Alladi Ramakrishnan Hall

A Sampler of the Mathematics of Voting and Choice

Karl-Dieter Crisman

Gordon College

We all know that there is some math when we hold elections - we have to
add up the votes! But isn't that it?

It turns out that there is mathematics at every turn when we choose
things. We could be:

• Deciding who wins an election.
• Deciding how to divide undesirable things - like rent or committees.
• Deciding how to apportion representation among unequally-sized states.

In all these situations (and many more), logical thinking and mathematics
play a big role in:
• Deciding whether the "right" candidate won (or how to ensure your choice
does win).
• Finding ways to negotiate divisions acceptable to all.
• Preventing (or encouraging!) gerrymandering to protect incumbents.

This talk will be a sampler of related topics, touching on a wide range of
connections between mathematics and choice. We will also give hints of
some more powerful mathematical tools which are starting to be used in this
area.