It certainly fills out the matrix of available methods, but I'm not sure when I'd actually use it. I'm more interested in hybrid geographical/proportional methods these days, as I think such methods have the best chance to prosper in the US or UK. It would be nice to even keep existing district boundaries. I think that PR-SODA is very close to being able to do this; yes, it's cheating, but the basic idea is to elect candidates and then assign each district one winner per elected party. Yeah, that means that some reps might have 1 district of constituents, while others might have 2; but otherwise it actually works surprisingly well.
Oops. Ignore that, I don't want to hijack the thread. Jameson 2011/10/21 Ted Stern <[email protected]> > I had an idea for how Condorcet methods could be used for an open list > Droop quota-based Proportional Representation method, as an > alternative to STV. I am motivated by these factors: > > * I would like to avoid STV's elimination of candidates. > > * I would like a PR method that requires only a single summable count > for each seat selection. > > * I would like lower-rank preferences to be considered when choosing > each seat. > > * I would like to give voters' higher ranks a bit more of a chance > than they would have with straight Approval Transferable Vote. > > Here's my idea: > > Choose a Condorcet method. Schulze (winning votes) or any other > robust clone-resistant method would be fine. However, there may be > advantages to using an approval-hybrid Condorcet method such as DMC or > Forest Simmons' Enhanced DMC. > > Use some kind of ranked ballot, or rank inferred from rating. Any > explicit rank or rating above the bottom will be interpreted as > Approval. > > Give each ballot an initial weight of 1.0. > > Choose a quota. For example, I prefer the "easy" quota, (Number of > ballots + 1) divided by (Number of Seats + 1), no truncation. This is > slightly different than the standard Droop quota. > > While seats remain unfilled, > > Loop over all ballots: > > Accumulate into the pairwise array, with each pairwise vote > scaled by ballot's weight. Note: Calculate pairwise array only > for standing candidates; i.e., those who have not already won a > seat. > > Accumulate ballot's contribution to Approval for each candidate, > scaled by ballot's weight. This can be stored in the diagonal > entry of the pairwise matrix, if desired. > > If there is only one standing candidate remaining on the ballot, > accumulate this ballot's weighted approval into the Locked > approval for this candidate. This will be used to ensure that > ballots with truncated rankings are used up completely, while the > non-truncated ballots voting for a winner get to transfer as much > of their vote as possible. > > Find the Winner (CW), as defined by your robust Condorcet method. > If that winner has total Approval that exceeds the quota, or no > candidates have Approval over the quota, that CW is seated. > > Then let > > T = Approval Total for CW. > L = Locked Approval Total for CW > Q = Approval Quota > QML = max(Q - L, 0.0) > TML = max(max(T,Q) - L, eps), where eps is a small epsilon, say 1.e-9. > > The fraction of CW's total score sum used up, U, from all unlocked > ballots voting for CW, is: > > U = QML / TML > > Apply the following rescale factor to each ballot that contains an > explicit ranking of the CW: > > F = 1.0 - U > > [For efficiency, rescaling can be delayed until the ballot loop on > the next iteration.] > > What do you do if the normal CW's Approval does not exceed the > quota, but there are other candidates whose score *does* exceed the > quota? > > In that case, compute a *reduced* Condorcet Winner from among those > candidates whose total Approval score exceeds the quota. > > This step is where an Approval-hybrid method such as DMC may be > useful -- if there are candidates above the quota, you can > terminate the search for the CW once you've descended below the > quota. > > In the single-winner case, this would also differentiate this > method from standard Schulze, for example. > > Note that in the other already-handled case where all candidates > have scores below the quota, there is no vote transfer -- each > ballot ranking the CW is used up completely. > > --------- > > This method is Droop Proportional: If a faction of voters approves M > candidates, and has at least L * Q votes, then L candidates out of > those M will be seated. > > This method would have significantly larger overhead than this > Bucklin-based PR method, Graded Approval Transferable Vote, which is > quite similar: > > https://github.com/dodecatheon/graded-approval-transferable-vote > > Why would a Condorcet-based variant of Approval Transferable Vote be > an improvement over a Bucklin-based method? The main difference is > that lower rank preferences will be considered for each seat, so cases > where two "clone" candidates have very close first-rank totals will be > decided more robustly. > > I think that in practice, the first few seats of any faction will be > chosen similarly by either method. The difference will come in the > last one or two seats, especially if the remaining votes are very > close to the quota. > > It might also seem like choosing the CW for each seat may be using too > low an approval and thus use up too much of each ballot that rank's > that seat's CW. > > However, in the Bucklin-based method, the "approval" total does not > necessarily include the total votes at any explicit rank. It depends > on how low the threshold has descended. So the actual approval score > used to calculate vote transfer will probably be quite similar when > comparing the methods, and the amount on each ballot that is used up > will also be similar. > > Any thoughts? I'll try coding up a version of this eventually ... > > Ted > -- > araucaria dot araucana at gmail dot com > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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