[EM] Delegate cascade and proportional representation

[Michael Allan]

Raph Frank wrote:
> Z(10) abstained/voted for self
> A(5) voted for Z
> B(3) voted for Z
> C(1) voted for Z
> 
> Y(5) abstained/voted for self
> D(1) voted for Y
> E(3) voted for Y
> 
> If there were 3 seats to assign, then would go
> Z gets 2 as holds 10 votes (2/3 of votes)
> Y gets 1 as holds 5 votes (1/3 of votes)
> 
> Y just keeps the seat assigned
> Z keeps one and passed the other down and it
> ends up with A.

Then I re-invented the same idea.  Maybe I can state it more simply?
Your notation is:

  c(W)

    c is a candidate (meaning one who receives votes)

    W is the voting weight (?)

  W = R + 1

    R is the count of votes received

The algorithm to populate an assembly of size N is simply:

  1.  Rank all c(W) in order of decreasing W

  2.  Choose the top N.
 
Votorola naturally ranks all its results in this fashion, so maybe
that's why the idea occured to me.

> With lots more seats and candidates, this would
> yield more accurate PR.

I guess it's an extreme example of a "tree pruning" exercise.  The
forest of all candidates is pruned down to the thickest roots and
branches, until it can fit into the limited space of the
assembly. (Picture the aftermath of a forest fire!)

Assuming complete freedom of voters and candidates to shift their
votes in the "living" forest, the PR in the resulting assembly will be
as accurate as possible (I imagine), given the constraint of N.  As N
increases, PR accuracy will smoothly approach 100%.

> Btw, is there a formal definition of delegate cascade.  Do
> voters just vote for 1 candidate?  (like standard DP)

Yes, just 1 immediate candidate - and then the cascade too, through
all of the intermediate delegates, to the end candidate.  Probably
this is standard DP (Abd says it is), but I have never seen a formal
definition of DP.  Do you have a reference for DP?

For delegate cascade, see:

  http://zelea.com/project/votorola/d/outline.xht

  http://zelea.com/project/votorola/d/theory.xht#delegate-cascade
    (very rough, badly needs weeding)

-- 
Michael Allan

Toronto, 647-436-4521
http://zelea.com/