Blockchains or public ledgers are (perhaps) half of a solution. Blockchains are a technology, and technology by itself cannot solve social problems, any more than construction equipment by itself can build a city. The social problem implicit in the franchise is the tension between accountability and secrecy, and while blockchains help to ensure secrecy, they are not particularly good at ensuring accountability.

Secrecy is an essential part of the franchise in order to prevent intimidation or retribution against citizens over their vote choices. Contrary to some of the other answers given, block chains would be quite effective at providing this. Yes, there is a traceable path back to the voting citizen so long as one can secure cryptographic details, and in principle that could lead to harassment, threats, or punitive measures. But in practice, that kind of intimidation isn't scaleable. Voter intimidation is only meaningful when voters can be intimidated in large numbers from a position of relative anonymity: e.g., when an industrialist makes it known that employees who vote the 'wrong' way might find themselves out of a job, or when unknown groups post flyers in minority neighborhoods warning of unspecified attacks if those people go to the polls (both of these, incidentally, are or were common practices). But block chains would guarantee that any potential intimidators would have to reach out to individual citizens directly (in order to gain access to their cryptographic information) which dramatically increases their risk public exposure while simultaneously decreasing the 'footprint' of their intimidation efforts. In simpler terms, it's easy to visualize a boss making it known (through some casual comment) that he will view all employees who vote for the other guy unfavorably, but it's laughable to imagine political operatives going door to intimidate voters one by one by one.

The problem of accountability is harder to address. Yes, a voter can ostensibly use his cryptographically secured information to check that his own vote was recorded properly, but this technology opens the possibility of double accounting: e.g., having one list in which which reports the citizen's vote back to the citizen as he cast it, and another list that is used for compiling totals in which some citizens' votes are recorded differently. This is extremely difficult to do with low-tech paper ballot voting, because of the huge numbers of people involved in the counting who would need to be complicit in the act. But digitizing and encrypting the ballot information places more and more information in the hands of fewer and fewer people: it limits accountability and increases the potential for malfeasance.

The accountability problem could be resolved through a classical check and balance system. In such a system, the encrypted vote data would not go one central location to be tallied. Instead, each political party — as well as interested organizations like newspapers — would get its own clone of the central vote data. Any discrepancies in vote-count between these interests could be traced back to individual ballots which show discrepancies between clones of the data, and individual voters could check multiple sources to make sure the their vote wasn't hijacked by one group or another. The more groups that voting tallies are spread over, the less likely that any one group can massage ballots to their own advantage.

Blockchains or public ledgers are (perhaps) half of a solution. Blockchains are a technology, and technology by itself cannot solve social problems, any more than construction equipment by itself can build a city. The social problem implicit in the franchise is the tension between accountability and secrecy, and while blockchains help to ensure secrecy, they are not particularly good at ensuring accountability.

Secrecy is an essential part of the franchise in order to prevent intimidation or retribution against citizens over their vote choices. Contrary to some of the other answers given, block chains would be quite effective at providing this. Yes, there is a traceable path back to the voting citizen so long as one can secure cryptographic details, and in principle that could lead to harassment, threats, or punitive measures. But in practice, that kind of intimidation isn't scaleable. Voter intimidation is only meaningful when voters can be intimidated in large numbers from a position of relative anonymity: e.g., when an industrialist makes it known that employees who vote the 'wrong' way might find themselves out of a job, or when unknown groups post flyers in minority neighborhoods warning of unspecified attacks if those people go to the polls (both of these, incidentally, are or were common practices). But blockchains would guarantee that any potential intimidators would have to reach out to individual citizens directly (in order to gain access to their cryptographic information) which dramatically increases the risk of public exposure while simultaneously decreasing the 'footprint' of their intimidation efforts. In simpler terms, it's easy to visualize a boss making it known (through some casual comment) that he will view all employees who vote for the other guy unfavorably, but it's laughable to imagine political operatives going door to intimidate voters one by one by one.

The problem of accountability is harder to address. Yes, a voter can ostensibly use his cryptographically secured information to check that his own vote was recorded properly, but this technology opens the possibility of double accounting: e.g., having one list which reports the citizen's vote back to the citizen as he cast it, and another list that is used for compiling totals in which some citizens' votes are recorded differently. This is extremely difficult to do with low-tech paper ballot voting, because huge numbers of people involved in the counting would need to be complicit in the act. But digitizing and encrypting the ballot information places more and more information in the hands of fewer and fewer people: it limits accountability and increases the potential for malfeasance.

The accountability problem could be resolved through a classic check and balance system. In such a system, the encrypted vote data would not go to one central location to be tallied. Instead, each political party — as well as interested organizations like newspapers — would get its own clone of the central vote data. Any discrepancies in vote-count between these interests could be traced back to individual ballots which show differences across clones of the data, and individual voters could check multiple sources to make sure the their vote wasn't hijacked by one group or another. The more groups the voting tallies are spread over, the less likely that any one group can massage ballots to their own advantage.