August Open Streets Festival: Election Simulation Results

Ballot for Riding 5

Ballot for Riding 5

On August 3 there was another Open Streets event in Uptown Waterloo, and once again Sharon Sommerville from the Waterloo Region chapter of Fair Vote Canada was present to run an election simulation.

Turnout for this election was low: only 25 votes were cast. Unsurprisingly, there were many ties for riding seats: Ridings 1, 2, 5 and 6 all had ties for first place (with one vote for each winning candidate, incidentally). There are too many possible outcomes to examine each riding exhaustively, so instead we flipped a set of coins twice, to come up with two different scenarios. As you go through the scenarios, notice how in both cases the MMPR results smooth out the distortions of the FPTP system, leading to similar (but not identical) seat distributions in the two outcomes.

The same number of votes were wasted in both outcomes (can you see why?): 13 out of 25 votes, for a wasted vote percentage of 52% in the first past the post election . That would be a good outcome in a Canadian election, which illustrates how many votes help elect nobody under our current voting system.

Tiebreaker Set 1

In the first set of tiebreakers, we ended up with the following outcomes for the riding seats:

  • Riding 1: Croissant (independent)
  • Riding 2: Cucumber (Sandwich Party)
  • Riding 3: Apple (Pie Party)
  • Riding 4: Cookie Dough (Ice Cream Party)
  • Riding 5: Peach (Fruit Party)
  • Riding 6: Meatloaf (Beef Party)

Here is a chart of the results:


The Sandwich Party was overrrepresented in these results, as was the independent vote. Other parties were underrepresented.

Once again, Croissant’s victory in this election skews the party list results, to the detriment of the Ice Cream Party, as shown in the following chart:


Other parties are fairly well represented. In particular, the skew favouring the Sandwich party diminishes considerably.

Using the “list-free” method of selecting party list winners, we end up with the following party seats:

  • List Seat 1: Strawberry (Ice Cream Party)
  • List Seat 2: Kiwi (Fruit Party)
  • List Seat 3: Lemon Meringue (Pie Party)
  • List Seat 4: Roast (Beef Party)

We will not bother to show closed list results, since (once again, sigh) we did not display those lists at the booth.

Tiebreaker Set 2

The riding seats were not nearly as evenly distributed in the second set of tiebreakers. Here were the outcomes of this scenario:


As you can see, the results are quite distorted: the Pie and Beef parties receive a significant fraction of the vote but no seats, while the Sandwich Party gets lucky and is dramatically overrrepresented.

The riding seat winners were as follows:

  • Riding 1: Lemon Meringue (Pie Party)
  • Riding 2: Cucumber (Sandwich Party)
  • Riding 3: Apple (Pie Party)
  • Riding 4: Cookie Dough (Ice Cream Party)
  • Riding 5: Salmon (Sandwich Party)
  • Riding 6: Strawberry (Ice Cream Party)

Once again, the list seats reduce the disproportionality of the result, although there are not enough list seats to eliminate the skew for the Sandwich Party:


Using the “list-free” method of selecting party list winners, we ended up with:

  • List Seat 1: Roast (Beef Party)
  • List Seat 2: Meatloaf (Beef Party)
  • List Seat 3: Kiwi (Fruit Party)
  • List Seat 4: Peach (Fruit Party)

List-Free MMPR

As it turns out, the list seat winners for each tiebreaker were unambiguous in this election. It is interesting to see that the overall set of candidates receiving seats is similar across the two scenarios. In Tiebreaker 1, the independent candidate Croissant wins a seat; in Tiebreaker 2, Salmon Sandwich wins a seat. Other than this, the same set of candidates win seats.

This is not an accident; those that lost ties in the riding seats led their ridings in the popular FPTP vote, and so ranked highly in the “list-free” rankings for party seats. This is not a property of the mixed-member proportional system overall, but it is a nice property of the list-free method for selecting list seat winners.

Further Exploration

If you would like to play with the results yourself, you can download the spreadsheets for Tiebreaker 1 and Tiebreaker 2 in this zipfile:

If you have not done so already, you might want to read writeups from previous runs of this election simulation:

These writeups go into more detail about how the different voting systems work. In addition, they demonstrate how different results in the vote totals can change overall election outcomes.