Two world-famous economists run into each other during the election day at voting booth:

– “What are you doing here?” – asked the first one being surprised.

– “My wife made me come here. What about you?” – the other answered.

After a short awkward pause:

– “The same but please don’t tell anyone that you saw me and I promise I’will keep what happened here a secret as well.”

They shaked their hands and finished their polling business in quiet.

Why should economists be embarrased with fulfilling their “civic duty”? Because voting causes costs – in time, transport costs, lost opportunities finally physical effort. What is the payoff then? It might be so called PIVOTAL VOTE.

Try to imagine a situation in which you are with 4 friends and you want to spend a nice evening togather. What is the problem? Where should we go. Two of your friends would like to go to the cinema to watch new movie with Brad Bitt (probably the female part) while two others would like to go to the derby game Sporting against Benfica. They are deadlocked on a vote where to spend evening and ask you to decide. How cool is that? Your vote holds much power. This kind of vote is called a pivotal (or decisive) vote and is a breaking-tie vote.

In the game theory sense, your vote matters only if it is pivotal. During elections it would be desired by a voter to alter the outcome. But what is the probability that your vote will change the final results and you will be in fact the only person that decide who will run your country for next years. Some numbers…

The odds that a single vote actually affect the outcome are extremely small. Face it. Economists Casey Mulligan and Charles Hunter conducted some analyses on this matter. They took into consideration over 1 bilion votes from 56,000 Congressional and state-legislative elections in USA since 1898. They found out that only 7 of them were decided by a single vote. Moreover, in this case theory stands for the final results of mentioned economists. The mathematical approach is to calculate how often other voters will end up tied. In theory, if the hypotetical election is decided by two or more votes your vote is actually not needed. If a methodology in which we treat each voter as a person that has the same probability of voting for one condidate or the other is used (which in reality isn’t that obvious) we get results that at 100 milion voters the probability that your vote is pivotal is less than 0,01%.

Short theory about pivotal voter model.

We consider the complete information participation game. There are two teams with all members free to decide if they want to vote or not. Utility function is linear as methodology says. The cost of voting is c and lies between 0 and 1. Abstention is costless. Each member of the winning team receive a payoff benefit B>0 while the members of losing team gets 0. Also, p denotes for a probability of having a pivotal vote. Then, the net return to voting is

R = pB – c

We receive any other benefits that one can get from instance “civic duty”. Normalizing B=1 it follows that players will rationally choose to vote whenever p>c and will rationally choose to abstain if p<c.

Does the historical low turnout of less than 60% of registered voters during the last Portuguese legislative election in 2011 means that Portuguese are better educated in economics? I will provide another surprising solution.

Since every single citizen is interested in national issues and take care about what happens in the country the voter turnout should be at around 100%. The reason why people don’t vote might be provided by Swing Voter’s Curse!

It is all about information. Some people are not aware about the current situation in the country and don’t understand programs of certain politicians. These uninformed voters are bearing the cost of possibility of making a major mistake in choosing the candidate to vote on. There is a chance that their votes can swing elections and because of their bad choise the country would have bad leaders for years. With the best intentions they abstain from voting in order to not suffer from Swing Voter’s Curse.

I would like to say that voting is the part of being a citizen and it shouldn’t be a duty but a privilege to participate in democracy. And what if noone vote? Please assume for a second that each person follows the rules of game theory and don’t vote. Now you are the one who has PIVOTAL VOTE. Use it!

Maciej Kimel

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