<div dir="auto">That method is NP-hard and involves complex tabulation. If you can demonstrate it more-simply, that helps.<div dir="auto"><br></div><div dir="auto">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.</div><div dir="auto"><br></div><div dir="auto">Thoughts?</div></div><br><div class="gmail_quote"><div dir="ltr">On Wed, Aug 8, 2018, 2:36 PM VoteFair <<a href="mailto:electionmethods@votefair.org">electionmethods@votefair.org</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">On 8/7/2018 9:05 AM, John wrote:<br>
> The fact that Condorcet methods fail participation is fairly<br>
> immaterial. I want to know WHEN they fail participation. I suspect, to<br>
> be short, that a Condorcet method exists (e.g. any ISDA method) which<br>
> can only fail participation when the winner is not the first Smith-set<br>
> candidate ranked on the ballot. Likewise, I suspect that the<br>
> probability of such failure is vanishingly-small for some methods, and<br>
> relies on particular and uncommon conditions in the graph.<br>
<br>
You have the right idea. The important point is the issue of HOW OFTEN <br>
a method fails one criterion or another.<br>
<br>
My prediction is that when this issue finally gets analyzed, the <br>
Condorcet-Kemeny method will have the fewest failures.<br>
<br>
As for simplicity (which you mention in your full message), the <br>
Condorcet-Kemeny method is easier to understand than the <br>
Condorcet-Schulze method. For clarification, both methods usually <br>
identify the same winner in most real-life situations.<br>
<br>
Currently I'm refining the design of the "VoteFair marble machine" that <br>
demonstrates Condorcet-Kemeny calculations using a marble machine -- <br>
which actually uses steel balls instead of marbles because they are <br>
smaller and don't shatter. A video of that machine in use will further <br>
demonstrate the method's simplicity. Here is the link to the current <br>
description/design:<br>
<br>
<a href="http://www.votefair.org/votefair_marble_machine.html" rel="noreferrer noreferrer" target="_blank">http://www.votefair.org/votefair_marble_machine.html</a><br>
<br>
I'll update that description when I've created the 3D-object file for <br>
the 3D "module" where a large "marble" hits a small "marble" from one <br>
side or the other.<br>
<br>
John, thank you for taking time to understand alternate election-method <br>
reform methods.<br>
<br>
In case you missed it, here is my latest article at Democracy Chronicles <br>
that puts election-method reform into perspective -- in a way that <br>
"average" (non-mathematical) folks can understand:<br>
<br>
<a href="https://democracychronicles.org/postwar-monopoly/" rel="noreferrer noreferrer" target="_blank">https://democracychronicles.org/postwar-monopoly/</a><br>
<br>
Richard Fobes<br>
Author of "Ending The Hidden Unfairness In U.S. Elections"<br>
<br>
<br>
On 8/7/2018 9:05 AM, John wrote:<br>
> Current theory suggests Condorcet methods are incompatible with the<br>
> Participation criterion: a set of ballots can exist such that a<br>
> Condorcet method elects candidate X, and a single additional ballot<br>
> ranking X ahead of Y will change the winner from X to Y.<br>
><br>
> <a href="https://en.wikipedia.org/wiki/Participation_criterion" rel="noreferrer noreferrer" target="_blank">https://en.wikipedia.org/wiki/Participation_criterion</a><br>
><br>
> This criterion seems ill-fitted, and I feel needs clarification.<br>
><br>
> First, so-called Condorcet methods are simply Smith-efficient (some are<br>
> Schwartz-efficient, which is a subset): they elect a candidate from the<br>
> Smith set. If the Smith set is one candidate, that is the Condorcet<br>
> candidate, and all methods elect that candidate.<br>
><br>
> From that standpoint, each Condorcet method represents an arbitrary<br>
> selection of a candidate from a pool of identified suitable candidates.<br>
> Ranked Pairs elects the candidate with the strongest rankings; Schulze<br>
> elects a more-suitable candidate with less voter regret (eliminates<br>
> candidates with relatively large pairwise losses); Tideman's Alternative<br>
> methods resist tactical voting and elect some candidate or another.<br>
