Measuring Proportionality

One of the challenges in the evaluation of electoral systems is: how do you measure proportionality? In my opinion, the best measure is one that compares voter’s first choice to the final distribution of seats in Parliament.

I have proposed a metric for proportionality called the democratic deficit.  The democratic deficit is the comparison of the “ideal” mix of seats to the actual distribution of seats by party.  In other words, it compares the distribution of party seats to the distribution of party votes.

This measure is necessarily a fractional number, since there is no perfect proportional representation in a representative democracy. After all, we can’t ask our MPs to be 30% this way and 70% that way!

In the last federal election in 2015, the difference between popular vote and actual counts of elected representatives per party shows that about 50.6 seats of 338 total are held by parties which are over-represented. In this example, the extra seats are all held by Liberals. These 50 or 51 seats should have gone to other parties, including Conservatives, NDP and Greens, to create a more proportional Parliament.

Another way to measure proportionality is to look at extent each parties votes are represented in Parliament.  In essence, we ascribe a number of votes that each seat represents and then compare that to an ideal proportional split.  The results will be about the same as the democratic deficit measure, but the unit of measure is number of under-represented votes rather than number of under-represented seats.  Both measures work well to measure effectiveness of a system.

For systems such as Single Transferable Vote (STV) or Alternate Vote (AV or Ranked Ballot), it is harder to measure effectiveness. In these systems, there are circumstances under which your first choice is voided due to that candidate not getting enough support, so your vote shifts to another candidate.  Under STV, your vote can transfer to another candidate for the same party in a multi-candidate riding, but under AV your vote transfers to another party.

Measuring AV is particularly difficult.  If we were to assign a perfect score of 1 to your vote if your first choice counts in electing an MP, then what do we assign if your second choice is elected?  It certainly isn’t 1 because you didn’t get what you wanted. Would it be 1/2, or 3/4, or even 1/4?  And what if it is your third choice that finally gets counted?  What weighting would we assign to that.

This has helped steer my thinking towards a mixed member proportional system. I believe that transferring my vote to my second or third choice is not actually representing my wishes, but rather, simply attempts to address the singular problem of strategic voting. By giving me more than one choice, I have a higher chance of being on a winning team. But is that really my team?