On 13.01.2023 20:38, Markus Schulze wrote:

The impression I got from reading Robert's paper is that he goes:

"Here are some properties that Condorcet methods have that IRV doesn't.
Among these are summability. IRV advocates don't seem to care much about
summability, so I'll play by their game; I'll propose a variant of IRV
that patches its greatest flaw."

I.e. that BTR is a way to fix IRV, but with the implication that better
methods exist if the voters want summability. He doesn't go into what
those methods are because it's beside the point.

I agree that it could be more clearly stated, though. And as a Condorcet
nitpicker, I would probably also say that the paper could mention the
theoretical existence of Condorcet cycles in passing, so that the
IRVists can't say "hey, the property he desires, that if A beats B
pairwise then B can't be elected... it sometimes is impossible to pass!
So avert your eyes from this propaganda and support IRV instead!".

-km

Kristofer is close.  Here is my spin on it.

Markus, I think that, even if BTR-IRV is the method that ultimately decides a state-wide RCV election, it makes sense for precincts to publish pairwise defeat subtotals (the defeat matrix, but I have to say that I think that the presentation format as a matrix is kinda dumb, even if that's the practice I see in voting methods lit).  If N is the number of candidates that's N(N-1) tallies to publish.  Now, already with RCV elections, we publish the tallies of first-choice votes.  So if you publish both, then the number of tallies reported at each precinct is N(N-1)+N = N^2.  Five candidates, that's 25 numbers.  If it's Hare RCV, it would have to be 205 numbers, clearly impractical to be printed, posted, and summed.

Now, in the U.S., we have had something more than 500 RCV elections that have been analyzed by FairVote and others, and of those elections, all but three have elected the Condorcet winner.  Two of the three RCV elections had a Condorcet winner and Hare failed to elect that candidate.  One of the three (2021 Minneapolis Ward 2) had no Condorcet winner.  So for 99.8% of the time, there is a CW and it doesn't matter what Condorcet method we use, these N(N-1) tallies suffice to tell us who wins.  Perhaps, for the 0.2% of the time there is no CW, we will be forced to learn of the outcome of the election from the seat of government because summing the pairwise defeat values will show there is a cycle.

But both Hare IRV and BTR elect someone whether there is a CW or not.  Now, suppose the Smith set is 3 candidates.  Rock-Paper-Scissors.  And let's say that the semifinal round has these 3 candidates.  Without loss of generality, let's label "Rock" as the candidate with the most votes in the semifinal round.

The order of candidate votes (not pairwise defeat) could be either Rock>Paper>Scissors or Rock>Scissors>Paper.  With Hare RCV, in the first case Paper wins and in the second case Rock wins.  But with BTR, Paper and Scissors have their runoff, Scissors wins, advances to the final round, and gets defeated by Rock.

So, for that 0.2% of elections that have a cycle, how often do you think that the cycle will be any more complex than Rock-Paper-Scissors?  With BTR-IRV, we know that the result will be the same as Condorcet-Plurality even more often than the 99.8%  Only in the super-rare case that there is a cycle and it's nastier than a Smith triplet will those N^2 tallies published at the precincts be insufficient to tell us who won the election.

If the election has a CW and the CW is elected, then if any loser is removed, the winner remains the same.  Then there is no spoiler and precinct subtotals suffice to tell us who wins on election night.  If there is no CW, this will happen only rarely (ca. 0.2%), and if it's Condorcet-plurality, the N^2 tallies still suffice to tell us who wins on election night.  If there is no CW and it's BTR-IRV, the N^2 tallies suffice to tell us who wins on election night if the Smith set is 3 candidates.  In the super-rare case that there is a Smith set bigger than 3, then we have to go to the seat of government and learn the outcome of the election in (given the track record of Alaska, Maine, or NYC) about 2 weeks and we do not have the redundant double-checking of the outcome that Precinct Summability would otherwise afford.

At least, that's how I'm gonna sell the product.

I'm not enamored by BTR.  I think Schulze or Tideman based on margins would be better.  But it's really hard to write self-contained legislation describing either procedures.  And if the language is too complicated, it's hard to sell to legislators who are suspicious of changing our voting method anyway.  Eric Maskin suggested to me that simple Condorcet with a completion method if no CW might be the best language.  So I also wrote templates for Condorcet-plurality, because it's simple.  The issue is, how do we tell the public the rationale for how the winner was selected in the case of no CW?

Condorcet-plurality is pretty simple to explain.  BTR is a little harder but, in comparison to IRV, not too bad to explain.  Ranked-pairs is harder yet, and my stab at legislative language is much wordier.  And I can't write legislative language for Beatpath.  Markus, might you post a concise and understandable description in common English usage that can be written into law?  I dunno how to do it.

