[EM] A DSV method inspired by SODA

[fsimmons at pcc.edu]

One of the features of SODA is a step where the candidates decide what their approval cutoffs will be.on 
behalf of themselves and the voters for whom they are acting as proxies.  One of the many novel features 
is that instead of making these decisions simultaneously, the candidates make them sequentially with 
full knowledge of the decisions of the candidates preceding them in the sequence.

I wonder if anybody has ever tried a DSV (designated strategy voting) method based on these ideas.

Here's one way it could go:

Voters submit range ballots.

Factions are amalgamated via weighted averages, so that each candidate ends up with one faction that 
counts according to its total weight. For large electorates, these faction scores will almost surely yield 
complete rankings of the candidates.

>From this point on, only these rankings will be used.  The ratings were only needed for the purpose of 
amalgamating the factions.  If we had started with rankings, we could have converted them to ratings via 
the method of my recent post under the subject "Borda Done Right."  In either case, once we have the 
rankings from the amalgamated factions we proceed as follows:

Based on these rankings the DSC (descending solid coalitions) winner D is found.  The D faction ranking 
determines the sequential order of play.  When it is candidate X's turn in the order of play, X's approval 
cutoff decision is made automatically as follows:

For each of the possible cutoffs, the winner is determined recursively (by running through the rest of the 
DSV tentatively).  The cutoff that yields the best (i.e. highest ranked) candidate according to X's faction's 
ranking, is the cutoff that is applied to X's faction.

After all of the cutoffs have been applied, the approval winner (based on those cutoffs) is elected.

It would be too good to be true if this method turned out to be monotone.  For that to be true moving up 
one position in the sequence of play could not hurt the winner.  Although I think that this is probably 
usually true, I don't think that it is always true.  Anybody know any different?