# [EM] What are some simple methods that accomplish the following conditions?

John john.r.moser at gmail.com
Mon Jun 10 05:04:55 PDT 2019

```I've suggested larger electoral systems for this.

If you use Single Transferable Vote for a nonpartisan blanket Primary
Election to get down to somewhere between 5 and 9 (I think 7 may be better
than 5), then Tideman's Alternative as a Condorcet system, you get a pretty
reliable result.

Consider the two-party oligarchy problem:  30% of voters vote D, 24% vote
C, the parties are {A,B} and {C,D}.  If A>B>C>D for an {A} voter, then C is

30%:  D>C>B>A
24%: C>D>B>A
46%:  {A,B}>C>D

24% + 46% consider C>D.  There's no marginal utility for C voters to vote
D>C as a way to band together and prevent a loss.

Now, the 30% can vote D>A>C>B, under the theory that A is the Condorcet
loser.  A few outcomes:

1.  An A vs. C pair where A defeats C creates a full cycle (A>C>{D,B}, D>A,
Smith set is all candidates).  We're looking at 23% give or take for each
of A and B, so the cycle will break in the runoff iteration, and C still
wins even with all 30% voting D>C.
2.  If 32% and 22% instead of 30% and 24% for {C,D} voters, then this huge
32% plurality can indeed defeat C.  If just 4% of C voters defect and
decide that D is f*\$%ing crazy and their vote is C>B>D>A (because A is
worse, to them)—and this is highly-likely, as we all well know and have
seen in real elections—then D voters just elected B, who is worse from
their perspective.

This tampering doesn't likely elect D, but rather pushes the winner farther
toward A.  The distortion from the other side also doesn't work, although
it might be possible for 21% A>B>C>D voters to rank A>D>B>C and elect D
(also a worse outcome).

Pretty much only D and A have any utility voting as such.  C and B voters
would be best off voting honestly, e.g. C>D>B or C>B>D.  Changing your
first choice is always weakening your first choice.

With a span of 7, you have {A,B,C,D,E,F,G} at roughly 14% of the vote.  The
impact of these groups and the usefulness or utility of tactical voting
falls away, so these failures simply stop happening.  Don't use group
voting tickets.

This proportional NPBP, Condorcet Election has a few other interesting
properties, notably due to vote impact.

Imagine of the 7, {C,D,E} being centered around {D} (the natural Condorcet
candidate), D defeats all other candidates, while E defeats all candidates
except D.  E loses to D by 10%.  If E can get out 10% more voters—out of
the whole election, not just 10% more E voters—then E can win.  That's
pretty heavy.

Likewise, social media propaganda has to make some major shifts.  It can't
change the winner to A or G or even E.  The change in ballots is immense
and complex and nonsense.  This system resists such propaganda.

On the other hand, CHANGING a vote is two votes.  If D offends A voters who
vote A>B>C>D>E, then A voters will change their vote to A>B>C>E>D.  That's
-1 D, +1 E—it's 2 votes.  Just a 5% movement here will switch the winner
from D to the substantially-similar E, even though the only people who
switched their votes were fringe voters who are nowhere near the base for D
and E.

This is more-sensitive with 7 candidates.  It does require voters to rank
so many candidates, and voters typically rank to six in practice (according
to Fair Vote).  If they tend to rank to three, then e.g. B>C>D and F>E>D
votes form the edges, and we have likely enough of those (A and G voters
are 2/7, then half of B and F voters makes 3/7, leaving 71% of voters who
likely explicitly rank the Condorcet candidate) to accurately locate the
Condorcet candidate.  I worry about 9 or 11 or 15 because it'll break.

Think in terms of larger electoral systems.  Think in terms of how many
candidates and the distribution of first-choice voters, and in terms of
engineering an election cycle to create the conditions which protect your
election from such failures.  You will not find one voting rule to rule
them all:  when 9 people show up from one party, 5 show up from another, 3
small parties send a candidate, and you have 2 independents, any
single-winner method will bluntly fail.  You need a primary election.