So that's my spin on it.

robert

--

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

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I agree that the discussion will inevitably get to superficially citing Arrow or Gibbard-Satterthwaite.  When IRV apologists do that, I want to engage the topic and will use the Minneapolis Ward 2 2021 election as a very nice illustration of when transitivity fails.  I'll explain this will happen less often (0.2%) than the cases when we know who the majority candidate is and a spoiled election can be averted but IRV fails to avert it (0.4%).  But with Rock-Paper-Scissors, if you elect Rock, then we know that Scissors is the spoiler.  No matter who you elect, you cannot avoid a spoiled election.  I will be up front with that.

And then I ask how Hare solves it?  It doesn't.  But a Condorcet RCV solves this spoiler problem for the 0.4% of the time Hare fails to.  And will be Precinct Summable to boot.  If they say that I'm worrying too much about this 0.4%, I bring up a comparison to real and rare events when a flaw in a procedure resulted in complete failure to accomplish what is meant to be accomplished.  A good example is of the rare and unfortunate times that the wrong limb was marked and amputated, which has happened occasionally.  When that happens, do we hear the hospital defending themselves saying "This happens so rarely that we believe our procedures that we have used for decades without trouble need not be reviewed."?

So when they bleat "Arrow", I respond that a cycle is an unavoidable failure, so let's do the best we can with it.  Let's elect the plurality winner in that case.  Or elect the IRV winner, or the runoff winner of the top-two.  Or if BTR is used, we accept the BTR winner as just as good as the plurality winner when there is no Consistent Majority Candidate (which is my neologism for the CW).

I'm gonna be quiet now and listen to you guys.  As an activist/schlub, I feel quite privileged to get critique from Markus and Kristofer.

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r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

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I just want to point out that although it is not always possible to elect a
Condorcer Winner, it is always possible to elect an uncovered candidate.

And putting our max gradient finisher on the back end of any other method
(including IRV) will take care of it ... simply and effectively at
negligible additional cost.

Forest

On Fri, Jan 13, 2023, 10:26 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:

The Hare system is at-large STV/PR. That does solve the problem of
representative democracy, as the greatest 19th century philosopher of
science, John Stuart Mill rea;lised, abandoning his own feeble remedies
to save democratic representation. The real problem is focusing on
single members, and mere single member majorities, which are not
democracy but minimal democracy, with the greatest scope for
dictatorship. As Mill said, and Lani Guinier, they are the tyranny of
the majority.

From a mathematical point of vew, the single majority is only a
decision based on more or less, that is ordinality, or the ordinal
scale, rather than proportionality, or the ratio scale, of many-member
majorities. As to the fanciful comparison of missing the Condorcxet
winner as accidentally amputating the wrong leg (as happens sometimes)
the assumption underlying this comparison may be likened to the
assumption that there is an absolute frame of reference in physics, like
the universal ether velocity. However that may be, the Condorcet Winner
is assuredly no such infallible bench-mark, by which all other results
must be struck down.

Pierre-Simon Laplace refuted  Condorcet pairing, over two centuries ago,
because it treats preferences as of equal importance. He thought Borda
better. In statistics, it's called weighting in arithmetic progression.
Statisticians prefer when they know the weights, rather than have to
assume them, which is the case of weighting in  arithmetic proportion.
This latter is what the improved method of JB Gregory does.

"The spoiler" candidate is only the point of view of the candidate
supporters, who want him removed for a Second Ballot. If you want to
adequately take into account the values of the spoilers supporters, then
you have to keep in context an over-all ballot of all the candidates,
otherwise this breaks the law of conservation of (preference)
information (which Binomial STV obeys).

Preference cycles rapidly disappear, at an exponential rate, the more
candidates there are. The three candidate cycle could only be important
to a focus on minimum choice elections. Two candidates are always a
cycle but no-one complains about that. Democratic elections are about
choice, not merely minimal choice.

Regards,

Richard Lung.

On 14/01/2023 06:26, robert bristow-johnson wrote:

On 1/14/23 07:26, robert bristow-johnson wrote:

I think my concern with Condorcet//Plurality is that Plurality is such a
bad method that if a botched strategy or a natural cycle happens, then
the result is really going to suck. It's not going to happen often, but
it would be a good idea to have somewhat less of a failure if it happens.

Doing top two (contingent vote) or IRV if there isn't a Condorcet winner
is better in almost every respect except for the one: you lose
monotonicity. As is Forest's summable approximation to Smith-IRV: Each
candidate has a penalty equal to the combined first preferences of the
candidates beating him pairwise. Lowest penalty wins.

