The election for mayor is coming soon in the small town of Ecolopolis (population 5000).The two candidates are Aaron Aardvark and Paula Platypus. Paula Platypus currently has a big lead, with 80% of the population ready to vote for her.
As usual, the politics turn ugly. Five days before the election, Aardvark’s campaigners (all
6 of them) decide that they will taint Platypus’ reputation by spreading the rumor that she has a
drinking problem. Naturally, everyone they tell believes this rumor and switches their allegiance over to Aardvark. What’s more, each person who hears the rumor then spreads the rumor to everyone they chat with.
The Platypus campaigners (all 6 of them) realize what is going on. Two days before the election, they go out and start telling the townspeople that the rumor is a lie. The people they talk with believe them and switch their allegiance back to Platypus (if they supported her originally),and then help refute the lie with others they chat with.
Who is likely to win the election? And how likely is it?
The Attempt at a Solution
I have tried multiple things to model this situation. However, I am thinking it required a higher understanding of second order differential equations. This is for an engineering class, but diff eq isn't required. Every project we have done this semester has been easily done with diff eq but our coursework hasn't gotten us to second order DE's yet. Any guidance AT ALL is extremely helpful. As of now I have two really, really weird equations that don't really do a good job at deciding who has a better chance of winning.
Also, we recently worked on a sensitivity analysis, and I think this deals with that too (For testing sensitivity of word of mouth variables), if that helps at all.
Thank you so much for any help you can offer.