There is no easy answer to your inquiry which is a legitimate one.
It is true to say that the federal Congress sits in a daily constitutional convention because it can pose amendments which the states would then either ratify or reject, in a procedure identical to the ratification or rejection of amendments proposed by the states in a convention of states according to the choice of Congress as to whether state legislatures or state conventions should ratify.
On the other hand, there is a great dispute about whether the convention, once constituted and conducted, may proceed according to its own lights or may it be restricted other by legislation emanating from Congress, or by restrictions placed on it by the states. Similarly, may the states impose limitations on the independence of delegates and control how they vote?
The answers to these questions determine whether or not the convention is free to set its own rules respecting quorums and, for example, whether votes should be taken on a state-by-state basis or on a individual delegates basis. The latter would suggest control by the big blue states and the former give the red states a much better chance. Who makes this decision, the Congress which "calls" the convention, the states which sends delegates, or the convention itself? The Constitution does not speak. There is, however, historical precedent for the ratification process and there are dicta from the Supreme Court.
In addition to all of this there is the question of the impact of one man one vote decisions of the Supreme Court and that might also affect how a convention votes.
Fortunately, we have a correspondent at FreeRepublic, Publius, who is very knowledgeable on these matters and has provided citations which are very valuable. I expect he will contribute to this thread as well.
It is true that whatever amendments emerge from a convention of the states, 34 states must propose and 38 states must ratify and it is difficult to conceive how that would be a "runaway" convention or a runaway amendment process. However, it is correct to observe that a convention might have more or less scope to propose amendments according to how the questions raised above are resolved.
While there has never been a convention of the states convened, so these questions and concerns are legitimate.
I welcome any comments or clarifications that anyone can post.
Lets clear up a few things. The States can and indeed MUST inform and instruct their delegations, and voting at any such convention will be on a State by State basis unless the several States agree otherwise by a State by State vote at the Convention.
The matters under debate and decision MUST remain within the ambit of the Convention as called.
All the Congress gets to do is to set the venue and date. Congress has no authority whatever to place any restrictions on the Convention.
The Convention is the creature of the States, solely, and the States not only have the right, but they have the duty to set the subject matter of the Convention. There must be a minimum of 34 States making Application for a Convention on precisely the same subject matter. 34 different applications on different subject matter will not aggregate and no Convention will be called by Congress.
The delegates must be chosen carefully by the State legislatures, and of course they will each have an individual vote but only within their State delegation. While this is not made explicit within the Constitution this is the precedent and the clear expectation of the Founders.
There is NO issue of “one man one vote”. This is “one State one vote”. The reasons why this must be so are historical, logical and practical.
First, there is no restriction on the States as to the makeup of their delegations. They could range from a single individual to dozens. And this is as it should be.
Second, the Constitution was adopted by the STATES, not by individuals. It is the States, not individuals that get to amend it. This too, is as it should be.
And as a practical matter, may I ask just who it might be who would would have the power to dictate that votes should be aggregated nationwide? I will offer my answer to this question: there is no individual or body with the power to so instruct the Convention.
ONLY the several States can instruct their delegations and I find that I cannot imagine that the several States would consent to such an aggregation.
Let’s keep this discussion going.