Even just proceeding with BTR-IRV is better, I'd say, C//P. Or minmax,
though I would rather prefer Smith: it's somewhat of a guarantee that if
a cycle happens, you won't elect someone obviously bad (outside the
cycle). It's too bad that outside of Copeland and BTR-IRV itself,
there's no really simple Smith mehod; Forest's approximate Smith-IRV is
about the best simple improvement you can do.

Aw, thank you!

-km

Hi Richard,

Le samedi 14 janvier 2023 à 08:54:57 UTC−6, Richard Lung voting@ukscientists.com a écrit :

Your method does seem similar to Borda. Do you have any arguments as to why Binomial STV is
better than Borda? There's nothing really wrong with Borda in your view, is there?

Well, I don't know what that law is, but I don't feel that Borda-likes adequately address
spoilers. Whenever a voted majority favorite isn't elected, there will be a debate about
who spoiled it.

In what way could there be a preference cycle with two candidates? Can you show the ballots?

Kevin
votingmethods.net

Hello Kevin,

Judging by the discussion on Borda's method, by JFS Ross, in Elections
and Electors. (1955) Laplace was aware Borda method is manipulable.
(Ross played this down.) It allows manipulation of the count weights
between candidates. The cumulative voting family of methods parades this
as a virtue. As Enid Lakeman said, cumulative votes count against each
other. The Gregory method, used in all STV, including my version,
over-comes this redundancy. (Parsimony is counted a virtue in scientific
theory construction.)

Borda may have the last word, however. The Quark and the Jaguar, by
Murray Gell-Mann discusses series patterns found in nature. (I made a
few notes on it, in an e-book, Science and Democracy Reviews.) For
instance the statistics of city populations follow a common series. The
biggest city as unity population, the next biggest city as roughly half
the size and so on. I forget now, all the examples, whether they were
harmonic, geometric or arithmetic series. Gell-Mann said they didn't
know why they did that. Maybe they have found out, by now. It may be
that similar marked patterns will also be found in voting data. In fact,
we already know that there is an exponential falling off in voters
stating their orders of preference. It may be possible to state more
precise similarities.

Enid Lakeman looked into the change in electoral law in Malta. They were
aggrieved that the party with the most first preferences didn't have the
most seats, and changed the law accordingly. Lakeman pointed out that
first preferences are not the full weight of the vote. The full weight
is not counted by removing candidates, as spoilers, from the contest.

Binomial STV differs from the general usage, and Borda, in that it
counts all the preferences, including abstentions, relative to the
available vacancies. The more candidates than seats, the more the lowest
preferences exclude, rather than elect. Counting abstentions serves a
significant purpose, because if abstentions occur later than sooner, the
more the (binomial) count is an election, rather than an exclusion of
candidates.

The law of conservation of information is an inter-disciplinary rule
that, in a closed system, information, like energy, can neither be
created nor destroyed. In physics, energy and information are being
translated. The holographic principle was introduced to refute the
supposed loss of information from an object passing beyond the point of
no-return, the event horizon, to a black hole. (Leonard Susskind
discusses it online.) In "electics" or election method, all the
preference votes are counted. The binomial count is by STV, because
traditional STV already makes the best use of the information, in a
rational election count. Binomial STV duplicates a rational count in the
exclusion count, replacing a crude "last past the post" type exclusion,
not a lot better than first past the post or simple plurality. ----- For
Binomial STV, I use a more convenient form of Gregory method, the keep
value, introduced by Meek method, but capable of much wider use.

 Two candidates are always in a cycle, with just two perms: AB versus
BA. Three candidates perms display only some cyclicity, which decreases
exponentially with the number of candidates.

Regards,

Richard Lung.

On 15/01/2023 14:19, Kevin Venzke wrote:

Hi Richard,

Thanks for your response. I am always confused when you write about a relationship or
similarity between traditional STV and BSTV, given that in the single-seat 3-candidate
case of BSTV which has been detailed, there seems to be no need to invoke STV, and the
results of the two are certainly not similar.

Just to check my memory, in the past haven't you stated that elections with partial rankings
are flawed? If voter truncation patterns are dictated by laws of nature, maybe it's best
not to disturb this.

Well, I only want to ask about the single-winner case. I'm not familiar with any definition
of multi-seat Borda.

Above you say that traditional STV "already makes the best use of the information" but I am
not sure whether you are suggesting that traditional STV obeys the "law of conservation of
preference information." The latter I am sure is not true, because traditional STV will
never regard some lower preferences. So in what way could it be called "conserved," if
nothing ever sees it or uses it.

Are you talking about candidate sequences that might occur on individual ballots?

Usually "preference cycle" refers to group preferences. So A and B can't be in a cycle
alone, because the electorate as a whole will prefer one of the two (or it's a tie).

Kevin
votingmethods.net