On Sun, Jun 9, 2019 at 10:20 PM C.Benham <cbenham at adam.com.au> wrote:

> Kevin,
>
> So to be clear the possible "complaint" some voters might have (and you
> think we should take seriously) is "We lied and the voting method
>
> So therefore it is good to have a less expressive ballot because that
> reduces the voter's opportunities to tell stupid lies and if the method
> is simple enough then maybe also the temptation for them to do so.
>
> To me that is absurd. If I agreed with that idea I would forget about the
> Condorcet criterion and instead demand a method that meets
> Later-no-Help,  such as  IRV or Bucklin or Approval.
>
> But I've thought of a patch to address your issue.  We could have a rule
> which says that if the winner's approval score is below some fixed
> fraction of that of the most approved candidate, then a second-round
> runoff is triggered between those two candidates.  What do you
> think of that?  What do you think that fraction should be?
>
> Chris
>
>
> On 10/06/2019 9:57 am, Kevin Venzke wrote:
>
> Hi Chris,
>
> >>I don't think it's ideal if burying X under Y (both disapproved) can
> only backfire when Y is made the CW.
> >>
>
> >Why is that?
>
> Because I think if voters decide to attempt to prevent another candidate
> from being CW, via insincerity, there should be risks to doing that. Of
> course there is already some risk. But if you "knew" that a given candidate
> had no chance of being CW then there would be nothing to lose in using that
> candidate in a burial strategy.
>
> >The post-election complaint (by any of the voters) would be .. what?
>
> For either a successful burial strategy, or one that backfires and elects
> an arbitrary candidate, I think the possible complaints are clear. Maybe
> someone would argue that a backfiring strategy proves the method's
> incentives are just fine. But that wouldn't be how I see it. I think if, in
> actual practice, it ever happens that voters calculate that a strategy is
> worthwhile, and it completely backfires to the point that everyone would
> like the results discarded, then that method will probably get repealed.
>
> >
> >If you don't allow voters to rank among their unapproved candidates then
> arguably you are not even trying to elect the sincere CW.
> >Instead you are just modifying Approval to make it a lot more
> Condorcet-ish.
>
> Not an unfair statement. If you require voters to have that much
> expressiveness then you can't use implicit.
>
> To me, the motivation for three-slot C//A(implicit) is partly about
> C//A(explicit) retains 1 of 3. (Arguably slightly less for the Smith
> version.) Possibly it has its own merits, but they will largely be
> different ones.
>
> >
> >A lot of voters like relatively expressive ballots. I think that is one
> of the reasons why Approval seems to be a lot less popular than IRV.
>
> I have no *inherent* complaints about the ballot format of explicit
> approval plus full ranking.
>
> Kevin
>
>
>
>
> Le jeudi 6 juin 2019 à 21:03:19 UTC−5, C.Benham <cbenham at adam.com.au>
> <cbenham at adam.com.au> a écrit :
>
>
> Kevin,
>
> Specifically should "positional dominance" have the same meaning whether
> or not the method has approval in it?
>
>
> If the voters all choose to approve all the candidates they rank, then
> yes.  (For a while I was wrongly assuming that Forest's suggested
> default approval was for all ranked-above-bottom candidates, but then I
> noticed that he specified that it was only for top voted candidates).
>
> One of my tired examples:
>
> 25: A>B
> 26: B>C
> 23: C>A
> 26: C
>
> Assuming all the ranked candidates are approved, C is by far the most
> approved and the most top-voted candidate.
> Normal Winning Votes (and your idea 2 in this example) elect B.
>
> I will go easy on these methods over failing MD, because it happens when
> some of the majority don't approve their common candidate.
>
>
> For me this this type of ballot avoids the Minimal Defense versus Chicken
> Dilemma dilemma, rendering those criteria inapplicable.
>
> 48: A
> 27: B>C
> 25: C
>
> The problem has been that we don't know whether the B>C voters are
> thinking "I am ranking C because above all I don't want that evil A
> to win" or  "My C>A preference isn't all that strong, and I think that my
> favourite could well be the sincere CW, and if  C's supporters rank
> B above A then B has a good chance to win. But if they if they create a
> cycle by truncating I'm not having them steal it".
