District Attorney race

What are the odds of a tie vote?

In the aftermath of the current 1,881-to-1,881 tie in the Republican primary election deciding the nominee for Livingston County District attorney, the question arises as to how likely is it — or how frequently will it be — that such ties occur in election races?

Some people believe the odds of getting this kind of tie are extremely unlikely — of the order of one in a million or even higher.

The County News asked statistician Ed Wallace at the SUNY Geneseo mathematics department to calculate the odds.

The results were surprising, even for Wallace. He did the calculation using the binomial distribution method, applicable when two equally likely options exist for successive trials — such as heads or tails in a coin toss, or a vote for candidate A or B in an election race which has in fact produced a tie result.

For 3,762 trials, the number of votes cast in the primary election district attorney race, the probability that there will be an equal number of votes for each candidate is about 1.301 percent — about 13 times in 1,000 elections or better than once every 100 elections.

The probably of a tie is in this same range for larger and smaller election races. If 1,000 persons were voting, the likelihood of a 500-to-500 tie is 2.523 percent or about 5 times for every 200 election races.

If 10,000 people were voting, the likelihood of a 5,000-to-5,000 tie is 0.789 percent, still almost once in every 100 election races.

If there is a lesson here, it is that tie votes are not nearly as rare as one might think.

When you stay home and choose not vote, you are forfeiting your opportunity to be the deciding factor in what just might be one of those ties.