Secret ballots prevent voters from proving or selling their votes [fact]
It is interesting to observe that political democracy itself depends on a game structure in which the communication of evidence is impossible. What is the secret ballot but a device to rob the voter of his power to sell his vote? It is not alone the secrecy, but the mandatory secrecy, that robs him of his power. He not only may vote in secret, but he must if the system is to work. He must be denied any means of proving which way he voted. And what he is robbed of is not just an asset that he might sell; he is stripped of his power to be intimidated. He is made impotent to meet the demands of blackmail.
XREF: Connects to game theory and mechanism design, where information asymmetry is deliberately engineered in political institutions.
Thomas C. Schelling, The Strategy of Conflict, loc. 343