[EM] Fwd: Duncan Proposal Draft

[Michael Ossipoff]

Richard—

No one is denying the desirability PR.

I don’t know where you reside, but, here in the U.S., PR for our national
legislature, Congress, is much less short-term feasible, due to
Constitutional structure.

The Constitution requires that every state gets a House representative,
regardless of how small it’s population is. If its population were 1, it
would nonetheless get a representative.

Additionally, the Constitution requires that every state must get the SAME
number of Senate-seats (two)…again, regardless of how small its population
is.

Those two Constitutional requirements would make nonsense of
proportionality.

Constitutional amendment is difficult & time-consuming.  …&, for various
reasons we needn’t go into, a Constitutional convention now would be a
rather terrifying thing.

So, here, electoral-reform is single-winner reform.

BTW, I hasten to emphasize that I’m not against the small states. I don’t
want to deny them equal representation. “ Equal” is the operative word..

Equal representation could be achieved, but not without repairing the
Constitution’s built-in disproportionality. It was “The Great Compromise”,
which compromised-away any chance of equal representation. A very
regrettable compromise.

Here’s an example of equal representation…my favorite one:

A unicameral at large (no districts or gerrymandering) Parliament (yes, no
president), 150 seats, elected by open-list party-list PR, allocated by
Sainte Lague, or, preferably, Bias-Free.

Of the divisor-method allocation-rules that are or have been used, Sainte
Lague is the very nearly unbiased one.

SL is only very slightly biased favoring larger parties.

Bias-Free is entirely absolutely unbiased.

Divisor methods involve the rounding, up or down, to a whole number, of a
party’s number of “quotas” ( details are outside the scope of this
discussion).

Sainte Lague rounds to the nearest whole number.

i.e. the round-up point is the average of the two surrounding integers.
I.e. …

R = (a+b)/2.

For Bias-Free, determine R as follows:

Divide b^b by a^a. Then divide the result by e.

e is the base of the natural logarithms, equal to about 2.718

But I re-emphasize that, with proportionality now Constitutionally
impossible, national PR is unavailable.

Electoral reform means single-winner reform.




On Fri, Oct 13, 2023 at 11:18 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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