Is Majority Voting Equilibrium Efficient?
In the majority voting equilibrium, the amount of the public good is decided by a 50% + 1 vote. The person who is that +1 vote is in the exact median position between the most extreme people on either side, so that person is the median voter. Think about a vote where we decide whether to provide a high level of service at high cost or a low level of service at low cost. Everyone has an opinion on the vote, and we can put them in a line based on which one they prefer and how much they prefer it. If the median voter prefers the high level, then everyone above him prefers the high level, so high gets at least 50% + 1. Same deal if the median voter prefers the low level. This means that in a majority voting system, the median voter is really the only one who matters. The preferences of the median voter fully predict the outcome of the vote. This is why in real elections, politicians focus so much on “independents” and “swing states,” trying to persuade that median voter. Now the median vot
