"Viva voce" ("with the living voice") voting in public elections was in effect in most states through the early 19th century, however, for example, the state of Kentucky continued the tradition up to as late as 1891. The tradition finally disappeared by 1896. Viva voce voting came to the United States from Europe, esp England, Scandinavia, the Netherlands, and the German provinces, where oral voting had been long established in electoral law.

Viva voce worked thusly: the voter would arrive at the polling place and ascend a platform where everyone could see and hear him. The election officials (separated from the crowd by an elevated enclosure) would him to attest to his identity and eligibility to vote (and that he hadn't already voted in that election) and then have him call out his choice candidates. His name, address, and choices would be entered by a clerk into a poll book, thus becoming part of the public record.

Accuracy in record-keeping was an issue; when examining poll books from the periods when viva voce was the electoral law, political historian Don Debats noticed that there appears to be an artificially higher skew in voter turnout, especially when checking against the census records. Census takers were less diligent and tended to omit voters along class lines (eg recent immigrants, the poor, non-landowners/people who lived in boarding houses). When doing a comparison of records and taking this into account, voter turnouts appear comparable to contemporary turnout.

Privacy was an early concern, but there was a general attitude of distaste for private or confidential voting/voting by ballot.

On p. 4 of Deliver the vote (2005), Tracy Campbell wrote that while viva voce voting was relatively uncomplicated, it did make the process of voting vulnerable to manipulation and intimidation. States like both Carolinas, Pennsylvania, and Connecticut experimented with secret ballots, but generally the public frowned upon private and confidential voting. Campbell gave the example of New York's attempt to make votes confidential in 1770; it failed in the State Assembly on the grounds that "ignorant or illiterate voters would become the pawns of powerful political interests". Campbell also says that New Jersey "even required lists of how people voted to be published after each election".

Paula Wasley wrote in Humanities magazine:

Not only was there no expectation of privacy for voters, but voting in secret, in the early days of the republic, was considered antithetical to the principles of democracy. The underlying reasons began with the idea that voting, rightly understood, should not be an expression of private interests or beliefs.

“The voter is under an absolute moral obligation to consider the interest of the public, not his private advantage,” wrote John Stuart Mill. The voter should give his support, “to the best of his judgment, exactly as he would be bound to if he were the sole voter, and the election depended upon him alone.” Secret voting, by contrast, suggested a very different meaning, thought Mill and others. It would be like telling the voter he may vote without regard to the public good and “simply as he feels inclined.”

In Structure, process, and party (1991), Peter H. Argersinger gave the example of 1801 Connecticut: the Stand-Up Law was passed, which abolished the ballot (some states early on also used ballot voting) and required voters to stand up when publicly polled. This was designed to intimidate Republican voters and favored incumbency of the traditional political elites (pp. 47-8).

The University of Virginia's site Voting Viva Voce: Unlocking the Social Logic of Past Politics has this to say about the concerns over viva voce methods:

The objection to viva voce, of course, was that it invited intimidation and coercion, of employees by employers, of the weak by the powerful, and of individuals by groups.

...Indeed the notion that open voting inevitably produced intimidated voters may be countered by an extreme case of power differentials: the electoral behavior of former slaves in Kentucky. As everywhere the men who had been enslaved were enfranchised by the Fifteenth amendment but Kentucky, because it was both a Union state and a slave state, was exempt from the Reconstruction Acts that made abolition of viva voce voting a condition of readmission to the Union. Instead Kentucky persevered with its ante-bellum laws and “by voice” voting persisted another quarter of a century.

Viva voce voting was the preferred electoral method for the early states in the East, and as new states joined the union, they followed suit. Public voting enabled the community to see where a voter's sympathies lay and their position on the issues at hand. Voting preference was shaped along social lines and often peer pressure and even coercion came into play in determining candidate choice. These concerns eventually led to states adopting the written, secret ballot, an import from Australia.

Sources

Debats, Don. “How America Voted: By Voice”. Voting Viva Voce: Unlocking the Social Logic of Past Politics, University of Virginia Institute for Advanced Technology in the Humanities, http://sociallogic.iath.virginia.edu/node/35.

Wasley, Paula. “Back When Everyone Knew How You Voted.” Humanities the Magazine of the National Endowment for the Humanities, The National Endowment for the Humanities, Fall 2016, https://www.neh.gov/humanities/2016/fall/feature/back-when-everyone-knew-how-you-voted.

Argersinger , Peter H. “Structure, Process, and Party : Essays in American Political History.” Internet Archive, Armonk, N.Y. : M.E. Sharpe, 18 May 2021, https://archive.org/details/structureprocess0000arge.

Campbell, Tracy. “Deliver the Vote : A History of Election Fraud, an American Political Tradition, 1742-2004.” Internet Archive, New York : Carroll & Graf, 8 Sept. 2010, https://archive.org/details/delivervotehisto00camp/page/4/mode/2up.