[EM] A variant of DSC

[fsimmons at pcc.edu]

Thanks for the thorough analysis, Chris.

It seems to me that the crux of the matter is the same as the open vs. closed primaries dilemma.

If you vote sincerely in a closed primary, you may be supporting a candidate that will not be competitive 
in the larger competition. On the other hand an open primary might be highjacked, among other 
problems.

Woodall's DSC is like a closed primary.  It narrows down on a clone set, and the ballots that rank 
members of that set highly are the ones that determine the winner.

My variant is more like an open primary; it allows all ballots equal voice in determining whom to elect 
from that clone set.

It seems that this dilemma is one of the most fundamental of our subject.

> From: "C.Benham" 
> To: election-methods-electorama.com at electorama.com
> Subject: [EM] A variant of DSC
>
> Forest,
> 
> Your suggested variant of DSC doesn't address DSC's bad failures 
> of 
> Mutual Dominant Third and Minimal Defense.
> 
> 49: A
> 48: B
> 03: C>B
> 
> The biggest solid coalition is {A}49, so both DSC and your 
> suggestion 
> elect A. But MD says "not A" and MDT says "B".
> 
> >"As near as I can tell, my version still has all of the 
> advantages of DSC, including later-no-harm, clone 
> >independence, monotonicity, etc."
> > 
> >
> 
> Your version fails Later-no-Harm:
> 
> 49: A
> 27: B>A
> 24: C>B
> 
> It (like DSC) elects A, but if the 49 A voters change to A>B 
> your 
> version eliminates C and then elects B.
> 
> DSC (like DAC, DHSC and SC-DC) meets Participation.
> 
> 31: A>C>B
> 33: B>A>C
> 36: C
> 
> Your version (like DSC) elects C, but if we add 6 C>A>B ballots 
> the 
> winner changes to A (a failure of both Participation and Mono-
> add-Top).
> 
> 31: A>C>B
> 33: B>A>C
> 36: C
> 06: C>A>B
> 
> And then if 2 of those C>A>B ballots changes to A>B>C the winner 
> changes 
> back to C, failing Mono-raise.
> 
> 31: A>C>B
> 33: B>A>C
> 36: C
> 04: C>A>B
> 02: A>B>C
> 
> >"the only advantage of DSC over DAC is that DAC does not 
> satisfy later-no-harm."
> >
> 
> DSC meets Independence from Irrelevant Ballots, but DAC badly 
> fails it, 
> as shown from this old example from
> Michael Harman (aka Auros):
> 
> 03: D
> 14: A
> 34: A>B
> 36: C>B
> 13: C
> 
> B wins, but if the 3D ballots are removed then C wins. 
> 
> (Also B is an absurd-looking unjustified winner.)
> 
> I regard DSC as FPP elegantly fixed up to meet Clone-Winner and 
> Majority for Solid Coalitions, but it's shortcomings
> help to show that its set of of criterion compliances isn't 
> sufficient 
> (and that Participation is 'expensive').
> 
> I still think IRV (Alternative Vote, no above-bottom equal-
> ranking, 
> voters can strictly rank from the top as many or few
> candidates as they like) is the best of the single-winner 
> methods that 
> meets Later-no-Harm.
> 
> 
> Chris Benham
> 
> 
> Forest Simmons wrote (Sun 7 Aug 2011):
> 
> That "Q" in the previous subject heading was a typo.
> 
> Here's an example that illustrates the difference in Woodall's 
> DSC and my modified version:
> 
> 25 A1>A2
> 35 A2>A1
> 20 B>A1
> 20 C>A1
> 
> Woodall's DSC assigns 60 points to {A1, A2} and then the only 
> other positive point coalitions that have 
> non-empty intersections with this set are {A2}, {A1}, {A1, B}, 
> and {A1, C}, with respective points of 35, 
> 25, 20 and 20. The 35 point set {A2} decides the result: A2 wins.
> 
> In my version, the 60 point coalition is the highest point 
> proper coalition {A1, A2}, so candidates B and C 
> are struck from the ballots and we are left with
> 
> 25 A1>A2
> 35 A2>A1
> 40 A1
> 
> This time A1 wins.
> 
> As near as I can tell, my version still has all of the 
> advantages of DSC, including later-no-harm, clone 
> independence, monotonicity, etc.
> 
> Note that Woodall and I get the same result for
> 
> 25 A1>A2
> 35 A2>A1
> 40 D>A1
> 
> namely, that A1 wins. But if you split the D faction in half, 
