I've attached a couple of Excel spreadsheets. The first is a spreadsheet I built to try to reverse engineer a formula. After some research I came across the notion that it might be a hypergeometric distribution I'm trying to formulate, but I honestly don't know. The second is the actual spreadsheet I'm trying to apply the solution to.

The problem: An election is underway and results are being reported, but are not completely reported. Given a certain percentage reported, what percentage of the remaining votes must the leader get above and beyond the runner-up in order to reach a target margin of victory?

For example: We expect 600 people to vote, and only 540 (90%) of them have voted so far. Candidate Adams gets 369 votes (68.33%), Brown gets 117 (21.67%), and Clark gets 54 (10.0%). Adams currently leads the runner-up, Brown, by 252 (46.67%). How many more of the 60 remaining votes must Adams get over Brown to reach a 50% margin of victory?

Through trial and error in this case I've found the answer is 48, or 80% of the 60 remaining. If Adams gets 48, Brown must get 0, and Clark 12. If Adams gets 54, Brown must get no more than 6, with Clark getting from 6 to 12.

What formula describes this relationship? What if 80% have reported, or 70%?

There are 9 other cases tested in the Testing.xls spreadsheet I attached. The answers in the test cases are:

90%: 6,048/7,560, or 80.0%

80%: 4,788/7,560, or 63.333..%

70%: 4,368/7,560, or 57.777..%

60%: 4,158/7,560, or 55.0%

50%: 4,032/7,560, or 53.333..%

40%: 3,948/7,560, or 52.222..%

30%: 3,888/7,560, or 51.428571..%

20%: 3,843/7,560, or 50.833..%

10%: 3,808/7,560, or 50.370..%

And they're charted on the spreadsheet as well.

Thank you for any insight!