>
> With the voters able to express explicit approval we no longer have to
> guess which it is.
>
> I don't think it's ideal if burying X under Y (both disapproved) can only
> backfire when Y is made the CW.
>
> Why is that?  The post-election complaint (by any of the voters) would be
> .. what?
>
> If you don't allow voters to rank among their unapproved candidates then
> arguably you are not even trying to elect the sincere CW.
> Instead you are just modifying Approval to make it a lot more
> Condorcet-ish.
>
> A lot of voters like relatively expressive ballots. I think that is one of
> the reasons why Approval seems to be a lot less popular than IRV.
>
> Chris Benham
>
> On 6/06/2019 5:34 pm, Kevin Venzke wrote:
>
> Hi Chris,
>
> I've been short on time so I don't actually have much thought on any of
> the methods, even my own.
>
> I suppose Idea 2 is the same as Schwartz-limited MinMax(WV) if nobody
> submits disapproved rankings. I'm not sure if it makes sense to reject the
> method over that. Specifically should "positional dominance" have the same
> meaning whether or not the method has approval in it? As a comparison, I
> will go easy on these methods over failing MD, because it happens when some
> of the majority don't approve their common candidate.
>
> I would have liked to simplify Idea 2, but actually Forest's eventual
> proposal wasn't all that simple either. As I wrote, if you add "elect a CW
> if there is one" it can become much simpler, so that it isn't really
> distinct from Idea 1. I actually tried pretty hard to present three "Ideas"
> in that post, but kept having that problem.
>
> I posted those ideas because I thought Forest posed an interesting
> challenge, and I thought I perceived that he was trying to fix a problem
> with CD. That said, I am not a fan of Smith//Approval(explicit). If all
> these methods are basically the same then I probably won't end up liking
> any of them. I don't think it's ideal if burying X under Y (both
> disapproved) can only backfire when Y is made the CW.
>
> Kevin
>
>
> Le mercredi 5 juin 2019 à 21:26:23 UTC−5, C.Benham <cbenham at adam.com.au>
> <cbenham at adam.com.au> a écrit :
>
> Kevin,
>
> I didn't comment earlier on your "idea 2".
>
> If there no "disapproved rankings" (i.e. if the voters all approve the
> candidates they rank above bottom),
> then your suggested method is simply normal  Winning Votes, which I don't
> like because the winner can
> be uncovered and positionally dominant or pairwise-beaten and positionally
> dominated by a single other
> candidate.
>
> On top of that I don't think it really fills the bill as "simple".
> Approval Margins (using Sort or Smith//MinMax
> or equivalent or almost equivalent algorithm) would be no more complex and
> in my opinion would be better.
>
> I would also prefer the still more simple Smith//Approval.
>
> What did you think of my suggestion for a way to implement your idea 1?
>
> Chris
>
>
>
> *Kevin Venzke* stepjak at yahoo.fr
> Sat Jun 1 12:48:27 PDT 2019
>
>
> Hi Forest,
>
>
> Idea 1:
> 1. If there is a CW using all rankings, elect the CW.
> 2. Otherwise flatten/discard all disapproved rankings.
> 3. Use any method that would elect C in scenario 2. (Approval, Bucklin,
> MinMax(WV).)
>
> So scenario 1 has no CW. The disapproved C>A rankings are dropped. A wins
> any method.
> In scenario 2 there is no CW but nothing is dropped, so use a method that
> picks C.
> In both versions of scenario 3 there is a CW, B.
>
> If step 3 is Approval then of course step 2 is unnecessary.
>
> In place of step 1 you could find and apply the majority-strength solid
> coalitions (using all rankings)
> to disqualify A, instead of acting based on B being a CW. I'm not sure if
> there's another elegant way
> to identify the majority coalition.
>
> Idea 2:
> 1. Using all rankings, find the strength of everyone's worst WV defeat. (A
> CW scores 0.)
> 2. Say that candidate X has a "double beatpath" to Y if X has a standard
> beatpath to Y regardless
> of whether the disapproved rankings are counted. (I don't know if it needs
> to be the *same* beatpath,
> but it shouldn't come into play with these scenarios.)
