And there are moves to attempt to limit this, it 
being considered an abuse, and if a "proxy vote" is merely an 
absentee vote, I agree. The systems I propose do not necessarily 
allow directed votes; rather, the proxy simply votes, and those 
represented are considered to have voted in the same way, unless they 
intervene and vote directly.)

Proxy democracy creates a perfect PR assembly, practically by 
definition, but it is not, generally, a peer assembly. There is a 
variant which, with a sufficient "district" size -- particular an 
election district which is the entire jurisdiction -- is usable with 
secret ballot, and which creates *almost* perfect proportional representation.

Note that I say proportional representation, not proportional voting. 
However, when we have party-based PR, and we assume party-line 
voting, then voting power and representation are essentially the same thing.

But the key to understanding PR is not voting power, per se, but 
rather moves two tumblers: (1) representation in deliberation, and 
(2) representation in voting.

One of the realizations I came across in this study was that the two 
were separable and have different requirements. One of the reasons 
that direct democracy has been considered impossible to scale has 
been that the two were not separated. Direct participation in 
deliberation is what is impossible for all, when the scale is large, 
the noise becomes insuperable.

(There are attempts to deal with the problem, to be sure, in certain 
web communities, but they involve software filtering based on voting. 
These are *not* direct democracy, they are machine-mediated 
representative democracy, where the machine acts as the 
representative, amalgamating judgements by members without exercising 
focused intelligence. I haven't participated in such communities, but 
I pretty much know what to expect: frustration. Nevertheless, there 
are hybrids possible which could ameliorate this, but then we would 
look at what the hybrid would involve... which is what I'm proposing.)

Direct voting has been possible for a long time. Direct voting has a 
severe problem if it is exclusive of representative voting, but this 
problem was solved long ago, or, more accurately, it never arose in 
the business applications, because the foundation in business was a 
full and direct democracy of money, i.e., of shares. If you owned 
shares, you had so many votes, period, and you could vote directly or 
by proxy. Some corporations (particularly co-ops and the like) had 
only one share per member allowed, any other capitalization was 
through loans and bonds, so these were, in fact, one-vote per member 
democracies. But, often, I've seen, proxy voting is prohibited.

And the arguments for the prohibition are not against proxy voting, 
per se, but against *directed voting*. In one organization, the 
argument against proxy voting was specifically given in the rule, and 
it clear was referring to an absentee vote, where a member present 
says, "I have the vote of so-and-so on this subject," which is 
offensive, because so-and-so did not participate in the deliberation 
leading to the vote, and has simply assumed that the vote is a fixed 
thing. Which is contrary to the basic principles of deliberative 
democracy, which include the *necessity* that people change their 
minds when exposed to debate and deeper consideration.

To the point: the standard for measuring PR, to my mind, is the 
extent to which voters are represented by free choice. While it is 
true that electoral systems create strategic necessities for voters 
to select representation from a limited set, we can still attempt to 
measure the performance of an PR system in terms of the degree to 
which it assigns representation proportionally to voting choices by 
the voters. We can also look, separately, at the limitations the 
system places on those free choices. But we would start by *assuming* 
that the choices were free, even if they are not in reality.

There is no way for any election system to match the representational 
power of delegable proxy, creating an assembly which represents in 
deliberation nearly all voters by a representative chosen directly or 
indirectly, without contests, and which allows all voters to vote 
directly, if they choose, but by proxy if they do not vote 
themselves. However, this creates an assembly where the voting power 
of members can vary greatly. But for representation in deliberation, 
voting power is not an issue, voting power only becomes an issue when 
decisions are being made. The issue is more complex than I can 
completely present in a few paragraphs, so at this point I'm simply 
holding up a PR assembly, created through delegable proxy and through 
participation rules set by the assembly itself, not by law. That is, 
the law creates the Assembly itself and provides it with whatever 
decisive power is considered appropriate, and does create or confirm 
basic rights of all "members," which can be all voters in pure DP, or 
"electors," in Asset Voting, but leaves the rules of the Assembly, 
which govern, among other things, floor access, to the Assembly 
itself, which may create whatever rules it considers appropriate to 
govern its process, provided that they preserve the basic rights of 
members as provided by law.

Asset Voting is a system which can create a PR assembly that is 
almost as representative as a DP one, but the ordinary voter has two 
choices: the voter may vote for anyone through secret ballot, and 
may, *in addition,* register as a "candidate," at very low cost -- or 
no cost. Any candidate who gets at least one vote (his own?) becomes 
an elector; an elector is a public voter, all votes cast by electors 
are public record.

Thus we can have a direct democracy -- direct democracy does, in 
fact, require public voting, if it is to be true deliberative 
democracy -- with a reduced set of voting members, who have variable 
voting power. In Asset, these members may create "seats" by 
amalgamating a quota of votes. But if it is Direct Democracy - Asset 
(DD-Asset), votes which are not assigned to seats are still active, 
they are not wasted. Seats are created for the purpose of standard 
representation in deliberation as well as with voting, and the vast 
majority of voters, I'd predict, would in fact have their vote 
assigned to a seat, so that if they do not vote directly, their 
voting power is exercised by someone they chose, directly or indirectly.

