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\centerline{Math 36 --- Daily Homework}

\centerline{Assigned: 11/8} 

\centerline{Due: 11/10}
  

\begin{questions}

\question 

The standard Borda count ($n-1$ points for first place, $n-2$ for second, ..., $0$ points for last place) is clearly not a dictatorship. You will show that the Borda count satisfies Unanimity but not Independence of Irrelevant Alternatives.
\vspace{0.5 in}

Prove that the Unanimity axiom holds. Recall that Unanimity means if every individual ranks $A$ above $B$, then society must rank $A$ above $B$.

\vspace{2 in}

Prove that the Borda count does not satisfy Independence of Irrelevant Alternatives. Show this with a counterexample by giving two sets of votes where each voter gives the same relative ranking of $A$ and $B$ in both, but by changing the position of another alternative $C$, the societal ranking of $A$ and $B$ is changed from profile to the other.

\end{questions}


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