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\include{syllabi}

\begin{document}

\title{A procedure for choosing the schedule}
\date{}
\maketitle

There are 6 people and 6 schedule slots. There's also a big pile of fancy candy. The basic idea is that people who don't get the slot they wanted will be compensated with fancy candy.

Each person fills out a ballot where they give a numerical value to each schedule slot. The numbers on your ballot should add up to 120. Each person's fair share is 20 points of value, so you should be satisfied if you get a slot which you valued 20, or if your slot is valued less you will get pieces of candy to raise your value to at least 20. (Each piece of candy is worth 1 point of value.)

\vfill

Here's how we will decide who gets what:
\begin{enumerate}
\item We assign the slot which has been given the highest value by any student without a slot. \label{loopstart}
\item The highest bidder gets the slot.
\item All people who did not get the slot are compensated with fancy candy, getting 1/6 of their valuation of the slot. 
\item Return to step \ref{loopstart} and assign the rest of the slots.
\end{enumerate}

There may be ties in some steps- ties are always broken randomly.

\vfill

Let's try this example:

\hfill
\begin{tabular}{l|c|c|c|c|c|c|}
 & A & B & C & D & E & F \\
 \hline
 $x$ & 80 & 10 & 5 & 5 & 10 & 10 \\
 \hline
 $y$ & 20 & 20 & 20 & 20 & 20 & 20 \\
 \hline
 $z$ & 15 & 25 & 30 & 10 & 19 & 21 \\
 \hline
 $t$ & 24 & 16 & 19 & 21 & 0 & 40 \\
 \hline
 $u$ & 0 & 0 & 120 & 0 & 0 & 0 \\
 \hline 
 $v$ & 1 & 2 & 3 & 4 & 5 & 105 \\
 \hline
 \end{tabular}
\end{document}