Question

The fundamental problem of social choice is aggregating individual preferences into a collective preference function that allows society to make a decision. We approached this question with both normative and positive theory and surprisingly found that they both point in the same direction. Normatively, Arrow's Impossibility Theorem started with a reasonable set of requirements for the social choice process and showed that they were internally inconsistent. Positively, McKelvey's Theorem showed that when the mechanics of social choice do not provide a decisive choice under majority rule, chaos ensues and democratic ideals are lost. Assume you are talking with a friend (also a political science major) who has not taken this class.  

                A.            Explain Arrow's and McKelvey's Theorems to your friend in terms that he or she can understand.

                B.            Indicate how the two theorems are related

                C.            Tell your friend why Professor Roberts can't sleep at night when he thinks about the results of these theorems. That is, describe what is disturbing about the theorems.

Answer 1

Arrow Impossibility theorem , mean where preference is ranked, It is Impossible to formulate a social ordering without violationg the certain condition. In case of voting System where ranked system is in operate. The wishes of multiple voters should be taken into consideration grao xa unanimous Inclinice al preference must be respected. If every vores prefers candidate A ones candidate B Candidate A should win. 3 f Chorce is removed, then the other oder should not change: le of candidate A rank ahead of candidate Bon A should candidate a should still be ahead of candidate B enen ir a third candidate C, is removed from participation

Example candidate A, B, C are in voting System • 4S Use A> B>С (ч рео о р, со Аоши в and prefer Bover c) o sso • o voks B> CSA (чо р о р р и в моел с and pr% и сошл А) . 30 votes c> A> B (30 people prefer c nostro ones A and prefer ones B o r Candidate A has the most votes, so he steht would be the winner howeries of B was not running, C would be meinnes as more people prefes Cover A. (A has 450 votes & c would I have 70 ) Mckelney - Schofield chaos theorem, It states that if preferences are defined i over a multidimensiones policy space, then. majority rule is in general unstable e there is no condorcet minnes. The w chaos theorem shows that this good neues does not continue in multiple dimension Example : like about example where is winnen, of condition of munner is 2% of total votes then no one is minnes. of condition of minne. 51trotes then с і шіп пе .

Both the theorem are based on preference based voring on three or more choices. Arrow paradox say that, essentially no Preference - based voting System can meet a list of specifico voting criteria and be accouale. group hond Mckelny say just notes that the opinion might not in simply it said Group opionion could quite possible est any of the individual opinion. match almost any of the Both dealing with preference 3 or more people stating that be or & is not faire voting on it could? UDOJ In my opionion Robert is thinking about the of a party win m onty with majority number of voting & It can't full fill the Demand or pronde Satisfaction to Public then the Mckelry theorem. applied here. Because of party not full filling Demand, then public create choas. then the party lost majority or is it still continues