Cryptocurrencies provide an alternative solution, explained in this Telegraph article by Matthew Sparkes.
A cryptocurrency such as bitcoin has a finite number of coins that is predetermined. Transactions using these coins aren't listed on a bank's ledger but exist on numerous decentralised computers using a blockchain system. If votes were counted as cryptocoins there would be no way for central authorities to miscount or manipulate the results without being discovered.
Another feature of cryptocurrencies is that they are anonymous. This means that voters could use their cryptovotes without fear of punishment for how they voted. In short it would be a secret ballot.
Contrary to my original notion of Interactive Democracy including something akin to a bank statement, listing transactions, the cryptovote system wouldn't need it. Instead transactions would be assured through the blockchain. The total number of votes cast would also match the total number of cryptovotes in existance - those not cast by the electorate would be "spent" by their representative.
As more youngsters come of age to vote and older ones die, more cryptovotes would need to be created and defunct accounts destroyed. The best way to do this would be to create new cryptovotes for each referendum, also ensuring that cryptovotes couldn't be amassed and "spent" on a single issue.
While there is some cost to the electricity used in creating and distributing each cryptovote, I expect this to be small in comparison with normal voting procedures. It could be funded via central government taxation. This is in contrast to the creation of bitcoins which are "mined" by numerous private computers for a small fee, paid in bitcoins and sufficient to cover the energy costs (at least initially). This aspect, and the issuing of cryptovotes to elligible voters, remains centralised, but operates on decentralised servers, immune to accident or attack. (Alternatively, I wonder if it is possible for each voter to mine their own cryptovote?) If you don't receive the cryptovotes you are entitled to, you should complain.
Of course, if you allow others access to your voting account (similar to a bitcoin wallet) they may spend your cryptovotes for you. The spending or stealing of someone's cryptovote would be a criminal offense, as would coercing someone to vote against their wishes. Today, similar problems exist with postal voting.
I like the idea that you can spend your vote well before the deadline and then change your mind as the debate develops. This is both convenient and accommodating. Cryptovotes could allow this by only releasing the transaction at the deadline even though the vote was earmarked (or cast) earlier.
My preference is that unspent cryptovotes would accrue to your Member of Parliament for them to spend but it would be possible to give them to others as you see fit, allowing them to vote on your behalf. Called Liquid Democracy, it may be far less palatable for MPs.