How the Top-Up MPs are selected

When the votes are counted, there will be a number of Local MPs selected.  The next step is to determine which parties deserve Top-Up Seats and which candidates should be selected to fill these seats.

The easiest way to see this is to use an example.  Let’s use the New Brunswick results from the 2015 general election.  Of course, we know that people will vote differently next time, but these results will give us a good view of how the system works.

New Brunswick has 10 seats in Parliament.  In the 2015 election, the Liberal Party won all 10 seats because they had the highest vote in each of 10 ridings.  However, the overall support was quite a bit different than that:

Party Popular Vote
Liberal 51.6%
Conservative 25.4%
NDP 18.4%
Green 4.7%

So, if we distribute New Brunswick’s 10 seats based on popular vote, we can calculate the “ideal” proportional representation.

Party Popular Vote Proportional Seats (of 10 total)
Liberal 51.6% 5.16
Conservative 25.4% 2.54
NDP 18.4% 1.84
Green 4.7% 0.47

Of course, you cannot split a seat into fractions, so we have to decide which parties should get the extra 5 top-up seats. We do this with a calculation called the “democratic deficit”, which is just a fancy term for the unrepresented popular vote.  In 2015, Liberals were awarded all 10 seats, so the democratic deficit is the total of the popular vote for those parties with no representation, which comes to 49.4%.  To understand this number, it means that 49.4% of the votes in New Brunswick were “wasted” in 2015, because these votes did not contribute to the selection of a sitting MP.

So how would we do it with Simple MMP?  Simple MMP cuts the number of ridings in half, so there would be 5 Local MPs elected and 5 Top-Ups elected. The 5 Local MPs using the 2015 data would all be Liberals. So, we start from there and do a “democratic deficit” calculation like this:

Party Proportional Seats Elected Seats Democratic Deficit (difference between ideal and elected)
Liberal 5.16 5 0.16
Conservative 2.54 2.54
NDP 1.84 1.84
Green 0.47 0.47

From this table, we can see that the party with the largest democratic deficit is the Conservative Party, so they would get the first top-up seat.  The candidate selected would be the Conservative candidate who got the highest overall percentage vote in New Brunswick, but has not yet won a seat.

Then, we would update the number of seats like this:

Party Proportional Seats Elected + Top_up Seats Democratic Deficit
Liberal 5.16 5 0.16
Conservative 2.54 1 1.54
NDP 1.84 1.84
Green 0.47 0.47

The party with the highest deficit is now the NDP, so they would get the next top-up seat, which reduces their democratic deficit to 0.84. Again, the candidate would be the NDP candidate with the highest percentage vote in the province who has not yet been elected.

Party Proportional Seats Elected + Top_up Seats Democratic Deficit
Liberal 5.16 5 0.16
Conservative 2.54 1 1.54
NDP 1.84 1 0.84
Green 0.47 0.47

The third top-up would go to the Conservatives.  This time, the candidate selected would be the Conservative candidate with the second highest popular vote.

Party Proportional Seats Elected + Top_up Seats Democratic Deficit
Liberal 5.16 5 0.16
Conservative 2.54 2 0.54
NDP 1.84 1 0.84
Green 0.47 0.47

As you can see, the party with the largest residual deficits are the NDP and the Conservatives, so they would get the final two top-up seats.  When it gets down to the final couple of seats, you can see that the democratic deficits are very close, and indeed, that every vote counts in making the final determination.  The final tally looks like this:

Party Proportional Seats Elected + Top_up Seats Democratic Deficit
Liberal 5.16 5 0.16
Conservative 2.54 3 -0.46
NDP 1.84 2 -0.16
Green 0.47 0.46

In the end, the total democratic deficit is 0.62 seats that are under-represented by the Liberals and the Greens (offset, of course by 0.62 seats which are over-represented by the Conservatives and the NDP). However, this compares very favourably to the outcome of the 2015 election, in which 4.84 seats were over-represented by the Liberals, offset by the equal under-representation of all of the other parties.