Public choice theory, also known as political economics, is the study of the economics of political behavior — how economic incentives and consequences affect voters, legislators, and bureaucrats. The democratic process is one in which, supposedly, the preferences of the public are expressed through elected representatives.
Public choice theory illustrates some scenarios where a majority vote would actually lower the benefit-to-tax ratio or where projects may be selected that have a higher cost over benefits for the economy as a whole. These inefficient outcomes are usually the result of the fact that people vote in their own interest, so even if a project yields a great benefit to a certain group but a small expense to the rest of the people, they will probably vote against it anyway. For instance, according to recent polls, most people are against the Patient Protection and Affordable Care Act (also known as Obamacare), which is a program to provide health insurance for most of the uninsured. Although the uninsured would greatly benefit from the national health insurance, most people were against it, according to polls, because they already have health insurance, and they were afraid of changing the status quo for fear that they might lose what they have or that they might be taxed more.
Of course, the benefit of most government projects cannot be ascertained accurately beforehand nor would individual taxpayers know of the exact cost to them, so public choice theory is really an abstract scenario, but it can show how allowing the public to choose may not yield the best results for the economy as a whole.
Public goods differ from private goods in that the exact benefit and cost to each individual is unknown, while the benefit and cost of a private good to an individual is certainly knowable to the individual.
Consider 3 taxpayers Wilma, George, and Peter. If a project would provide $1000 worth of value to Wilma, $500 to George, $400 to Peter, and this benefit can be obtained by taxing each $500, then the benefit to each of the 3 taxpayers would be $1900. But the tax would only be $1500, so the net benefit to the 3 taxpayers would be $400. However, since people generally vote in their own interest, Peter and George probably would not vote for the tax to provide the benefit, since they would not be the main beneficiaries. Alternatively, if Peter and George would gain $600 worth of benefit from a project but Wilma gained only $100 from the project, but each would have to pay a tax of $500, then George and Peter would probably vote for the project even though it would cost Wilma more than George and Peter would benefit. Thus, the total cost to this economy would be $200 greater than the benefit.