# KimKlinger-Logan

kling202 (at) umn (dot) edu

# Mathematics of Voting

"It's not the voting that's democracy; it's the counting."

-- Tom Stoppard, Jumpers

Here are the slides and worksheet from my talk at St. Olaf in Febrary 2016. There are some many avenues for investigating voting theory and even doing undergraduate research in this area. This is just the tip of the iceberg.

## Arrow's Impossibility Theorem

Proof of Theorem: I found it difficult to find a concise proof of Arrow's Impossibility Theorem. I wrote up this proof based off of what can be found on Wikipedia. Unfortunately, Wikipedia they tried to make it intuitive by avaiding mathematical notation, the wording of their proof is very confusing (likely due to having too many people editing) and the pictures that they have used are misleading. I hope that what I have written up is clearer than what can be found there while still not being impenetrable.

## Links to other Voting Theory related things

Radio Lab's Tweak the Vote: I love Radio Lab. In this episode they mostly discuss the Pluraity-with-Elimination method. However, they do bring up other examples of elections where this method is used and present some ideas about how using such a method would alter candidates actions. Also if you have not listened to Radio Lab before take the time ti check out their stuff -- they have some amazing episode relating to science and math and all sorts of cool stories!

More Perfect's Who's Gerry and Why Is He So Bad at Drawing Maps?: The Radio Lab people made this great spin-off podcast called More Perfect which is all about Supreme Court cases that have shaped our country (I promise it's entertaining!). This episode is about Gerrymandering.

Tom Stoppard's Jumpers: This play is a quick read. Tom Stoppard is an amazing Brittish playwrite. Wikipedia describes the play this way: "It explores and satirises the field of academic philosophy, likening it to a less-than skilful competitive gymnastics display. Jumpers raises questions such as "What do we know?" and "Where do values come from?" It is set in an alternative reality where some British astronauts have landed on the moon and "Radical Liberals" (read pragmatists and relativists) have taken over the British government (the play seems to suggest that pragmatists and relativists would be immoral: Archie says that murder is not wrong, merely "antisocial"). It was inspired by the notion that a manned moon landing would ruin the moon as a poetic trope and possibly lead to a collapse of moral values."