The Birthday Paradox

“In a room of just 23 people there’s a 50-50 chance of at least two people having the same birthday. In a room of 75 there’s a 99.9% chance of at least two people matching.“ This is the Birthday Paradox.

Last night there were 750 people in a room and it was one person’s birthday blowing the Birthday Paradox out of the water. We are back in Kiev for a debriefing from the OSCE/ODIHR core team. They collate our Election Day observations so that we can see if what we saw was typical across the whole of Ukraine. It’s interesting and the statistical analysis is formidable. It pleased me that a problem I encountered was shared by almost half my colleagues. In our reports we note whether there are observers at polling stations representing political parties and/or civil society organisations. In Moldova in February there were almost always both. In Ukraine there were always political observers and seldom civil society observers. My problem was differentiating the two categories. The only way was to go to them and ask.

Another issue is access to polling stations for people with disabilities. It’s often a hard call to decide if there is wheelchair access and on both missions I have spent a disproportionate amount of time discussing this with my partner; wondering if steps are shallow enough or if a ramp is usable or too steep, etc. Of course I don’t want voters with disabilities to be disenfranchised but the subject is irrelevant. A disabled voter can ask for a mobile ballot box to come to their home.

Let’s get back to the Birthday Paradox. At the debrief yesterday evening the Head of Mission asked whose birthday it was and just one person stood up. In fact there should have been two more. He knew because to get accreditation as observers we submit our dates of birth, amongst other things. I would have expected there to be more than three amongst 750 people. The fact there was actually only one reveals a pitfall of statistical analysis. The other two must have swerved the debriefing to go out and party.

Ternopil Oblast, March 2019.

This church lies out in the countryside in a depopulated village. The school has closed and there are only 153 voters but nevertheless there is a polling station in the old school and 101 people voted on Sunday – that’s higher than the national turnout. It’s where Anna and I went to observe the close and the count. The sun was setting when we arrived. The polling station closed at 8.00 pm and you may be surprised that we did not leave until 00.45 am. That’s a long time to count 101 votes.