The Talking Stick Blog

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Caucusing and the Four-Color Theorem

(January 30, 2020) Last week I made up a silly example of laws about dairy-product usage and decided today that I’m just going to run with it.

“Suppose that your state is going to vote for a leader and that all citizens and candidates only care about one issue: the law that you can keep dairy products in your refrigerator for no more than 21 days. You hold a caucus. What happens when the following four candidates run and the puppets vote?

  • DAIRY-LOBBY CANDIDATE (dark blue): The soy milk industry is damaging the dairy milk industry. Our state’s workers feed their families with money earned from working with cows. I will work to make soy milk illegal, and if not illegal, pass a law against calling it “milk.”
  • COW-OWNER CANDIDATE (light blue): I have some cows but also have child who is lactose intolerant and needs an alternative to dairy products. I support the applying the 21-day rule to both dairy and non-dairy milk products.
  • HEALTH-PERSPECTIVE CANDIDATE (green): Since expired dairy milk and expired soy milk have different health consequences, the 21-day law should only apply to dairy milk. I will pass a law exempting soy milk.
  • NO-NANNY-STATE CANDIDATE (pink): What is the government doing in our refrigerators? The 21-day milk law should be struck down. The government has no business making and enforcing laws about how we use products.”

First the students reacted to these candidates. Disbelief that someone would propose criminalizing the word milk applied to non-dairy beverages. Confusion about what soy milk is. Uncertainty about the word “exempt.” Laughter...

We had the puppets (so that we don’t get into discussions of student preferences) caucus for these candidates. We explored all sorts of scenarios of first and second alignment, based upon explanations from the Des Moines Register.*

 

After experiencing a caucus first-hand, I asked the big question: I told the students the 5 changes that Iowa was instituting this year and asked the students for conjectures on the reasons for each change.

MAP COLORING

Can you make a map that requires 5 colors to color? At various points students thought they did. We talked about how a mathematician’s job is to make patterns and break patterns. I walked around trying to break patterns (in other words burst people’s bubbles of hope that they had succeeded in this mission). In most cases I was able to point out a way to use fewer colors.

But there were 2 maps where I couldn’t do this quickly or easily.

I promised students that next week, they (not I) will try to reduce these student-created 5-color maps to 4—or-fewer color maps.

ANTI-PLURALITY VOTING

We played out and analyzed Wikipedia’s Tennessee capital example of anti-plurality voting. Students discussed and realized about how this method can lead to results where a more middle-of-the-road/bland/non-extreme candidate is more likely to win. “Is that a problem?” I asked. Students were split. My helper Ellen then read from an article on presidential candidate Andrew Yang’s website about voting methods.

QUESTIONS/UNEXPECTED TOPICS

Our mathematical explorations led students to pose some new questions. (Some of you may be familiar with Rochelle Gutiérrez’s work on rehumanizing mathematics. Giving students opportunities to follow their own curiosity and to connect math to other disciplines are two of the ways we can rehumanize mathematics.) Our students wondered and investigated/discussed

  • HISTORY: Which candidate is a Freemason?
  • ETYMOLOGY: Why is milk called milk?
  • CURRENT EVENTS: Are Republicans caucusing in Iowa too, or is it just the Democrats?
  • POLITICAL SCIENCE: If the Senate convicts the president and he cannot run for a second term, would the Republican party be able to field a candidate at this point, and if so, whom?

Rodi

‘* Our discussions were based upon good background info from the Des Moines Register and NPR.

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