Dear All,
I am finding quite difficult to receive any comment [positive or negative] on a proposal on the underlying reason of Arrow's and Gibbard Satterthwaite Impossibilities.
In my view they both rely on an incorrect formalization of majority rule, and if such rule is correctly formalized, they both can be overcome.
In the text, I also explain in detail a procedure for transforming preferences into collective choice that in my view fulfills every requirement for social and democratic choice.
If you are interesting in reading a prelim copy of the text [21 pages] in exchange for making a [brief] assessment, please send me your email, so I can forward you a link to the text.
Ricardo
Ps. Some knowleged of logic and ocial Choice is required to understand the text.
Hi Wald
My approach is a combination of two methods.
In a way it is more similar to first approach to Majority Rule for collective decisión making when the univers of posible options is greater than 2. This approach was proposed by Llul ca.1280.
While Llul's approach is first pairwise comparison of options and then choosing the option winning more comparisons [hence, it makes a comparison among all options for the decisión making], this approach is subtle modified by Condorcet [1785], who eliminates the second step.
Arrow's [1951/1963], May's [1952], Sen's [1966] works build all of them on Condorcet's formalization of majority rule, which inconsistency prooves my text [it makes two non equivaletn statemenst which become clearly inconsistent if |X|>2]
What I propose is therefore somehow a continuation of Llul's first idea, a combination of pairwise comparison with a comparison among all options at every step, in a secuencial process [the only manner of solving cycles].
The procedure I propose always chooses the Llul's/Condorcet winner if there is one, and matches frequently the Schulze Method [but not always].
Also the results provided seem to be manipulation resistent as well as not affected by later no harm, participation and separability paradoxes, since they are based on Condorcet's paradigm.
Does it answer you question?
Great Daniel!
Only that I received yesterday some comments from Markus Schulze on some issues which I need to solve prior to issue it again. As son as I have upadted it again, I will let you know.
Best
I dare recommend my anthology "On Arrow´s possibility theorem", cf. my contributions on ResearchGate.
Hi Bjorn. Thank you for your sugestions, but I checked your ink and it appears only to be an introduction to your book, but does not explain any particular view on the issue... Maybe in the rest of the book there is such explanation.?
May be you couldd just pose a brief summary of your ideas here....
The article "On the fundamental thought behind voting rules" could be the reading start. It is among my contributions on ResearchGate.
Chapters II.D.3 and 4 in my book Democracy with sequential choice and fund voting covers the most. They are short. The postscript in the mentioned "On Arrow´s possibility theorem" is a new and important overview.
Hi bjorn
I read your text 'On the fundamental thought behind ....". While I agree with you on some parts, not so sure on others. Let me explain:
As far as I recall, Borda rule does not undertake pairwise comparison... No at least in the classic: BORDA, JEAN CHARLES DE [1781] ‘Mémoire sur les élections au scrutin’, Mémoires de L’Académie Royale des Sciences, pp. 657-664
In fact, Borda proposes his rule prior to Condorcet discovering of cyclic paradoxes....
And, also as far as I know, it is no longer used as an aggregation procedure, because it is very very easily manipulable.
Thank you for your reminder of Arrow later correcction of IIA, which I did not recall. However, if you review his definition in bothe 1951 and 1963 it does not seem arbitrary at all, since he states taht 'the choice between x and y does not depend on other choices different thatn x and y' [more or less].
To me it does not sound arbitrary at all.
What I am stating, is that if you model any rational preference in the realm of fuzzy [not binary] logic, IIA as stated by Arrow is self inconsistent.
But if you model the premises system in the realm of binary logic, then there is no way to conceptualzie Monotonicity.
From that POV, Arrows impossibility result would be simply a proof of the erroneous choice of a premises system, not of the impossibility of proposing rules for democratic elections.
Is in that sense that I think many people have misinterpreted Arrow's theorem, assigning it a meaning that it does not have.
In epistemology is widely acknowledged that if you introduce an inconsisten premise into any system of premises, the system will necesarily lead to inconsistent results.
If you are interested, I can forward you a link for a free read of my text [text is 80 pages, while annexes are another 80 pages]. Just let me know.
Best, Ricardo
If you have a suscription to Amazon, you can read it free at KDP.
http://www.amazon.com/vote-veto-possibility-democratic-choice-ebook/dp/B019LIX62K/ref=sr_1_1?ie=UTF8&qid=1458159822&sr=8-1&keywords=from+vote+to+veto
I guess the interesting part for you would be chapter 3, and annex II.
Best, Ricardo
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