[EM] Participation criterion and Condorcet rules

[VoteFair]

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.
>
>
>
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