We have discussed applying economic behavior - namely, the MB>MC condition - to voting in elections. In Johnson's simple yet effective model, the expected marginal benefit of casting one's vote in a two-option election is E(U) = P(the vote is decisive) * [(Net utility if option 1 succeeds) - (Net utility if option 2 succeeds)]. But does this equation hold in edge cases? Consider two examples:
1. In my history class, the professor had two students act out a debate of a historical controversy. The rest of the class was then able to vote on the winner with the vote totals appearing on the projector. I had a slight preference as to the winner, but was too lazy to get out my phone and cast my vote. That was, until I saw that the vote was tied! Suddenly, P(decisive) was 1 for my vote, and with a much higher E(U) I chose the winner of the debate.
2. I enjoy cooking with my girlfriend. But cooking requires choosing what to cook, so it is not uncommon for her to summon two options and ask me to select from them. If I desire one meal over another, I will vote accordingly, but what if I value each choice equally? I am forced to say that I have no preference and thus will not choose. This is not an admission that I do not like the options - I may like them both very much! But if I expect their utility to be equal, the two will cancel, and I have no reason to cast my vote.
Tuesday, October 03, 2023
The Marginal Benefit of Writing A Short Title Does Not Exceed The Marginal Cost Of Thinking of Said Title.
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2 comments:
I am not sure if you are eluding to the idea that This equation doesn't hold in both of the edge cases presented, but I thought I would answer your hypothetical anyways.
1. I believe this edge case exemplifies perfectly the effectiveness of the equation. By holding out on voting till you were the last participant left, you created a situation where you knew exactly what p(decisive) would be. Because p(decisive)=1, you decided to vote because 1*B - c >0, where c was the cost of you having to pull out your phone and vote. Now in an alternate reality, where the vote wasn't tied, p(decisive) would equal 0, you would face no benefit from voting and would've rationally chosen not to vote.
2. In this example, I believe your conclusion is slightly off. When you expect the utility between both alternative to be equal, B=0. And although your vote is decisive [p(decisive)=1], p*B will always be less than C. However, you are not accounting for D, the additional utility you gain from voting. In this case, by voting you may make your girlfriend happy and get to cook with her, both of which increase your utility. So while choosing one dish over the other makes no difference in your expected utility; the third option, not voting, has the lowest expected utility, which should leave you to randomly select one of the two options.
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