Yes, that would help in theory. But in practice it would only change the way how the people inducing the pressure would verify that the votes have in fact been cast according to their preferences.
For instance, if voting multiple times is allowed and only the last vote counts, they would require the people to vote during the last 10 minutes of the polling period and afterwards they would withhold their ID card with the signing capability from them until the polling is closed.
If there are multiple private keys to choose from, they would require people to at first prove which one is usable for this particular election by checking it with the issuing authority. The owner must have been given this information in some verifiable form at some time, so the demand will simply extend to include that information as well.
For instance, if voting multiple times is allowed and only the last vote counts, they would require the people to vote during the last 10 minutes of the polling period and afterwards they would withhold their ID card with the signing capability from them until the polling is closed.
If there are multiple private keys to choose from, they would require people to at first prove which one is usable for this particular election by checking it with the issuing authority. The owner must have been given this information in some verifiable form at some time, so the demand will simply extend to include that information as well.