User talk:Mousomer
From Wikipedia, the free encyclopedia
Hello, welcome to Wikipedia. Here are some useful links in case you haven't already found them:
If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page. I hope you enjoy editing here and being a Wikipedian!
Tip: you can sign your name with ~~~~
snoyes 15:16, 28 Jan 2004 (UTC)
[edit] Glossary
Hi there - Thanks for joining the wikiproject on game theory, we're happy to have you around! I noticed your note on your user page. Are you referring to the Glossary of game theory? --best, kevin ···Kzollman | Talk··· 18:51, September 3, 2005 (UTC)
[edit] non-imposition & monotonicity => Pareto
Hi -- thanks for your comment. I think we may need to clarify the definition of monotonicity in the article. The way I understand it, I think what you wrote isn't right, but you may have a stronger definition of monotonicity in mind.
Consider a single-individual society with three alternatives with the following social welfare function:
ABC -> BAC
BAC -> BCA
ACB -> ABC
CAB -> ACB
CBA -> CAB
BCA -> CBA
This is non-imposing, non-Pareto and non-independent of irrelevant alternatives. As I understand the monotonicity definition in the article, however, it is monotonic -- you can't demote any alternative in the social preference simply by promoting it in the individual preference without changing the order of the other two alternatives. If the latter is supposed to be allowed, that should be clarified in the definition of monotonicity. Joriki 09:54, 6 October 2005 (UTC)
- Hi Mousomer -- sorry it took me half a year to respond to your reply to this! You wrote: "I have a feeling that this should be no more than a freak pathology having to do with having just one voter. Can you show this phenomenon in general with any number of voters?" I think the social welfare function that ignores all but one voter and depends on the one voter in the above way is also non-imposing, non-Pareto, non-independent of irrelevant alternatives and monotonic. You also asked: "Where did this example come from?" I made it up for this occasion :-) Joriki 20:45, 30 April 2006 (UTC)
[edit] Arrow theorem: restricted domain
Have you a reference for the following your assertion in the section "Some possibilities" of Arrow's impossibility theorem. IMHO such reference should be presented in the article.
Indeed, many different social choice functions can meet Arrow's conditions under such restricting of the domain. It has been proved, however, that any such restriction that makes any social choice function adhere with Arrow's criteria, will make the majority rule adhere with these criteria
--Y2y 08:46, 21 February 2006 (UTC)
