[EM] Fwd: Duncan Proposal Draft

[Toby Pereira]

 I also like proportional representation, but there are many different elections for many different things, and there will always be a need for single-winner methods. Because of that I'm not sure it's necessary to make the same point in every discussion about single-winner methods, especially specific discussions about solving specific problems (e.g. burial) rather than more general discussions.
Toby
    On Friday, 13 October 2023 at 19:18:06 BST, Richard Lung <voting at ukscientists.com> wrote:  
 
  

 
 
"Cycles" (in the paper-scissors-rock sense) are a problem of the  (under-candidated) single member systems own making. They rapidly disappear with a representative sample of candidates proportionally elected to large constituencies. The problem is not the 'pesky' cycles, it is the pesky single member system. Unless the politics in political science is to dictate to the science, it is up to academics to point out, as hundreds of American political scientists have, in conjunction with The New York Times, I believe, this requirement of a quota-preferential method.
 
Remedies to the single member system are cosmetic. They cannot possibly please more than half the population, whatever you do -- and probably a good deal less. UK monopolistic elections are a minorocracy not a democracy, and that is probably a fair indication of the US state of affairs.
 
 
Time to move on from the ancient Greek conception of democracy, as to elect a tyrant, unconditionally -- making Britain what Hailsham called an "elective dictatorship." Which shares some of the all too evident failings of any dictatorship, elected or otherwise. This should be a spur to avoid another Vietnam war or second Iraq war, which even W. may deplore, in his heart.
 
 
Regards,
 
Richard Lung.
 
 

 
 On 13/10/2023 18:11, Forest Simmons wrote:
  
  Dear EM List Friends, 
  We need your feedback on this draft of a proposal before we submit a version of it to the voting reform community at large. 
  ---------- Forwarded message ---------
 From: Forest Simmons <forest.simmons21 at gmail.com>
 Date: Thu, Oct 12, 2023, 5:35 PM
 Subject: Duncan Proposal Draft
 To: Michael Ossipoff <email9648742 at gmail.com>
  
 
 Michael Christened our new Q&D burial resistant method "Duncan" after Duncan Black who popularized the idea of using  Borda's Method as a fallback "completion" when the ballots fail to  unambiguously reveal the sincere "Condorcet" pairbeats-all candidate. 
  Our Duncan method has the same form as Black's in that the official version directly specifies electing the unambiguous Condorcet Candidate when there is one, and falls back to another procedure that relies on Borda Scores, otherwise. 
  It should be emphasized that in both cases the fall back Borda based expedient is rarely needed. For that reason some misguided voting reform advocates have cavalierly opined that any decisive completion/ fallback method would be plenty adequate to supplement the Condorcet Criterion requirement. 
  However, this casual attitude ignores the  feedback aspects of voting systems in that various voting methods vary in the degree that they encourage or discourage the creation of artificial beat cycles that subvert/ hide the Condorcet Candidate from view, bringing the completion method into greater prominence in a potentially unstable cycle. 
  Unfortunately most of the extant methods fall into this "positive" feedback category, including Borda itself.  Some less sensitive methods like Approval  and IRV/RCV have a built in "friction" that dampens the feedback; but as systems engineers know, the high performance components are the ones that need the addition of some carefully engineered negative feedback "circuit" to stabilize the system as a whole. 
  In our Condorcet Completion context, our use of the Borda Count scores is carefully designed with that stabilizing influence in mind: adventurous strategists who are aware of this feature, when acting rationally will be deterred from creating these cycles that come back to bite them. Those not aware will find out when their ploys backfire or otherwise disappoint them. 
  How do these pesky cycles arise so easily in Borda and other rank based methods? 
  Suppose that your personal preference schedule for the alphabetized candidates looks like ... 
  A>C>X>Y>Z, and that C is the Condorcet Candidate projected to win the election if nobody acts nefariously. 
  You, and like minded friends, get the idea to insincerely move your second choice to the bottom of your ballot (so it now reads A>X>Y>Z>C) ... not to be "nefarious" so much as to just increase the winning chances of your favorite A. 
  Could this work? 
  Yes, under Black's method if your friends follow your lead, this "nurial" of C under the "busses" X, Y, and Z, could easily subvert one or more of C's pairwise victories over X,Y, and Z, into defeats of C by them, thereby hiding C's identity of sincere Universal "pairbeater" status to just one more member of a "beatcycle" of the form A beats X beats Y beats Z beats C beats A. 
  Note that the buried candidate C still beats the buriers' favorite, A ... because lowering C  does not decrease the number of ballots that support C over A ... which is how easily and innocently beatcycles like this can be created in Condorcet style elections ... at least in the absence of negative feedback from the cycle resolution fallback method. 
  In traditional Black that fallback method is Borda. Does that fix the problem? ... or does it exacerbate it. 
  Well ... the same burial that put C at disadvantage in the pairwise contests with X thru Z, also lowered C's Borda score by 3 counts per ballot, and raised  the Borda score of each of X thru Z to the tune of one count per ballot. 
  The likely outcome is that C will end up with the lowest score, and come in last in the finish order. 
  By way of contrast, under our new Duncan method, the most likely winner is X, and the least likely winner is A, the burier faction's favorite ... thus disappointing the burier faction supporters ... teaching them that if they try to outsmart new Duncan with insincere ballot rankings, they are apt to end up helping elect their third (or later) choice instead of their first choice or their second choice ... the one that they so cleverly buried (however innocently or without malice). 
  Too many dabblers in voting method reform (as well as most professionals) are unaware of these dynamics. 
  But now, with your new understanding, you, at least, can become part of the solution. 
  Duncan Definition: 
  In the vast majority of the cases ... those in which the pairwise counts of the ballots unambiguously identify the candidate that pairbeats each of the others ... elect that candidate. 
  Otherwise, elect the highest score candidate that pairbeats every candidate with lower score. 
  [Nominally "score" = Borda Count, though STAR Voting scores, for example, could also serve] 
  How does this Duncan fallback procedure work to prevent A from getting elected in our scenario regarding A thru Z? 
  Well, could A pairbeat every lower score candidate? In particular, could A pairbeat C, which is now at the bottom of the Borda score pile ... certainly lower than A ...? 
  Well, remember that "C beats A" was the last step in the beatcycle created by A's friends. 
  So A does not pairbeat every lower score candidate, and therefore cannot win. 
  New Duncan is burial resistant. 
  Next time ... more examples and insights ... 
  fws 
  
  
      
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