McCarthy Ousted and Voters Utility Function

 Today there was a historic move to oust Kevin McCarthy from Speaker of the House. This unprecedented event occurred after McCarthy decided to work with Democrats and keep the government open by keeping spending at the 2023 levels halfway through November. Matt Gaetz and other far right-leaning congresspeople told McCarthy beforehand they would remove McCarthy from his role as Speaker if he tried to pass a spending bill with the Democrats.

It looks like Gaetz fulfilled on his promise because he made a motion to vacate on Monday. Even though Gaetz filed a motion he still needed a simple majority of people to oust McCarthy. The normal expected utility function of voting looks like this E[B]= P (probability that vote is decisive) x B (benefit you receive from voting) + D(the other incentive driving the bevarior). For this example we can ignore D, normally “D” is the main reason people vote because the probability that your vote is decisive is normally very small, to the extent we just label it as 0. And this is true for House as well, in theory. The expected benefit of a single vote in the House without “D” is E[B]= .0023 (1/435 representatives) x B. For a House member to be indifferent between receiving a dollar and voting the benefit of voting would have to be approximately $435. 

However, for Gaetz, the benefit of voting was larger and it was not necessarily because "B" was bigger. Gaetz knew that just a few votes would decide whether McCarthy remained speaker. This was the case because he knew that almost all if not all the House Democrats would vote to oust McCarthy and that almost all Republicans would vote to keep McCarthy. He also knew that it took a historic 15 tries to get McCarthy in office in the first place, meaning the margins were razor thin. This meant that Gaetz's probability of being the decisive vote was very high. In other words, Gaetz had a high "P". Therefore, on a rare occasion, the expected benefit of voting was very high, given that he had a reasonable B and so Gaetz rationally voted.