[EM] average over time proportionality election method

[Abd ul-Rahman Lomax]

At 07:18 AM 3/6/2006, Raphael Ryan wrote:
>If the number of votes needed to be elected is constant, then it 
>follows automatically.
>
>A candidate who gets 10% of this value every election will win the 
>seat every 10th election.  Someone who gets 25% of this value will 
>win the election every 4th election.
>
>The question comes down to how constant that threshold is.  It isn't 
>perfectly constant so the system isn't perfectly proportional.

It will never be "perfectly proportional." The quantization noise, 
very likely, would be too great. And it should be realized that there 
is a severe risk.

There is quite often a significant minority in favor of actions that 
would endanger the community. While there would be little harm in a 
few representatives in a large parliament being elected through this 
scheme, there would arise a risk that more than just a few would be elected.

There are other complications: candidates don't run again for various 
reasons. The transfer of votes mechanism was passed over with what 
look to me like major unsolved problems.

*However*, while the method is interesting, delta-sigma communication 
works when the update frequency is high. Delta-sigma with an update 
frequency of a year would not track the electorate very well. Indeed, 
what this system would do is to influence present assemblies by how 
the electorate felt years earlier.

Further, since the goal seems to be proportional representation, and 
there is already an excellent method on the table that *quickly* 
creates proportional representation without lost votes, and it does 
so almost immediately (and without party-list), the idea seems a 
purely abstract exercise in possibilities, something that we should 
certainly do, but not likely to be very fruitful in terms of ever 
seeing the light of day.

(The method is Asset Voting, and I've proposed a simple variant that 
uses existing ballots, FAAV, Fractional Approval Asset Voting. It is 
really a form of secret-ballot delegable proxy to create an 
"electoral college" and, when used for an assembly with substantial 
numbers of members, will use votes efficiently. It likewise considers 
"excess votes," i.e., votes that a candidate receives that are above 
the quota, which the candidate may reassign, and, likewise candidates 
not receiving the quota may negotiate with others to create 
additional winners. Wasted votes would, I think, be rare, and the one 
responsible for the waste easily identified (the candidate who 
received votes and who refused to reassign them) so that voters can 
respond appropriately the next election.

Asset Voting was invented by Warren Smith, and in it voters may 
assign fractional votes of any value to any candidate. I simplified 
that in FAAV by using a standard ballot and dividing any multiple 
votes. The effect is that the voter is either directly attempting to 
elect a representative, or is dividing his or her votes among a 
committee. Only one total vote is cast.

(An even simpler method would only allow one vote, but I dislike 
discarding ballots with overvotes, which is what happens and will 
happen. The down side is that FAAV would be more complex to count. 
That really should not be an issue in modern circumstances, and it 
could be done without computers without difficulty, but if it is an 
issue, single-undivided-vote Asset Voting would work almost as well.)

(To count fractional votesquickly by hand, given that the fractions 
would all be of the form 1/N, one simply tallies the fractions 
separately, so that for a single candidate, there would be M lists, M 
being the number of candidates, a tally would be kept of votes which 
were 1/1; 1/2; 1/3; ... 1/M. Then, when counting is done, the 
fractions are added to yield the reported vote. The total of all 
reported votes should exactly equal the number of votes cast aside 
from blanks, within roundoff error. If not, there is an anomaly.)