[EM] Participation criterion and Condorcet rules
John
john.r.moser at gmail.com
Wed Aug 8 11:43:35 PDT 2018
That method is NP-hard and involves complex tabulation. If you can
demonstrate it more-simply, that helps.
Alternative Scwartz is O(n^2) polynomial and simple. It selects from the
same set as Schulze, whereas Alternative Smith uses the whole Smith Set.
Both resist tactical manipulation; Kenemy seems to fail clone independence.
Thoughts?
On Wed, Aug 8, 2018, 2:36 PM VoteFair <electionmethods at votefair.org> wrote:
> On 8/7/2018 9:05 AM, John wrote:
> > The fact that Condorcet methods fail participation is fairly
> > immaterial. I want to know WHEN they fail participation. I suspect, to
> > be short, that a Condorcet method exists (e.g. any ISDA method) which
> > can only fail participation when the winner is not the first Smith-set
> > candidate ranked on the ballot. Likewise, I suspect that the
> > probability of such failure is vanishingly-small for some methods, and
> > relies on particular and uncommon conditions in the graph.
>
> You have the right idea. The important point is the issue of HOW OFTEN
> a method fails one criterion or another.
>
> My prediction is that when this issue finally gets analyzed, the
> Condorcet-Kemeny method will have the fewest failures.
>
> As for simplicity (which you mention in your full message), the
> Condorcet-Kemeny method is easier to understand than the
> Condorcet-Schulze method. For clarification, both methods usually
> identify the same winner in most real-life situations.
>
> Currently I'm refining the design of the "VoteFair marble machine" that
> demonstrates Condorcet-Kemeny calculations using a marble machine --
> which actually uses steel balls instead of marbles because they are
> smaller and don't shatter. A video of that machine in use will further
> demonstrate the method's simplicity. Here is the link to the current
> description/design:
>
> http://www.votefair.org/votefair_marble_machine.html
>
> I'll update that description when I've created the 3D-object file for
> the 3D "module" where a large "marble" hits a small "marble" from one
> side or the other.
>
> John, thank you for taking time to understand alternate election-method
> reform methods.
>
> In case you missed it, here is my latest article at Democracy Chronicles
> that puts election-method reform into perspective -- in a way that
> "average" (non-mathematical) folks can understand:
>
> https://democracychronicles.org/postwar-monopoly/
>
> Richard Fobes
> Author of "Ending The Hidden Unfairness In U.S. Elections"
>
>
> On 8/7/2018 9:05 AM, John wrote:
> > Current theory suggests Condorcet methods are incompatible with the
> > Participation criterion: a set of ballots can exist such that a
> > Condorcet method elects candidate X, and a single additional ballot
> > ranking X ahead of Y will change the winner from X to Y.
> >
> > https://en.wikipedia.org/wiki/Participation_criterion
> >
> > This criterion seems ill-fitted, and I feel needs clarification.
> >
> > First, so-called Condorcet methods are simply Smith-efficient (some are
> > Schwartz-efficient, which is a subset): they elect a candidate from the
> > Smith set. If the Smith set is one candidate, that is the Condorcet
> > candidate, and all methods elect that candidate.
> >
> > From that standpoint, each Condorcet method represents an arbitrary
> > selection of a candidate from a pool of identified suitable candidates.
> > Ranked Pairs elects the candidate with the strongest rankings; Schulze
> > elects a more-suitable candidate with less voter regret (eliminates
> > candidates with relatively large pairwise losses); Tideman's Alternative
> > methods resist tactical voting and elect some candidate or another.
> >
> > Given that Tideman's Alternative methods resist tactical voting, one
> > might suggest a bona fide Condorcet candidate is automatically resistant
> > to tactical voting and thus unlikely to be impacted by the no-show
> paradox.
> >
> > I ask if the following hold true in Condorcet methods where tied
> > rankings are disallowed:
> >
> > 1. In methods independent of Smith-dominated alternatives (ISDA),
> > ranking X above Y will not change the winner from X to Y /unless/ Y
> > is already in the Smith Set prior to casting the ballot.
> > 2. In ISDA methods, ranking X above Y will not change the winner from X
> > to Y /unless/ some candidate Z both precedes X and is in the Smith
> > set prior to casting the ballot.
> > 3. In ISDA methods, ranking X above Y will not change the winner from X
> > /unless/ some candidate Z both precedes X and is in the Smith set
> > /after/ casting the ballot.
> > 4. In ISDA methods, ranking X above Y and ranking Z above X will either
> > not change the winner from X /or/ will change the winner from X to Z
> > if Z is not in the Smith Set prior to casting the ballot and is in
> > the Smith Set after casting the ballot.
> > 5. in ISDA methods, ranking X above Y will not change the winner from X
> > to Y /unless/ Y precedes Z in a cycle after casting the
> > ballot /and/ Z precedes X on the ballot.
> >
> > I have not validated these mathematically.
> >
> > #1 stands out to me because ranking ZXY can cause Y to beat W. If W is
> > in the Smith Set, this will bring Y into the Smith Set; it will also
> > strengthen both Z and X over W. Z and X beat Y, as well.
> >
> > This is trivially valid for Ranked Pairs; I am uncertain of Schulze or
> > Tideman's Alternative. Schulze should elect Z or X.
> >
> > In Tideman's Alternative, X can't win without being first-ranked more
> > frequently than Z and W; bringing Y into the Smith Set removes all of
> > X's first-ranked votes where Y was ranked above X (X* becomes YX*). Y
> > cannot suddenly dominate all candidates in this way, and should quickly
> > lose ground: X might go first, but that just turns XZ* and XW* votes
> > into Z and W votes, and Z and W previously dominated Y and so Y will be
> > the /second/ eliminated if not the /first/.
> > /
> > /
> > #2 is similar. If you rank X first, Ranked Pairs will tend to get to X
> > sooner, possibly moving it ahead of a prior pairwise lock-in of Y, but
> > not behind. The losses for X get weaker and the wins get stronger. X
> > also necessarily cannot be the plurality loser in Tideman's Alternative,
> > and will not change its position relative to Y. X must be preceded by a
> > candidate already in the Smith Set prior to casting the ballot for the
> > winner to change from X to Y.
> >
> > #3 suggests similar: if a candidate Z precedes X and is not in the
> > Smith set after casting the ballot, X is the first candidate, and #2
> > holds (this is ISDA).
> >
> > #4 might be wrong: pulling Z into the Smith set by ZXY might not be
> > able to change the winner from X.
> >
> > #5 suggests you can't switch from X to Y unless the ballot ranks Z over
> > X /and/ Y has a beatpath that reaches X through Z.
> >
> > I haven't tested or evaluated any of these; I suspect some of these are
> > true, some are false, and some are weaker statements than what does hold
> > true.
> >
> > The fact that Condorcet methods fail participation is fairly
> > immaterial. I want to know WHEN they fail participation. I suspect, to
> > be short, that a Condorcet method exists (e.g. any ISDA method) which
> > can only fail participation when the winner is not the first Smith-set
> > candidate ranked on the ballot. Likewise, I suspect that the
> > probability of such failure is vanishingly-small for some methods, and
> > relies on particular and uncommon conditions in the graph.
> >
> >
> >
> > ----
> > Election-Methods mailing list - see http://electorama.com/em for list
> info
> >
>
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