> Now, you'd want to set both values in the same transaction for obvious reasons. But, since Postgres uses MVCC, the two tuples that are added to the database both contain the same transaction ID (XID), so there's the connection between user and vote again.

The simple solution is that at each change, you rewrite the whole election, not just the new votes, and clear out all outdated tuples (basically, that you make the "periodic and manual" process you are currently doing automatic and integrated with the "real" transactions rather than additional side process.)

Alternatively, you don't do the changes in the same database transaction but in the same business domain transaction which is managed outside the database, and where any database artifacts related to the management of the business transaction are deleted and vacuumed after the transaction is completed.