MATH 170 · Markov chains · Political Party Dynamics

Where should the Avians campaign? Animalia · Markov chains

You are a bird, and a grassroots organizer for the Avian Advancement Party in the nation of Animalia. Your party has raised enough money for exactly two campaigns, and there are four cities to choose between. The analysts have handed you, for each city, a table of how voters change party in a single year. Elections come every four years. These matrices and the 2024 populations are the analysts' report — you cannot edit them here, because the argument you are being asked to make has to survive the numbers you were given. Step each city forward and see which two are worth the money.

The analysts' report

Row = the party someone belonged to in 2024. Column = the party they move to within one year. Read across a row and the numbers should total 1.

Step the city forward

Each circle is a party; its size is the share of voters affiliated with it right now. Each arc carries the probability of switching that way in one year.
oldernow
One bar per year, oldest at the top and palest. Left to right inside a bar, the four parties always sit in the same order; the numbers under the newest bar are the current shares.
t = 0

The worksheet's questions, for this city

Try: ask each city for its 2024 Avian share, then for its long-term one. The two rankings are not the same — that is the whole recommendation.