><br>
> Given that Tideman's Alternative methods resist tactical voting, one<br>
> might suggest a bona fide Condorcet candidate is automatically resistant<br>
> to tactical voting and thus unlikely to be impacted by the no-show paradox.<br>
><br>
> I ask if the following hold true in Condorcet methods where tied<br>
> rankings are disallowed:<br>
><br>
> 1. In methods independent of Smith-dominated alternatives (ISDA),<br>
> ranking X above Y will not change the winner from X to Y /unless/ Y<br>
> is already in the Smith Set prior to casting the ballot.<br>
> 2. In ISDA methods, ranking X above Y will not change the winner from X<br>
> to Y /unless/ some candidate Z both precedes X and is in the Smith<br>
> set prior to casting the ballot.<br>
> 3. In ISDA methods, ranking X above Y will not change the winner from X<br>
> /unless/ some candidate Z both precedes X and is in the Smith set<br>
> /after/ casting the ballot.<br>
> 4. In ISDA methods, ranking X above Y and ranking Z above X will either<br>
> not change the winner from X /or/ will change the winner from X to Z<br>
> if Z is not in the Smith Set prior to casting the ballot and is in<br>
> the Smith Set after casting the ballot.<br>
> 5. in ISDA methods, ranking X above Y will not change the winner from X<br>
> to Y /unless/ Y precedes Z in a cycle after casting the<br>
> ballot /and/ Z precedes X on the ballot.<br>
><br>
> I have not validated these mathematically.<br>
><br>
> #1 stands out to me because ranking ZXY can cause Y to beat W. If W is<br>
> in the Smith Set, this will bring Y into the Smith Set; it will also<br>
> strengthen both Z and X over W. Z and X beat Y, as well.<br>
><br>
> This is trivially valid for Ranked Pairs; I am uncertain of Schulze or<br>
> Tideman's Alternative. Schulze should elect Z or X.<br>
><br>
> In Tideman's Alternative, X can't win without being first-ranked more<br>
> frequently than Z and W; bringing Y into the Smith Set removes all of<br>
> X's first-ranked votes where Y was ranked above X (X* becomes YX*). Y<br>
> cannot suddenly dominate all candidates in this way, and should quickly<br>
> lose ground: X might go first, but that just turns XZ* and XW* votes<br>
> into Z and W votes, and Z and W previously dominated Y and so Y will be<br>
> the /second/ eliminated if not the /first/.<br>
> /<br>
> /<br>
> #2 is similar. If you rank X first, Ranked Pairs will tend to get to X<br>
> sooner, possibly moving it ahead of a prior pairwise lock-in of Y, but<br>
> not behind. The losses for X get weaker and the wins get stronger. X<br>
> also necessarily cannot be the plurality loser in Tideman's Alternative,<br>
> and will not change its position relative to Y. X must be preceded by a<br>
> candidate already in the Smith Set prior to casting the ballot for the<br>
> winner to change from X to Y.<br>
><br>
> #3 suggests similar: if a candidate Z precedes X and is not in the<br>
> Smith set after casting the ballot, X is the first candidate, and #2<br>
> holds (this is ISDA).<br>
><br>
> #4 might be wrong: pulling Z into the Smith set by ZXY might not be<br>
> able to change the winner from X.<br>
><br>
> #5 suggests you can't switch from X to Y unless the ballot ranks Z over<br>
> X /and/ Y has a beatpath that reaches X through Z.<br>
><br>
> I haven't tested or evaluated any of these; I suspect some of these are<br>
> true, some are false, and some are weaker statements than what does hold<br>
> true.<br>
><br>
> The fact that Condorcet methods fail participation is fairly<br>
> immaterial. I want to know WHEN they fail participation. I suspect, to<br>
> be short, that a Condorcet method exists (e.g. any ISDA method) which<br>
> can only fail participation when the winner is not the first Smith-set<br>
> candidate ranked on the ballot. Likewise, I suspect that the<br>
> probability of such failure is vanishingly-small for some methods, and<br>
> relies on particular and uncommon conditions in the graph.<br>
><br>
><br>
><br>
> ----<br>
> Election-Methods mailing list - see <a href="http://electorama.com/em" rel="noreferrer noreferrer" target="_blank">http://electorama.com/em</a> for list info<br>
><br>
</blockquote></div>