[EM] Fwd: Duncan Proposal Draft

Tue Oct 17 11:51:39 PDT 2023

With regard to the Saint Lague divisor, this has been argued, for 
instance by Carstairs, as the most equitable share-out. My findings 
substantiate this system also called Webster apportionment after its 
original discoverer.

The Droop quota is a minimum proportional representation, which largely 
replaced the Hare quota for maximum representation in large 
constituencies. (Because politicians wanted to safeguard their safe 
seats from the greater electoral competition of being in large 
constituencies.) But the average quota of the two, found by taking their 
harmonic mean, is, on examination, a more optimally democratic 
representation than maximum or minimum PR. The Harmonic Mean quota, 
which I introduced, is V/(s+ ½). This is effectively equivalent to 
Webster apportionment.

The democratic principle of voters lists (STV) compared to the 
oligarchic principle of party lists, may use a no less proportional 
principle (the Harmonic Mean quota) than some party lists use of the 
Saint Lague divisor count

I briefly discussed this in my most recent e-book, Don't You Ever read 
Anything But Serious Books?, in the review of Carstairs brief history of 
West European voting methods.

The Harmonic Mean quota is one of te four averages I use in the higher 
order counts of Binomial STV (STV^x]. Hence Four Averages Binomial STV 
(FAB STV). The four averages are to make the count more representative, 
not so much of candidate popularity, but for the representation of 
information in general.

First order Binomial STV (STV^1) is probably sufficient for 
representation of candidates. But it is still the first binomial count 
and the first one-truth voting method, that uses the same count for both 
election and exclusion of candidates - one persons election being 
another persons exclusion, in principle.

Regards,

Richard Lung.

On 13/10/2023 20:22, Michael Ossipoff wrote:
> 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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