This week, I am working mostly on a paper with the awesome Laurence Wilse-Samson, about voting after a poll where the set-up is better suited to a small-scale thing, i.e. a small committee or something.
First, the voting problem: in a huge election, your probability of being "pivotal", i.e. for your vote to count, is really small. If you have a small cost of voting, e.g. time, you shouldn't go vote. However, if nobody votes, then you will always matter.
In real life, with a cost of voting, it is hard to explain why so many people vote. With no cost, or a benefit, it is hard to explain why so many people abstain.
Since we are economists, we are trying to see how people might behave strategically. The main model right now just says that people have a small cost of voting(that can be negative if you like to go vote). If G is your gain from winning the vote compared to losing, and p is the probability that you are "pivotal", then you will go vote if
That's the equation you want to have in mind to think about it.
In any case, you can show several things with this. If people have different cost of voting, people with low costs will vote and those with high cost will not. If you have a binary vote, you will see that people in the minority will vote with a greater probability. The reasoning is that with a cost, the guys in the majority should free-ride and let the others vote in their place. Then they still win, and do not bear the cost.
Now, let's introduce polls. Given the effect above, you might see what can happen. Assume that everybody participates in the poll. They have an incentive to misrepresent their position: by saying they are Democrats instead of Republicans, they make Democrats believe the election is in the pocket, they turn out less, and Republicans win.
In our model, with a simple cost of voting that differs across agents, we find that the only symmetric equilibrium(where everybody plays the same thing) is the equilibrium where the poll is completely uninformative, i.e. where people randomly state their position on an issue.
This is weird: we tend to think that polls contains at least some information
Now we are thinking about different things. The sexy idea is the cost of lying literature. A lot of laboratory experiments showed that people tend to tell the truth more often than necessary. More on that in the next post.