Should states continue to allow ballot initiatives and other forms of direct democracy?

This is largely a matter of opinion, and it is important to examine both sides of the argument carefully. Speaking personally, I would argue against ballot initiatives and other forms of direct democracy for a number of reasons. First of all, it goes against the long-established principles of American democracy. When the Founding Fathers established the Republic, they instituted a system called representative democracy. This means that we elect people—Senators, members of Congress, state legislators—to make decisions on our behalf. Even when the population of the United States was fairly small, this was felt to be a more efficient way of expressing the people's will.
The Founding Fathers were very suspicious of direct democracy because they feared that it would lead to the establishment of mob rule; people would act on the spur of the moment in making crucial political decisions. They would act on their emotions instead of taking the time to examine the issues carefully before reaching a decision. Although we may regard the Founding Fathers' innate suspicion of direct democracy as somewhat overstated, we can still sympathize with their anxiety to avoid the consequences of a lack of deliberation and reasoned reflection in the process of formulating legislation.
This leads me on to the next criticism of direct democracy. Decisions made in plebiscites, referenda, ballot initiatives, and so forth provide nothing more than a snapshot of how people are feeling at any particular time. One could argue, however, that meaningful democracy is a process that develops over time. It involves a constant interaction between the voters and their elected representatives. The whole process transcends those single moments of history captured when democratic decisions are made in popular initiatives. This means, among other things, that representative democracy is better able to respond to changes in public opinion. With direct democracy, once a policy has been adopted, there is little that can be done to change it no matter how disastrous the consequences.
There are all kinds of other objections to direct democracy, such as the notoriously low turnouts it often encourages and the frankly ludicrous, trivial proposals that somehow manage to find their way onto the ballot. (In 1993, voters in San Francisco were asked if a police officer should be allowed to walk his beat with a ventriloquist's dummy.) But the final objection I want to raise is a simple one. If we have direct democracy initiatives, then what is the point of having elected representatives? Representatives are precisely that: those who represent us. They are not delegates; they are not there simply to carry out the voter's instructions to the letter. They must be given some leeway in the use of their judgement. If we do not like how they use their judgement, this is not a problem; we can always vote them out of office during the next election.
We cannot do this with direct democracy, so there is a disturbing lack of political accountability. If I do not like how an elected official behaves, then I can always reject them come election time. In other words, like all other voters, I am able to hold elected representatives accountable for the decisions they have made in office. But if those decisions are made by the voters themselves in a direct ballot initiative, then who carries the blame when things go wrong? How can the voters ever possibly hold themselves accountable? The very notion is absurd.
In the meantime, I would submit that our representatives must be allowed to get on with the job for which they are being paid and for which they have been authorized to perform by the United States Constitution. They represent; we are represented. That is how it works, and that is how it should continue to work.