Help with a DAX measure to count based on latest dates

Grateful if someone can help me come up with a measure for such a scenario:

The process for job promotion is that a group of voters periodically submit batches of votes for any employees at a company that they wish to support. This can happen at irregular intervals, with different voters voting at different times. Once the voter has voted for an employee, they are considered to support them unless a later batch of votes is received without any record for that employee. 

The table of vote records is called VoteHistory and has columns Voter / Employee / Submission Date. 

This is linked to a typical Date table. 

I want to be able to chart a time series for specific employees that will show the total Votes that they had received at different points in time. So at a certain point in time, the total votes would be determined by filtering the most recent batches of votes prior to that date (across all voters), then counting the number for that employee. Any suggestions on how to write something like this please?