Midterm Rational Voting

Last week in my Transition to Higher Math class, my professor was trying to get our input on midterm scheduling, between two dates: November 6th and November 13th. This was her attempt to get us to reveal both preferences and intensity, as only people with previously scheduled exams conflicting would bother raising their hand, as the cost of having to actually justify your excuse to her was otherwise too high. However, since the class initially seemed pretty split, she then turned to a simple majority vote between the two, with 11 voters favoring November 6th and 10 voters favoring the 13th, as well as nine abstentions (myself included). While this is a 52% margin, she didn’t want to decide by only one person’s whim. To better the odds, we then voted between November 4th, 6th, 8th, and the 13th.

However, because the class realized that the race very well could be decided by one person, we understood that the marginal cost of voting was much higher than in most government elections. For me personally, without any other midterms on the horizon, the expected value of each day of studying can best be calculated by how many hours I will call out of work in order to hit the library. Any additional day of studying might then be worth about $40 to me. The expected benefit of voting was then the chance of breaking a tie in a 30 person class (0.03) * 40 = $1.33. Now that no verbal explanations were necessary, the cost of voting was just the effort of raising my hand, which I would not pay more than $0.10 to avoid. Therefore, it would be irrational for me to continue abstaining, risking a $1.23 net benefit for every day voted earlier than the 13th (for example, the 4th would cost $11.07 more than the 13th). Others were similarly recalculating their utility functions, and participation rose to 100%. 
November 8th won out of the four options, but the difference between it and the next highest choice, the 6th, was still one vote. We then had a run-off election using the Hare method, removing the two options with the fewest first place votes (4th and 6th, which received only 2 and 3 votes respectively). Finally, November 8th was again chosen, now with a difference of two votes rather than one. We chose the Condorcet winner, as November 8th was preferred to all pairwise elections. While I did not end up being the tie breaking vote in the final election, it was worth it to participate in the democratic process as a rational voter.