Rational Voting at Chapter

This Sunday, my fraternity held elections for our executive positions. However, as I thought about our election, my mind went to Johnson’s rational abstention theory and I wondered if I even should vote. 

This election, or series of elections, is quite different from the one Johnson writes about. For this election, it is rational for one to vote. Looking at the basis for his argument, E[MB] < MC, I will show how it is, in fact, rational to vote. 

First, the expected marginal benefit side. As a fourth year, I will only have one semester with the new executive board, so the different utility I face from either candidate will be lower than others in the fraternity, but still measurable. As for the case my vote will be the deciding vote, the probability is low, but not nearly as low as a local, state, or national election. With 60 members of my fraternity, my expected marginal benefit is 1.66% multiplied by the difference in the utility I face from each candidate.

Second, the marginal cost side. As chapter is mandatory and I plan to attend every week, the cost I face attending chapter is negligible to this analysis as the costs are unchanged whether I vote or not. Also, as I already know Robert's Rules and voting is simply counted by raising a hand, I face no costs to the action of voting. 

Although the expected marginal benefit of voting is low, the marginal cost of voting is practically zero in this case. For chapter voting, E[MB] > MC and I decided to vote, in this case rationally. As it turns out, after a tie and further discussion, our new recruitment chair won in favor of my vote.