> you get the original scenario above. It seems 
> to me that A1 should continue to win, but classical DSC switches 
> to A2 without any good reason. In 
> other words, it lacks a certain kind of consistency that our 
> modified version has.
> 
> Jameson, 
> 
> the only advantage of DSC over DAC is that DAC does not satisfy 
> later-no-harm. In the context of 
> chicken this would keep the bluffer from truncating, but to no 
> avail; the plurality winner (with 48 points) 
> would win, since (singleton) it would form the highest point 
> solid coalition all by itself. 
> 
> Under DAC the bluffer would truncate but would still form an 
> assenting coalition with the guy who did not 
> truncate her, but not a solid coalition. An even bigger 
> assenting coalition would be the plurality winner 
> together with the bluffer. Of these two, only the bluffer would 
> be in the second largest coalition, so the 
> bluffer would win under DAC.
> 
> 
> 
> 
> 
> 
> 
> ----- Original Message -----
> From: 
> Date: Saturday, August 6, 2011 3:13 pm
> Subject: AQ variant of DSC
> To: election-methods at lists.electorama.com 
> > electorama.com>,
> >/ One way of looking at Woodall's DSC method is that it is 
> />/ designed to elect from the clone set that 
> />/ extends up to the top rank on the greatest number of 
> ballots, 
> />/ i.e. kind of the plurality winner among 
> />/ clone sets.
> />/ 
> />/ There are two ways in which this description is not precise, 
> but 
> />/ maybe we would get a better method if 
> />/ we follwed this description more closely.
> />/ 
> />/ (1) The solid coalitions look like clone sets on the ballots 
> />/ that reach up to the top, but they don't have to 
> />/ look like clone sets on the other ballots.
> />/ 
> />/ (2) This description doesn't tell how DSC narrows down after 
> />/ finding the plurality winner solid coalition. 
> />/ In fact the entire set of candidates is automatically the 
> solid 
> />/ coalition that extends to the top rank on 
> />/ 100% of the ballots, so for starter we need to narrow down 
> to a 
> />/ proper sub-coalition.
> />/ 
> />/ With regard to (1), imagine a one dimensional issue space 
> with 
> />/ the candidates distributed as follows:
> />/ 
> />/ 
> A..............B1..B2..B3...................C......................D1..D2...........E/>/ 
> />/ The set {B1, B2, B3} and the set {D1, D2} will be solid 
> />/ coalitions that extend to the top rank on the 
> />/ ballots of the voters that have a favorite among them, and 
> they 
> />/ will appear as clone sets on all of the 
> />/ ballots that do not rank C first. But voters near C may well 
> />/ intermingle the B's and the D's like
> />/ 
> />/ C >B3>D1>B2>D2>B1>E>A
> />/ 
> />/ This shows that a geometrical clone doesn't have to end up 
> as a 
> />/ classical ballot clone except on the 
> />/ ballots of the voters that are situated in the middle of the 
> />/ clone set, in which case they will appear as 
> />/ solid (or assenting) coalitions that extend to the top rank. 
> />/ 
> />/ So Woodal had the right idea for making his method clone 
> independent./>/ 
> />/ If I uderstand correctly, Woodall invented DSC to prove a 
> point, 
> />/ viz. that a method can satisfy later no 
> />/ harm, be clone free, and montone. He didn't invent the 
> method 
> />/ as a serious proposal. So I don't think 
> />/ his feelings will be hurt if we suggest an improvement.
> />/ 
> />/ My suggestion is that once we have found the proper subset 
> solid 
> />/ coalition that extends to the top rank 
> />/ on the greatest number of ballots, strike from the ballots 
> the 
> />/ candidates that are not in that coalition, and 
> />/ iterate until there is only one candidate left. Elect the 
> sole 
> />/ remaining candidate.
> />/ 
> />/ For incomplete rankings we can modify DAC in the same way, 
> by 
> />/ replacing the term "solid" with the 
> />/ term "assenting."
> />/ 
> />/ 
> /
> 
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