Right,
You could have a couple different scenarios.
Overall you want a vote/ballot/voting set of tables where the vote table is the main one, ballots uses the vote id to store all possible voting choices and voting tables which uses the ballot id to store the record of what was cast along with the vote ID of the first table as an identifier.
Example:
Table 1 - voteID as Primary Key - autonumber
Table 1 - fldVoteTitle as Text
Table 1 - fldVoteDetail as Text
And Vote possiblities.
Table 2 - ballotID as Primary Key - autonumber
Table 2 - fldVoteID as Number
Table 2 - fldItem as Text
And finally Vote Casting
Table 3 - castID as Primary Key - autonumber
Table 3 - fldVoteID as Number
Table 3 - fldVoteCast as Text (or number)
For relationships you match up the obvious
Table 1 - voteID relates to Table 2 fldVoteID
Table 1 - voteID relates to Table 3 fldVoteID
What this lets you now do is count either with VBA, Reports or Queries inside Table 2 for the specified Vote.
Example Records
Table 1
voteID - 1, fldVoteTitle - "vote for budget", fldVoteDetail - "We need you to vote now on budget 2015"
Table 2
ballotID - 1, fldItem - "Yes"
ballotID - 2, fldItem - "No"
Table 3
castID - 1, fldVoteID - 1, fldVoteCast - 1 (voted yes on budget vote)
castID - 2, fldVoteID - 1, fldVoteCast - 1 (voted yes on budget vote)
castID - 3, fldVoteID - 1, fldVoteCast - 2 (voted no on budget vote)
castID - 4, fldVoteID - 1, fldVoteCast - 2 (voted no on budget vote)
castID - 5, fldVoteID - 1, fldVoteCast - 3 (voted no on budget vote)
The No's barely carry the day with 3 against 2 for.
Attached an example table.
--update--
I had initially wondered the same thing that gemma did - and you could solve it by adding a 4th table for person - and add another column to the votes cast table with the primary id of the person casting the vote - and count out that way.