Private Members’ Bills and Balls from Urns

A statistical ideal becomes literal.

In September, a lottery chose 20 backbench MPs. Those MPs can then propose laws to the House of Commons, ordered by their place on the ballot. No MPs from the main opposition party were selected in this ballot. How likely is that?

The Chairman of Ways and Mean draws numbered balls from an urn. (Image: House of Commons)

Balls from urns

Statistics textbooks often consider problems of drawing balls from urns. The urn contains a number of black and white balls. In the problem, a person draws one ball at random, looking at its colour. That person may put that ball back in the urn, or not. That selection process is repeated. Numerous questions arise, including:

• Suppose we know how many black and white balls there are in the urn. What is the chance of drawing a specific number of black and white balls?

For the Private Members’ Ballot in the House of Commons, this statistical ideal is literal. The Chairman of Ways and Means draws 20 numbered balls from a glass urn. Each ball represents an MP. The last chosen person gets the first available slot for changing the law. This year, Kim Leadbeater MP (Labour, Spen Valley) won the ballot. Her bill proposes to legalise assisted dying. However, no Conservative MPs were among the 20 chosen.