[EM] SODA

[fsimmons at pcc.edu]

From: Jameson Quinn 
> Here's the scenario you used to first show your tree method of 
> determiningdelegation order.
> 
> 16 A1>A2>B
> 12 A2>A1>B
> 24 B>A1=A2
> 48 C
> 
> What if some candidate outside the A1 A2 faction had an A2>A1 
> preference? I
> mean either:
> Scenario S
> 16 A1>A2>B
> 12 A2>A1>B
> 24 B>A2>A1
> 48 C
> 
> Or:
> Scenario T
> 16 A1>A2>B
> 12 A2>A1>B
> 24 B>A1=A2
> 43 C
> 5 C>A2
> 
> Or even:
> Scenario U
> 16 A1>A2>B
> 12 A2>A1>B
> 24 B>A1=A2
> 43 C
> 5 A2>C
> 
> I believe that A2 should go first in all of the above scenarios. 

I agree, and my coalition tree/DAG idea doesn't work, so let's scrap it.

However, before we settle on a quick and dirty way of deciding the player order, I suggest that we do find 
an ideal way as a standard of comparison for competing approximations.

The ideal way should generate a clone consistent monotonic list from ballot rankings.

Short of CSSD itself, note that DAC (Descending Acquiescing Coalitions) elects A2 in all three of the 
scenarios S, T, and U above, and A! in the original.  So use DAC to get the first player, and then to get 
the next player use DAC to choose from the remaining candidates, etc.

DAC is easy to describe and easy to do in O(n*m) steps where n is the number of candidates, and m is 
the number of factions, which in our case is also n.

On another note,  I think it is important to get a fairly complete ranking for each faction to avoid the 
temptation of playing chicken before the approval stage by truncating the rankings.  I'm not saying that 
the candidates have to submit a complete rankings, but we need a way of more or less completing the 
ballots that have truncations and equal rankings.

Here's what I suggest.  To complete (or nearly complete) the ranking submitted by candidate X, take a 
weighted average of all of the approval ballots (i.e. non-delegating ballots) that approve X, with the weight 
of each such ballot being the reciprocal of the number of candidates approved by that ballot.  Use this 
weighted average of approval ballots to break as many ties as possible in the ranking submitted by X.

Note that if candidate C bullet votes, then the supporters of candidate C who have strong opinions about 
second and third choices will have significant incentive to submit approval ballots.

Once the approval ballots have been used in this way to help fill out the rankings, we restore full weight 
to each of them for the final approval count..