The Asset creates a peer assembly that is likewise pure PR, with 
deviations from it being extremely small and practically trivial. No 
votes are lost, no voters are unrepresented unless they are not 
electors and they chose someone who defaults. TANSTAAFL.

(Note that if electors use DP to amalgamate their power, and if proxy 
voting is allowed for electors, *outside of the assembly*), the 
electors with no seat assignment still, nevertheless, have the 
advantage of concentrated voting power and the associated efficiency.)

Now, if we neglect the constraints on choice, STV with many seats can 
get pretty close to this. A very rough estimate of the degree to 
which STV fails this Representation criterion is the difference 
between the Hare quota and the Droop quota. The Droop quota assumes 
representation failure!

Asset, accordingly, would use the Hare quota, and would accept the 
possibility of a vacant seat, or even of a few. Given the direct 
voting possibility, and the existence of sub-seat representation in 
effect, the loss of a seat or two is actually harmless. Even that 
could be remedied, but I won't go there now.

Now, where does Swerdfeger go with this?

>but most of these reforms fail to recognize that that Seats do not equal
>power. So we are still still stuck with a similar problem (votes != power)

I don't find the proposition "seats do not equal power" clear. That 
is, neither the meaning of "seats" or "power" are defined. If you 
have a standard by which you can amalgamate seats to consider them a 
block, then you are defining a block with so many seats worth of 
voting power. In Asset, though, the voting power associated with 
seats is only a default, in actual votes, the votes of those with 
seats can be deweighted according to how many direct votes are cast.

Ah, yes, it should be mentioned. In Asset, the votes that create a 
seat are identified, and they come from specific electors, they are 
not just assigned as a pool. (Warren's original Asset completely 
ignores this issue, he has been interested in "election methods," not 
in representational process.) So we know which seat's vote to devalue 
if an elector votes. This also has the highly desirable trait that 
electors (and thus voters, who know whom they voted for) have a 
specific seat representing them. And then we can also see why direct 
democracy of this kind requires public voting. Without public voting 
-- or some god-machine running things -- there is no way to have 
simultaneous direct voting and representative voting.

Completely missed in many discussions of representative democracy is 
the back and forth between voters and those they represent. Some 
assume that the ideal representative would vote the way the voter 
would vote, always. But that is actually quite sub-optimal! If I 
manage to elect, as my representative, a perfect person, who always 
gets all decisions right, I'm quite sure I will disagree with some of 
them! (By "right," I mean that, if matters were sufficiently 
explained to me, I would agree. I'm not necessarily proposing an 
absolute right or wrong. I'm simply acknowledging that, generally, my 
representative will be more informed on the matters being voted on, 
and when he or she is not, that I can discuss it with my rep. Or if 
not with my rep directly, because the scale is too large, then with 
someone who has better access than I to my rep. And with Asset, I 
have that specific chain of representation. If I'm an elector, it is 
quite specific and known by the rep as well, if I'm a voter but not 
an elector, I know and can, if I wish, represent that I voted for a 
specific elector, and precinct records would confirm at least one 
vote from my precinct -- which is also public record. Not proof, to 
be sure! But so what?

>I was looking into 2 methods of measuring power in a weighted voting system.
>
>http://en.wikipedia.org/wiki/Banzhaf_Power_Index

This index does not apply to an Asset assembly because the power of 
all voters to change the outcome is equal. Nor, in fact, does it 
apply to a PR assembly where seats have equal voting power. Only if 
we attribute the voting power of seats to the voters who created them 
with their votes do we see, with STV, for example, variation. The 
variation is between 100% (i.e., 1/N in an Assembly with N seats), 
down to 100% * Droop/Hare. Do I have that right?

>http://en.wikipedia.org/wiki/Shapley-Shubik_power_index

Reflects the power of coalitions. What's a "coalition"? For this 
purpose, it is people who vote together. Could be a political party, 
could be any kind of caucus.

>I was wondering first if there are any methods of measuring power in a
>legislature that I am unaware of? Secondly if anybody has tried to
>design a generic system where by votes are kept proportional to power,
>via allocation of seats?

Yes. DD-Asset does it perfectly. If you look at the default voting 
power of seats, they are identical (down to a fraction of a vote, for 
seat assignments in Asset are created through *exact* quotas, which 
are not generally integers. In Assembly votes, I'd assume that each 
seat would have exactly one vote, and that this represents Q voters, exactly.

I've said all of this before, and there is an obvious contradiction 
in what I've written in this post. But most readers don't read 
carefully enough to notice it. I wonder if any will. Yes, there is 
answer, a resolution of the contradiction, but I've never written 
about it. And I won't at this point.... I won't even give a hint, 
except through the position of this note, unless asked. In any case, 
the point belongs in a full discussion of Asset and what it could do.