Math 210 - Fall 2010, Creative Homework Solutions

Homework 4

Problem 5 on this homework was to describe a situation of interest to you in which three or more parties had to vote on three or more options. The problem asked for an analysis of strategic voting in the case you describe. Here are some excerpts from the solutions which were submitted, in no special order:

  1. ``In the jungle, Nature, the harshest mistress of al, completely dominates. For a trio of monkeys, this means but one thing: monkey see, monkey do. Each monkey wants to pursue a different path: the first monkey wants to see no evil, the second monkey wants to hear no evil, and the third monkey wants to speak no evil. .... In actuality, the fact remains that they're a group of monkeys. In reality the probably got together with 97 of their friends and a crate of typewriters and put together some Shakespearean plays. Or most likely, they ran hooting into the jungle, hands over their ears.

  2. ``The status quo concerning which of three roomates A, B, and C will live in the smallest of three rooms is represented by A followed by B followed by C, based on physical fierceness."

  3. ``A situation for me where three or more parties had to vote on three or more optoins was my family choosing its vacation destination.... . This accurately describes what occures every two years. We always go to the because it is the best optin for one group and the second best optoin for the other of two groups... When my brother and I became old enough to drive, we demanded that our say mattered more, essentialy by refusing to help drive somewhere we thought boring like the National Park..."

  4. ``One situation I regularly experience where three or more parties have to vote on three or more options is when my mother, my father and I have to decide what to do for dinner....My mother prefers to stay at home (to economize), my father likes Indian food, and I like Chinese food....I don't think that I vote strategically (although maybe subconsciosly I do)."

  5. ``Three friends, call them A, B and C, want to go to dinner and choose between Chinese food, Italian food and American food.....A and B have no dominant strategy, so they should work together to prevent the worst outcome for them."

  6. ``Most evening I go to dinner with two of my roomates.... Eliminating dominated strategies we can see that the Greek lady is our choice dining establishment (which is true)."

  7. ``In the NBA, the issue of players salaries has been a topic of debate. The players would prefer to keep the current salary system, the owners prefer a new salary systme, and the commisioner favors a compromise but understands the owner's concerns. ..My predictions do reflect the reality of the situation. The owners and commissioner realize that it is unlikely that they will get their most preferred option. Therefore, they will vote for the other's option more frequently, hoping to overcome the Player's strictly dominating option. Unlike baseball, the NBA has been better at preventing collusion, so mixed strategies are the only way to get optimal outcomes."

  8. ``Say there are three individuals who are stranded together on an island. After spending weeks starving and living off of only cocnuts, they come across a tiny settlement. They notice that the settlement has an abundance of food, but an over abundance of weapons as well. The three invidivuals have different preferences concerning the three strategies of (i) talking with the natives in a friendly manner, (ii) avoiding the natives, and (iii) sneaking into the settlement to steal some things....The outcome is option (ii), avoiding the natives. I believe this reflects the real life situation, since the settlement's huge arsenal will scare off most stranded strangers. No one would risk their life to steal from or to be a part of such a crazy settlement."

  9. ``Say two sisters are dating two men who are best friends. One couple has a breakup and the other couple continues to date. All are thrown into a dilemma of whether to take sides or to try to remain neutral. The status quo is Neutral >= sides with the ex of the sister >= sides with the sister who breaks up... These calculations reflect a reality, for in this situation, the girl in the couple that stays together will have to side with her sister, but the outcome will be neutral because the boyfriend will side with his friend. The members of the remaining couple don't want to be caught in the middle."

    Last updated: 10/14/10
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