User talk:Y2y
Arrow theorem: restricted domain
[edit]- 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
There was a lot of work on graph theory and Agregation of preferences. Gil Klai from the Hebrew University did some research on that, I think. But I haven't read these things in the last couple of years, so I'll have to search. mousomer 20:14, 21 February 2006 (UTC)
The main issue with the image is that there are no "hard" values for the graph. The 'M' stands for median and by its very nature must be at the peak of the curve, which by its very nature must be symmetrical. The Y-axis is somewhat arbitrary and the X-axis represents increments of people, and goes from 0% to 50% towards the M.
"Already won" signifies the voters who have made up their minds, or decided to vote for a certain candidate who endorsed their opinion on the issue. The idea is that there are some people who will be extremists and others who are more middle of the road - say the issue at hand is the eradication of all apple trees. Some people will right away be for it (those maybe allergic to apples?) while others will right away be against it. Those are the starting points, the edges of the skirt of the graph. Others might need more convincing to make a decision. In such an idealized representation, one would think that the people with the most extreme views are very small in number, and that most people are indifferent or wavering on the topic. In this schematic Party A only has to approach the median - or water down their policy on the matter - to a much smaller degree than Party B.
Sorry, I can't get into too many details about the exactness of this type of graph, but hopefully this explanation will allow you to see it in a different light and reflect on its data. Please respond with any other queries or comments on the article's talk page. JesseRafe 02:05, 7 April 2007 (UTC)