Gary sent along this news article from the Syracuse Post-Standard:

Dead heat: Obama and Clinton split the Syracuse vote 50-50

by Mike McAndrew

In the city of Syracuse, the strangest thing happened in Tuesday’s Democratic presidential primary.

Sen. Hillary Clinton and Sen. Barack Obama received the exact same number of votes, according to unofficial Board of Election results.

Clinton: 6,001.

Obama: 6,001.

“Wow, that is odd,” said Jay Biba, Clinton’s Central New York campaign coordinator. “I never heard of that in my life.”

The odds of Clinton and Obama tying were less than one in 1 million, said Syracuse University mathematics Professor Hyune-Ju Kim.

“It’s almost impossible,” said Kim, who analyzed the statewide and citywide votes.

Lisa Daly, Obama’s Syracuse campaign coordinator, said she thought a mistake had been made when she was first told the tally by the Board of Elections.

What are the chances of it happening?

“Good thing it wasn’t a mayor’s race,” quipped Grant Reeher, a political science professor at Syracuse University’s Maxwell School of Citizenship and Public Affairs.

A total of 12,346 votes were cast for Democrats in the city. Four other Democrats also received votes: John Edwards, 114; Dennis Kucinich, 113; Bill Richardson, 90; and Joe Biden, 27.

The tie is likely to be broken when elections officials recanvass the voting machines and add in the absentee and affidavit votes.

But for now, it’s all even.

Update

The story The Post-Standard broke about Sen. Hillary Clinton and Sen. Barack Obama battling to a tie vote in the city of Syracuse was being posted Thursday on internet sites across the country.

Clinton and Obama each received 6,001 votes in Syracuse in the unofficial Board of Elections results. A total of 12,346 votes were cast in the city.

After doing a statistical analysis for The Post-Standard, Syracuse University mathematics professor Hyune-Ju Kim noted that the odds of Clinton and Obama getting the exact same amount of votes in Syracuse was less than one in 1 million.

To come to that conclusion, Kim factored in the state-wide and city-wide results in the Democratic primary.

Elaborating on Thursday, she noted: “The “almost impossible” odd is obtained when we assume the Syracuse voter distribution follows the New York state distribution. Since it is almost impossible to observe what we have observed, statistically we can conclude that Syracuse voter distribution is significantly different from the New York state distribution.”

There would be less than one in 1 million chance of a tie occurring between Clinton and Obama in voting by a randomly selected group of 12,346 New York Democratic voters, she said.

Not to pick on some harried mathematics professor who’d probably rather be out proving theorems, but . . . of course Syracuse voters are not a randomly selected group of New Yorkers. You don’t need a statistical test to see that. Regarding the probability of an exact tie: I don’t think that’s so low: a quick calculation might say that either Clinton or Obama could’ve received between, say, 5000 and 7000 votes, giving something like a 1/2000 chance of an exact tie. That’s gotta be the right order of magnitude.

Anyway, I know this is silly–as pointed out in the article, it doesn’t matter if there’s a tie in Syracuse anyway. This might make a good classroom example, though. (See also here and here for more on the probability of a tied election.)

Doesn't the 1/2000 assume that the prior probability of voting for either candidate was equal? If say 60% was used as a prior for voting for Clinton based on demographics and the voting across the state then the probability of a tie becomes much lower. The article does state "To come to that conclusion, Kim factored in the state-wide and city-wide results in the Democratic primary".

Andrew, you're too kind to the math professor.

Ken, you seem to be suggesting that the voting in Syracuse can be modeled as if the votes constituted a simple random sample of the New York vote! That's surely a pretty bad model. It's probably the same mistake the math prof made.

Phil, if all I had was the information that in the rest of New York that 60% voted for one candidate then it would not be a good model but would be better than the assumption of 50%. If the percentage for the rest of NY was 90% would you still estimate probabilities based on 50% ? In practice it would be better to use the demographics (she did) and fit a multilevel model (not stated) to model any additional variation.

It seems a good example of why care is needed in answering questions from journalists. After all, the probability of Clinton:6000 and Obama:6002 would also be 1 in a million.

If we take as a prior that each voter votes for each candidate with a probability 50%, the chance of a tie turns to be p = C(12002,6001) / 2^12002 = 1 chance in 137, assuming I got it right.

If they vote one candidate 55% and the other 45%, then the chance of a tie goes up to around 1 in 10^28.

Of course, people don't toss a coin to vote, but if your prior is extremely narrow around 50%, a tie gets really likely, a lot more likely than one in a million.

Ken, Geego,

Your calculations are mathematically correct but substantively irrelevant. First, as Phil said, voters in Syracuse are not a random sample of voters in the state; second, voters are not voting independently with equal probability. The relevant probability distribution is for the election outcome itself.

Please see the linked articles above for further discussion.

So, was it rational for them to vote?

Since some people seem to still be confused, look at it this way. Suppose each city or town in New York has a different percentage of Clinton supporters. Even if the statewide percentage that favors Clinton is pretty different from 60%, there will be some towns where the percentage is close to 50%. A tie is not all that unlikely.

What strikes me most is this comment:

"

Since it is almost impossible to observe what we have observed, statistically we can conclude that Syracuse voter distribution is significantly different from the New York state distribution.".Do I understand correctly that the mathematician interprets the probability of obtaining a tie as if it was a p-value for testing a difference in voter distribution ?

Because in this case, the probability of obtaining any individual result (such as 6,234 vs 5,936) is always very low too, and she would reach the same conclusion of difference in voter distribution whatever the result…

Frédéric

Speaking of the primaries, what's the history of primary versus election turnout for the Republican and Democratic parties? Does anyone have any figures? I'm curious if the result of Presidential elections is well predicted by how many voters came out to vote in the primaries earlier that year.