When ballots are not secret, they can influenced by social, political, or economic actors through punishment and reward. For example, voters in many places used to face extreme peril if they voted against the candidate picked by their social group, party, or union. This peril ranged from reduced social standing, to loss of employment, and even physical violence. As such coercion is contrary to the democratic objectives of an election, secret ballots were introduced to ensure ballots represent the free will of the voters.

There are mechanisms by which one could both keep the ballot secret and allow a public tally. But to avoid hacking, like the floating-point vote-value in GEMS outlined in another story, the system does require bullet-proof crypto.

Regardless of how the ballots are counted, I do believe there should always be paper backups, scanned, and filed so that citizens can examine them digitally and in person if necessary. With that system one could spot-check any suspected irregularity. Only with such physical redundancy would I trust digital voting systems at this point.

Sometimes there's no substitute for good old dead trees.

https://en.wikipedia.org/wiki/Secret_ballot

Article 21.3 of the Universal Declaration of Human Rights states, "The will of the people...shall be expressed in periodic and genuine elections which...shall be held by secret vote or by equivalent free voting procedures."[19]

Article 23 of the American Convention on Human Rights (the Pact of San Jose, Costa Rica) grants to every citizen of member states of the Organization of American States the right and opportunity "to vote and to be elected in genuine periodic elections, which shall be by universal and equal suffrange and by secret ballot that guarantees the free expression of the will of the voters".[20]

Paragraph 7.4 of the Document of the Copenhagen Meeting of the Conference on the Human Dimension of the CSCE, obligates the member states of the Organization for Security and Cooperation in Europe to "ensure that votes are cast by secret ballot or by equivalent free voting procedure, and that they are counted and reported honestly with the official results made public."[21]

Article 5 of the Convention on the Standards of Democratic Elections, Electoral Rights and Freedoms in the Member States of the Commonwealth of Independent States obligates electoral bodies not to perform "any action violating the principle of voter's secret will expression."[22]