[EM] Delegate cascade and proportional representation

[Michael Allan]

Raph Frank wrote:
> The problem I would have with your idea is that it
> encourages long voter chains (at least near the top).

Yes, I see what you mean.  My algorithm can only be an approximation
because it breaks down for extreme trees.  Your's is better:
 
> 1) Use d'Hondt to split seats between all root candidates

OK.  I thought a simple division would split them neatly, but I guess
it requires d'Hondt (or some other highest averages method) to
properly handle the remainders:

  http://en.wikipedia.org/wiki/Highest_averages_method
 
> 2) Each candidate, who receives seats, takes one.
> 
> 3) Algorithm is applied recursively, with each candidate assigning
> any spare seats to his clients proportionally.

Right, so the assembly is deeply proportional.

> This doesn't handle loops well/at all.  It basically requires a tree
> structure.

The general structure of a delegate cascade is actually a cyclic
graph.  But cycles can occur only at the bottom of each casacade,
where they result in pools.  Pools are equivalent to roots, so d'Hondt
(etc.) should still work.

Now I see another use for this algorithm.  I figure I can use it to
summarize the election results.  A pruned forest of trees is a better
summary than a ranked list of candidates, even for ordinary elections
(single office or norm).

-- 
Michael Allan

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