Question

4. Suppose 3 people (Angelie, Bernard and Carly) are deciding between three choices for dessert: Cream, Boba Guys and Salt & Straw. The table below shows each of their preferences in descending order. (Eg. Angelie prefers Cream to Boba Guys, Boba Guys to Salt & Straw and Cream to Salt & Straw.) Angelie Bernard Carly Order of Preference Cream Boba Guys Salt & Straw Boba Guys Salt & Straw Cream Salt & Straw Cream Boba Guys a. Based on the three individual's preferences which restaurant would win in each of the following cases? (Assume they will use a simple majority rule when voting) i. Boba Guys vs Cream (L.e. Angelie, Bernard and Carly each vote either Boba Guys or Cream and the restaurant with the most votes wins) ii. Boba Guys vs Salt & Straw ill. Cream vs Salt & Straw b. For each of the following state if the statement is true or false, and briefly explain i. Ir Cream beats Boba Guys and Boba Guys beats Salt & Straw, then Cream beats Salt & Straw. ii. If Cream beats Boba Guys it's because everyone prefers Cream to Boba Guys.

Answer 1

Denoting Angelie, Bernard and Charlie as A, B & C respectively, and

Cream, Boba Guys and Salt & Straw as X, Y, Z respectively, we can compute the following regarding preferences (≻) of A, B, C :

A: X ≻ Y ≻ Z

B: Y ≻ Z ≻ X

C: Z ≻ X ≻ Y

a) Clearly, no single desert has a majority as each individual A, B, C possess an independent preference ranking of commodities.

Thus, for all three sub-parts (i, ii, ii), there is no clear winner.

b)

i) If Cream beats Boba Guys and Boba Guys beats Salt & Straw, it means Cream beats Salt & Straw.

This directly follows from the axiom of TRANSITIVITY, which says:

“If X ≻ Y and Y ≻ Z, then X ≻ Z.”

ii) If Cream beats Boba Guys, its because everybody prefers Cream to Boba Guys.

This directly follows from the axiom of DOMINANCE, which says:
“More is better than Less.”