How can paper ballots violate constitutional rights?

I saw on Instapundit — through to Slashdot — that the ACLU was suing a county for moving from touchscreen machines to paper ballots, and I couldn't even think of a bad argument. Slashdot describes the argument this way:

[T]he system chosen tabulates all votes at a central location. This means that voters don't get notified if their ballot contains errors, and thus they have no chance to correct it.

What? I still don't get it.

More here:

The ACLU alleges that the optical-scan system and centralized vote tabulation would not give voters notice of ballot errors — such as voting for two candidates for one office.

Opponents of the system say scanning should be done immediately at the precinct level to alert voters to such errors and allow them to correct invalid ballots.

So the constitutional violation is that the paper doesn't prevent you from mismarking it? If you're supposed to check one box and you check two, the paper doesn't call you a fool?

IN THE COMMENTS: Rastajenk writes:

I am a precinct captain in Ohio...

The system used in our county places scanners at each precinct; the voter marks his paper ballot and slips it into the scanner himself. If it is marked properly, the voter sees the ballot counter increase by one...he knows his ballot has been counted, right there on the spot.

If he doesn't mark it correctly...if he marks three school board members when he should have voted only two...or if he leaves blank an issue where he had no opinion...or if he doesn't vote at all for an uncontested position...any of these kinds of situations, the scanner would beep and produce a message saying where the error occurred, and give the voter a chance to repair the error, or accept it as is.

It's a very simple safeguard to address the whole undervote/overvote issue that Florida 2000 introduced to the world. If a person needs a new ballot, there are very simple procedures for giving him one and voiding the original.

What the ACLU is doing is promoting the system used in our county over the system proposed in Cuyahoga, wherein all the paper ballots are collected and sent to a central counting location. Any number of shenanigans can occur there that cannot occur in our situation. For once in my life, I am in the ACLU's corner on this one.

Ohio Sec of State Brunner issued a report last month recommending all counting be done in central locations. Brunner is a Dem; connect the dots.

Another feature of our precinct-counted system is that at the end of the day, I produce and post at that location a report of our activity: how many votes each candidate or issue received in our precinct. I can compare that report to official reports on the county's website and verify that they are the same; each precinct official can do the same for his precinct. At no point can the numbers suddenly change or not add up correctly using this system. Accountability starts at the bottom, not at some closed-door top level. This is what the ACLU is against. Forget the invectives about stupid voters; support them on this as I have.

I'm persuaded that the scanners are better, but I still don't see a constitutional argument.

ADDED: Here's how the complaint puts it:

The dual system of voting created by Defendants has resulted in the following inequity: voters living in election jurisdictions using voting systems without error notification... are significantly less likely to have their intended votes counted than voters who live in election jurisdictions that use voting systems with error notification....

This seems to be an attempt to use the Equal Protection argument from Bush v. Gore:

Equal protection applies... to the manner of [the exercise of the right to vote]. Having once granted the right to vote on equal terms, the State may not, by later arbitrary and disparate treatment, value one person's vote over that of another. See, e.g., Harper v. Virginia Bd. of Elections, 383 U.S. 663, 665 (1966) (“[O]nce the franchise is granted to the electorate, lines may not be drawn which are inconsistent with the Equal Protection Clause of the Fourteenth Amendment”). It must be remembered that “the right of suffrage can be denied by a debasement or dilution of the weight of a citizen’s vote just as effectively as by wholly prohibiting the free exercise of the franchise.” Reynolds v. Sims, 377 U.S. 533, 555 (1964)....

The question before the Court is not whether local entities, in the exercise of their expertise, may develop different systems for implementing elections. Instead, we are presented with a situation where a state court with the power to assure uniformity has ordered a statewide recount with minimal procedural safeguards.