At 12:22 PM 11/8/2009, Terry Bouricius wrote:
A somewhat more accessible (and available online for free) analysis of
strategic vulnerability of various methods is in this doctoral paper by
James Green-Armytage (Strategic voting and Strategic Nomination:
Comparing seven election methods). He
Abd ul-Rahman Lomax wrote:
Notice that the requirement of Arrow that social preferences be
insensitive to variations in the intensity of preferences was
preposterous. Arrow apparently insisted on this because he believed
that it was impossible to come up with any objective measure of
On Nov 16, 2009, at 10:53 AM, Andrew Myers wrote:
Abd ul-Rahman Lomax wrote:
Notice that the requirement of Arrow that social preferences be insensitive
to variations in the intensity of preferences was preposterous. Arrow
apparently insisted on this because he believed that it was
On Nov 16, 2009, at 11:53 AM, Stéphane Rouillon wrote:
Would this suggest it could be possible to overcome Arrow's theorem using
range ballots?
I do not want to say Arrow's theorem is false. All I ask is:
Are prefential ballots one of the hypothesis used in Arrow's theorem proof?
Because
Jonathan Lundell wrote:
This is in part Arrow's justification for dealing only with ordinal
(vs cardinal) preferences in the Possibility Theorem. Add may label it
preposterous, but it's the widely accepted view. Mine as well.
Arrow's Theorem seems like a red herring in the context of the
How should we continue from this? Should we divide the seats
proportionally at top level to the top level branches of the tree, and
then repeat the process towards the leaves.
What are the main differences between the tree if derived from the
ballots using clone analysis vs. if given by
On Nov 16, 2009, at 2:15 PM, Andrew Myers wrote:
Jonathan Lundell wrote:
This is in part Arrow's justification for dealing only with ordinal (vs
cardinal) preferences in the Possibility Theorem. Add may label it
preposterous, but it's the widely accepted view. Mine as well.
Arrow's Theorem
Yes, Arrow's Theorem does assume ordinal ranking, since the whole goal of
the decision process was to find a community-wide decision about how
options should be placed in an order from favorite to least favorite
(rather than just find a winner), and he expressly dismissed cardinal
scores as
Jonathan Lundell wrote:
I don't have his proof in front of me (I'm on the road), but I'm pretty sure
that it assumes ordinal ranking.
It seems fairly obvious that the theorem also holds for ratings, because
ratings can be projected onto rankings without affecting any of Arrow's
criteria.
The theorem states (from wiki) that there is no method which has the
following properties:
* If every voter prefers X over Y, then the group prefers X over Y.
* If every voter prefers X over Y, then adding Z to the slate
won't change the group's preference of X over Y.
* There is no
Strictly speaking I don't think Range is an election method according
to Arrow, because you can't determine the winner from the orderings.
It would be hard to make statements about the effect of introducing
candidate Z when you don't have an assumption about what the outcome is
based on.
You can
On Nov 16, 2009, at 4:58 PM, Raph Frank wrote:
The theorem states (from wiki) that there is no method which has the
following properties:
* If every voter prefers X over Y, then the group prefers X over Y.
* If every voter prefers X over Y, then adding Z to the slate
won't change the
fsimm...@pcc.edu wrote:
Here's a suggestion for detecting clone sets based on Range Ballots:
Define the distance between two candidates as the square root of the
sum (over the ballots) of the squared diffference of their respective
ratings.
If the ballots are approval style, this becomes the
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