For the profile(s) in which there is successful manipulation, specify the person
ID: 1151705 • Letter: F
Question
For the profile(s) in which there is successful manipulation, specify the person as well as the ranking she will reveal instead of the truthful one. 5.7 Exercise 187 from Kelly's (1987) book In the following figure, a rule is specified that gives the alphabetically earliest of the Pareto optimal alternatives for the case of two individuals with strict preferences only. Check that this rule is non-dictatorial. Find the tour profiles at which this aggregation rule is manipulable. 5.8 Consider the following profile for three individualsExplanation / Answer
5.7) Here we are presented with different preferences for two individuals arranged alphabetically.Now,based on the list of preferences presented in the table,we can try figuring out the socially preferred/optimal choice that is commonly agreed by both individuals.Alternatively,a non-dictatorial preference reflects socially autonomous preference or choice that commonly represents the will of both individuals in this particular instance.
First if we focus on the preference between x and y,notice that out of the 6 preference list presented in the left hand most column,in 3 preferences,x is preferred to y and in rest of the 3,y is preferred to x.Hence, we cannot stricly state any strict preferential relation between x and y.Now focusing on the preferentialrelation between x and z,we can see that again in 3 of the 6 preference list,x is preferred to z and in other 3 z is preferred to x.Again,notice that y is preferred over z in 3 of the preference lists and z is preferred over y in other 3.Therefore,in this instance there is no dictatorial preference or socially optimal preference exists in this instance as there is strict preferential dominance of one choice over the other and all choices are represented/preferred equally considering all the 6 preference lists.
However,if we focus on preference lists xyz,xzy,zxy and zyx we can find a pattern where in the first three choices we find a strict preferential choice representing dictatorial preference.Based on Social Welfare Function or Aggregation Rule we can state that although looking at the all the preference lists,there is no strong dictatorial choice but however for these four particular lists,the aggregation rule can be manipulated where some strong preferential choices are reflected.