Results 1 to 6 of 6

Thread: 'Three Brief Proofs of Arrow's Impossibility Theorem', John Geanakopolis

  1. #1
    Banned
    Join Date
    Jun 2006
    Location
    Washington Island, across Death's Door, Wisconsin, USA
    Posts
    9,193

    Post imported post

    The proof
    http://cowles.econ.yale.edu/P/cd/d11a/d1123-r3.pdf

    The Wikipedia's synopsis
    http://en.wikipedia.org/wiki/Arrow%2...bility_theorem

    The Wiki's introduction
    In social choice theory, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a certain set of reasonable criteria with three or more discrete options to choose from. These criteria are called unrestricted domain, non-imposition, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. The theorem is often cited in discussions of election theory as it is further interpreted by the Gibbard–Satterthwaite theorem. The theorem is named after economist Kenneth Arrow, who demonstrated the theorem in his Ph.D. thesis and popularized it in his 1951 book Social Choice and Individual Values. The original paper was entitled "A Difficulty in the Concept of Social Welfare".[1] Arrow was a co-recipient of the 1972 Nobel Prize in Economics.


  2. #2
    Founder's Club Member
    Join Date
    Nov 2006
    Location
    Fairfax Co., VA
    Posts
    18,766

    Post imported post

    Doug,

    I don't have my PhD, yet.

    Can you break that down for us.

    And maybe tie it to OC in accordance with the forum rules.


    I'll make you an offer: I will argue and fight for all of your rights, if you will do the same for me. That is the only way freedom can work. We have to respect all rights, all the time--and strive to win the rights of the other guy as much as for ourselves.

    If I am equal to another, how can I legitimately govern him without his express individual consent?

    There is no human being on earth I hate so much I would actually vote to inflict government upon him.

  3. #3
    Banned
    Join Date
    Jun 2006
    Location
    Washington Island, across Death's Door, Wisconsin, USA
    Posts
    9,193

    Post imported post

    I have no intention of defending my decision to bring this to attention. If the owner/mods find it disruptive then poof - sic transit gloria mundi!

    I believe worse has been allowed to remain to damage us all. This is entirely uplifting and enlightening to any that will understand it.

    In the incoming administration of PEBO we see the effect of democracy's unintended consequences.

    General Discussion
    Use this area for discussions that are somewhat off-topic or that do not fit anywhere else. Topics should still be related to the focus of the forum and all other rules of behavior still apply here.

  4. #4
    Founder's Club Member Hawkflyer's Avatar
    Join Date
    Feb 2007
    Location
    Prince William County, Virginia, USA
    Posts
    3,315

    Post imported post

    Citizen wrote:
    Doug,

    I don't have my PhD, yet.

    Can you break that down for us.

    And maybe tie it to OC in accordance with the forum rules.

    There can never be a pure democracy, because you will never get everyone to agree on what should be done. That disagreement eventually lead to total anarchy. In an anarchical world it is best to go armed.:celebrate

    As you can see I too am stumped.
    "Research has shown that a 230 grain lead pellet placed just behind the ear at 850 FPS results in a permanent cure for violent criminal behavior."
    "If you are not getting Flak, you are not over the target"
    "186,000 Miles per second! ... Not just a good idea ... It's the law!"

  5. #5
    Banned
    Join Date
    Jun 2006
    Location
    Washington Island, across Death's Door, Wisconsin, USA
    Posts
    9,193

    Post imported post

    No, you got it exactly.

    A voting system can be configured to make any candidate the winner.

    I'm doing a statistics review and this was rigorously demonstrated by considering all possible alternatives among a reasonably limited set of candidates.

  6. #6
    Founder's Club Member
    Join Date
    Nov 2006
    Location
    Fairfax Co., VA
    Posts
    18,766

    Post imported post

    Hawkflyer wrote:
    SNIP There can never be a pure democracy, because you will never get everyone to agree on what should be done. That disagreement eventually lead to total anarchy.
    And we needed ivory-tower PhD's and researchers to tell us that?

    I don't know what's scarier. That it highlights the disconnect of academia, or that it indicates what it takes to penetrate their murkiness--convert common-sense to lots of $50-words and arrange it in way that it can't be argued against under their "accepted" rules of engagement. And only then does it get through.

    After peer review, of course.
    I'll make you an offer: I will argue and fight for all of your rights, if you will do the same for me. That is the only way freedom can work. We have to respect all rights, all the time--and strive to win the rights of the other guy as much as for ourselves.

    If I am equal to another, how can I legitimately govern him without his express individual consent?

    There is no human being on earth I hate so much I would actually vote to inflict government upon him.

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •