[EM] Delegate cascade and proportional representation

[Michael Allan]

Raph Frank wrote:
> On 8/22/08, Michael Allan <mike at zelea.com> wrote:
> > ...  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.
> 
> Maybe a rule like
> 
> 1) Find the candidate with the highest score that is part of a loop.

Except that all candidates are formally equal.  Their inputs (votes
received) all flood out to the same level (pool), giving them equal
measures of assent from the voters.  Without additional information,
there is no fair way to choose among them.

> 2) If there is a tie exclude from consideration any candidate who
> votes for a candidate who is also part of the tie.
> 
> 3) Of the ones remaining, pick one somehow (random?)
> 
> 4) Designate that candidate as abstaining
> 
> 5) If there are loops remaining goto 1)
> 
> This will create a tree structure.

In pruning for a PR assembly, maybe it's OK (at least for starters) to
iterate randomly, picking candidates from the cycle in any order.
Cycles ought to be rare, anyway.  The only motivation I can imagine is
where two candidates vote for each other because they happen to work
well together, as a team, and hope to attract more votes that way,
than as separate candidates.

In pruning for other types of election, where the purpose is only to
summarize the results, I would treat the cyclic pool as a single node,
and then make it clear (in the diagram, or whatever) that the node
actually represents multiple candidates.

But d'Hondt (etc.) will work nicely in both cases, as you originally
suggested.  Thanks for pointing this out.  (I'm unfamiliar with PR and
party lists.  We don't use them, here.)

-- 
Michael Allan

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