## PR in Wales

I wrote, nearly two years ago, welcoming the change on the composition and size of the Welsh Senedd, [or on Medium] and was pointed today at what they’ve become. While using the d’Hondt method  i.e. the generally preferred counting method for PR for the new and much larger constituencies, they propose that there are no top up members. The mathematical purpose of the top-up members is to ensure proportionality and the higher the proportion of top up members, the closer to proportionality one gets. It is usual for the top up members to be elected based on a party vote.

The Welsh system proposes to have 16 constituencies each electing six members of the Senedd, meaning a quota and thus a wasted vote of 14.29% and a requirement that the constituencies are of equal size.  I wonder what the impact of abolishing the top-up members will be. Perhaps I’ll build a model.  …

## The Senedd, proportionality and size

I have been thinking how many politicians is the right number and how to build proportional voting systems, these came together in a chat about the Senedd, so I thought I’d share.

The Welsh Parliament is elected in two classes, one class (40 seats) is elected in constituencies by first past the post, the remaining 20 are elected in five super constituencies of four members elected using a D’hondt count. The D’hondt count is done allocating the first places won in the count by a party to their constituency assembly members. This means that the results i.e. the number of assembly members/party are proportional within the super constituencies subject to rounding. This is as is done in London.

Acadmemia may suggest that assemblies that are too small become dominated by the executive, which in Wales is limited to 14, while those that are too large become prone to low quality legislation and corruption. It has been suggested that the optimum size of the Welsh assembly would be 147 based on a cube root rule. See also, “Wales needs 20 or 30 more Members of the Senedd, says committee” at Wales Online.  Other work suggests that we, in the UK have too few elected politicians because we have the House of Lords and too few councillors.

Proportionality depends upon the ratio of list AMs to constituency AMs. In Wales it’s ⅓, 43% in Scotland, 44% in London and 50% in Germany, who also have very finely calculated additional seats to eliminate rounding errors and any ‘crowding out’ effect.  i.e. the Bundestag is not of a fixed size, but as one reduces the size of the top-up class of seats, we reduce proportionality. …