We'd each each have a piece of paper that - if we choose too - can not only use to verify our vote, but utilize to prove who we voted for.
In fact, any other website or service could ask you to scan your receipt, and if you choose to comply, access your entry on the database, and register who you voted for.
But why would you do so? One possible reason to normalize such a transaction of information, might go into use is the Primaries. Your party's would be able to prove that you have voted for your party in past elections before they let you vote for a new candidate to represent that party.
Now, let's say that a system adopts this. More specifically, let's say that a council system of Representatives adopts this (parliamentary/congressional/etc).
In such a case, a web service could allow you to prove to your Representative - anonymously if you'd prefer - that you are among his voters. The same web service could then enable verifiable polling data, by giving you a live account of what is happening in session, and you could use your receipt (or an account made on the basis of a receipt) to say what you would like your Representative to vote for. In turn, both the media and your Representative would be able to see the data - what his verified voters want him to vote for and what percentage of his voters do they make as a whole.
Hypothetically, in cases where the Representative has then taken a stance against his majority voters, it could become an outrage, a media scandal marking his failure to do his job and Represent the will of the people, a sure case that he shell never get elected again. Realistically, the system above in itself is not enough to make this a likely scenario. While in some rare cases, an upcoming session within the body of Representatives might garner enough attention and media campaigns from various interests groups to get enough people to cast what they want their Representative to vote for in order for the verified poll takers to account for large enough majority and declare that the Representative is voting against his own voters wishes, in most cases, the majority of people do not have the time or interest to pay such close attention to the ongoing of politics.
But what if you add another layer? For the most part, people have a generalist stance, rather then a case by case one. So let's say an independent body or an interest group you share your stance with, enables you to verify your vote through them. Maybe its your brand of tea party, or an environmentalist movement. Maybe they represent your profession, or your socioeconomic interests. Maybe it's just someone you always agree with, an independent voice or blogger you feel speaks your mind. Either way, they give you a guideline as to what cases interest them and how they are going to vote for in those cases. They then verify their collection of voters through the above system, and in any case in which you didn't decide take a verified-voter's poll stance directly, they will take the poll for you. You can then go and check that their voting history complies with your wishes, and change your registration with them whenever you want. With such a layer, it becomes a lot easier to accumulate a mass large enough to make the verified-voter's poll to count, and easy enough to create a scandal when the official Representative doesn't do what people are asking for.
In addition, a pro-active layer can also enable discussion groups among the verified voters and the middle-layer, in which new bills and reforms and decisions can become popular enough and pushed to an internal vote, and a representative not placing the bill on the floor (in systems enabling him to do so) might equally be considered incapable of doing his job and representing the will of his voters.
The system of representation organically changes from a one-layer system to a direct e-democracy with a multi-layered system of Representatives supporting it, in which every layer's interest is to do the best job in representing your stance, and the official council of representatives is nothing but middle management, without anyone in power deciding to give their power away or that such a movement is a good idea.