Arrow and Gibbard-Satterthwaite

[Steve Eppley]

Markus wrote:
> Steve wrote:
-snip-
>> To Ken Arrow, all non-winning candidates are "irrelevant".  
>> Your own definition of "relevance" may not be as strict as
>> Arrow's.
> 
> I thought, I used Arrow's definition of "relevance"
> in my e-mail "Arrow, Gibbard, and Satterthwaite". Could
> you tell me, where my definition differs from Arrow's
> definition?

When I wrote "Your own definition..." above, I wasn't referring 
to Markus' definition.  I was referring to definitions which 
readers of my message (not just Markus) might wish to use.

Though I don't always maintain a consistent email style, in
maillists where many people may be reading I generally try to
use the second person ("you", "your", etc.) to refer to the
unknown readers, and the third person (e.g., "Markus wrote such
and such...") to refer to the author of the message to which
I'm replying. 

>> Bruce Anderson, an EM subscriber, wrote that the
>> thrust of his research involves relaxing the definition of
>> "relevance" so it includes all the alternatives in the Smith 
>> set (in other words, all the circularly tied alternatives) 
>> and investigating which methods satisfy this "relaxed IIAC" 
>> as well as all the rest of Arrow's criteria.
> 
> I couldn't find Anderson's investigations in the election
> methods list. Could you post it to me or to the election
> methods list? I am very interested, whether Anderson found
> other methods, that fail to meet Pareto.

Bruce didn't post the details.  He mentioned his research,
without providing details, in a private message.  I don't
recall him ever mentioning Pareto, so I don't know whether 
he's investigated methods which fail Pareto.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)