> 3. Disqualify from winning any candidate who is not in the Schwartz set
> calculated using double
> beatpaths. In other words, for every candidate Y where there exists a
> candidate X such that X has a
> double beatpath to Y and Y does not have a double beatpath to X, then Y is
> disqualified.
> 4. Elect the remaining candidate with the mildest WV defeat calculated
> earlier.
>
> So in scenario 1, A always has a beatpath to the other candidates, no
> matter whether disapproved
> rankings are counted. The other candidates only have a beatpath to A when
> the C>A win exists. So
> A has a double beatpath to B and C, and they have no path butt. This
> leaves A as the only candidate
> not disqualified.
>
> In scenario 2, the defeat scores from weakest to strongest are B>C, A>B,
> C>A. Every candidate has
> a beatpath to every other candidate no matter whether the (nonexistent)
> disapproved rankings are
> counted. So no candidate is disqualified. C has the best defeat score and
> wins.
>
> In scenario 3, the first version: B has no losses. C's loss to B is weaker
> than both of A's losses. B
> beats C pairwise no matter what, so B has a double beatpath to C. However
> C has no such beatpath
> to A, nor has A one to B, nor has B one to A. The resulting Schwartz set
> disqualifies only C. (C needs
> to return B's double beatpath but can't, and neither A nor B has a double
> beatpath to the other.)
> Between A and B, B's score (as CW) is 0, so he wins.
>
> Scenario 3, second version: B again has no losses, and also has double
> beatpaths to both of A and
> C, neither of whom have double beatpaths butt. So A and C are disqualified
> and B wins.
>
> I must note that this is actually a Condorcet method, since a CW could
> never get disqualified and
> would always have the best worst defeat. That observation would simplify
> the explanation of
> scenario 3.
>
> I needed the defeat strength rule because I had no way to give the win to
> B over A in scenario 3
> version 1. But I guess if it's a Condorcet rule in any case, we can just
> add that as a rule, and greatly
> simplify it to the point where it's going to look very much like idea 1. I
> guess all my ideas lead me to
> the same place with this question.
>
> Oh well, I think the ideas are interesting enough to post.
>
> Kevin
>
> >Le jeudi 30 mai 2019 à 17:32:42 UTC−5, Forest Simmons <fsimmons at
> pcc.edu> a écrit :
> >
> >In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.  One
> consequence of these constraints is that in all three profiles below the
> cycle >A>B>C>A will obtain.
> >
> >I am interested in simple methods that always ...
> >
> >(1) elect candidate A given the following profile:
> >
> >P: A
> >Q: B>>C
> >R: C,
> >and
> >(2) elect candidate C given
> >P: A
> >Q: B>C>>
> >R: C,
> >and
> >(3) elect candidate B given
>
> >
> >P: A
> >Q: B>>C  (or B>C)
> >R: C>>B. (or C>B)
> >
> >I have two such methods in mind, and I'll tell you one of them below, but
> I don't want to prejudice your creative efforts with too many ideas.
> >
> >Here's the rationale for the requirements:
> >
> >Condition (1) is needed so that when the sincere preferences are
>
> >
> >P: A
> >Q: B>C
> >R: C>B,
> >the B faction (by merely disapproving C without truncation) can defend
> itself against a "chicken" attack (truncation of B) from the C faction.
> >
> >Condition (3) is needed so that when the C faction realizes that the game
> of Chicken is not going to work for them, the sincere CW is elected.
> >
> >Condition (2) is needed so that when  sincere preferences are
>
> >
> >P: A>C
> >Q: B>C
> >R: C>A,
> >then the C faction (by proactively truncating A) can defend the CW
> against the A faction's potential truncation attack.
> >
> >Like I said, I have a couple of fairly simple methods in mind. The most
> obvious one is Smith\\Approval where the voters have
> >control over their own approval cutoffs (as opposed to implicit approval)
> with default approval as top rank only. The other
> >method I have in mind is not quite as
> >simple, but it has the added advantage of satisfying the FBC, while
> almost always electing from Smith.
>
>
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> www.avg.com