[EM] Borda-likes (was: Just to let you know...)

[Richard Lung]

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,
>
> Le samedi 14 janvier 2023 à 08:54:57 UTC−6, Richard Lung <voting at ukscientists.com> a écrit :
>> 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.
> 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?
>
>> "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).
> 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.
>
>> 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.
> In what way could there be a preference cycle with two candidates? Can you show the ballots?
>
> Kevin
> votingmethods.net