The following is the opening paragraph from a column written by the Washington Post Editorial Board dated May 20, 2013.
More than a quarter of Virginia’s electorate considers itself Republican, which translates to almost 1 million voters. Of that number, about 8,000 — less than 1 percent — showed up at the party’s convention in Richmond over the weekend to choose the GOP candidates in this November’s races for governor, lieutenant governor and attorney general.
As I have written before, most states have the conventional open and closed primary systems are used. In each case, a nominee is chosen by the public for each party. In open states, party affiliation is not a prerequisite for voting in either party’s primary. In closed primary states, you can only vote in the party primary under the label you are registered.
Why then would a state want to have a convention, which is more “closed” than a closed primary?
For more information about the Virginia Republican Party Convention, read this Washington Post column.
Politics Matters 
A state would want to have a convention in order to give a higher chance of success to one candidate. With more people, as there would be in the primary, there would be less chance for the GOP’s most favored candidate to win. So, they make it much more exclusive, and this makes it more difficult to unseat the major candidate.
They would want to make the chances of that one candidate winning better. It makes it easier for the one candidate to win with having less people. By not allowing a lot of people to be there, the one candidate would have a harder time of losing.
I think they would hold a convention to narrow the margin between two candidates in one party. Because they are more closed than a closed primary, one candidate would have more success. Narrowing the number of people actually increases the odds of winning for one person over all other candidates.
Why would a state want to have a convention, which is more “closed” than a closed primary? I’d say that they are trying to keep the convention one-sided (either one team or the other). When you have people that are open, it can be something. I guess they’re just trying to keep the one-sided people in to make sure one side wins. A two-sided person can cause quite a confusion.
Having a convention would help decrease the chances of one candidate winning over the other. Since the convention had a little turn out the amount the people were limited to who they can vote for. This decreases the chances for the republican party, since only 8000 republican voters showed up.
Why then would a state want to have a convention, which is more “closed” than a closed primary?
I believe that a state would want to have a convention which is more “closed” rather than open when they only want to talk about the features that apply to one side. They may think that if they do this they have already won those people over and they will definitely get the vote. This would not work in their advantage if there are not a lot of people that show up.
A state would hold a convention to ensure that their candidate has a greater chance of winning. By doing this they are making the race more exclusive, leaving out potential candidates. The state is trying to narrow the race down to one candidate but that just shows that they are biased.