Summary: CS 7910 Homework 4: Social Choice
I want you to play with social welfare functions so that you get familiar with the concept.
I want you to see that the various voting mechanisms choose very different candidates (so that
you do not mistakenly believe that all of them will select the same "most preferred" candidate).
I want you to try to develop a social choice mechanism yourself.
Arrow's impossibility theorem says that there is no social choice mechanism that takes individual
preference patterns and generates a fair societal preference pattern. Arrow defined fairness according
to axioms, and showed that all the axioms could not be simultaneously satisfied. Voting methods are
attempts to take individual preference patterns and create a "fair" societal preference pattern. We
should be able to identify situations where the voting mechanism breaks down. Since there is no way
for voting to be fair, the task of somebody who is designing a voting mechanism is to minimize the
Consider a society of seven voters (A-G) who are trying to reach a consensus on which of the
alternatives they want (say, Coke, Sunkist, Root Beer, Milk, OJ) for the title "CS Department Favorite
Drink". 1 represents the first choice and 5 the last choice. Each agent ranks them as 1 (meaning the
best) and 5 (meaning the worst).
One method will utilize a confidence in the vote. Each individual has a varying confidence in his/her
vote. We will use confidence as follows: Since voter B has confidence 4 (conf 4) in its ranking, we